diff --git a/include/boost/integer/common_factor_rt.hpp b/include/boost/integer/common_factor_rt.hpp
index 6d035b0..c52067d 100644
--- a/include/boost/integer/common_factor_rt.hpp
+++ b/include/boost/integer/common_factor_rt.hpp
@@ -1,32 +1,28 @@
-//  Boost common_factor_rt.hpp header file  ----------------------------------//
+//  (C) Copyright Jeremy William Murphy 2016.
 
-//  (C) Copyright Daryle Walker and Paul Moore 2001-2002.  Permission to copy,
-//  use, modify, sell and distribute this software is granted provided this
-//  copyright notice appears in all copies.  This software is provided "as is"
-//  without express or implied warranty, and with no claim as to its suitability
-//  for any purpose. 
-
-// boostinspect:nolicense (don't complain about the lack of a Boost license)
-// (Paul Moore hasn't been in contact for years, so there's no way to change the
-// license.)
-
-//  See http://www.boost.org for updates, documentation, and revision history. 
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 
 #ifndef BOOST_INTEGER_COMMON_FACTOR_RT_HPP
 #define BOOST_INTEGER_COMMON_FACTOR_RT_HPP
 
-#include <boost/integer_fwd.hpp>  // self include
+#include <boost/assert.hpp>
+#include <boost/core/enable_if.hpp>
 
 #include <boost/config.hpp>  // for BOOST_NESTED_TEMPLATE, etc.
 #include <boost/limits.hpp>  // for std::numeric_limits
 #include <climits>           // for CHAR_MIN
 #include <boost/detail/workaround.hpp>
+#include <iterator>
+#include <algorithm>
+#include <limits>
+#ifndef BOOST_NO_CXX11_HDR_TYPE_TRAITS
+#include <type_traits>
+#endif
 
-#if !defined(BOOST_NO_CXX11_NOEXCEPT) && !defined(BOOST_NO_CXX11_HDR_TYPE_TRAITS)
-#  include <type_traits>
-#  define BOOST_INT_NOEXCEPT(T) BOOST_NOEXCEPT_IF(std::is_arithmetic<T>::value)
-#else
-#  define BOOST_INT_NOEXCEPT(T)
+#if (defined(BOOST_MSVC) || (defined(__clang__) && defined(__c2__)) || (defined(BOOST_INTEL) && defined(_MSC_VER))) && (defined(_M_IX86) || defined(_M_X64))
+#include <intrin.h>
 #endif
 
 #ifdef BOOST_MSVC
@@ -34,427 +30,538 @@
 #pragma warning(disable:4127 4244)  // Conditional expression is constant
 #endif
 
-namespace boost
+#if !defined(BOOST_NO_CXX11_HDR_TYPE_TRAITS) && !defined(BOOST_NO_CXX11_NOEXCEPT)
+#define BOOST_GCD_NOEXCEPT(T) noexcept(std::is_arithmetic<T>::value)
+#else
+#define BOOST_GCD_NOEXCEPT(T)
+#endif
+
+namespace boost {
+
+   template <class I>
+   class rational;
+
+   namespace integer {
+
+      namespace gcd_detail{
+
+         //
+         // some helper functions which really should be constexpr already, but sadly aren't:
+         //
+#ifndef BOOST_NO_CXX14_CONSTEXPR
+         template <class T>
+         inline constexpr T constexpr_min(T const& a, T const& b) BOOST_GCD_NOEXCEPT(T)
+         {
+            return a < b ? a : b;
+         }
+         template <class T>
+         inline constexpr auto constexpr_swap(T&a, T& b) BOOST_GCD_NOEXCEPT(T) -> decltype(a.swap(b))
+         {
+            return a.swap(b);
+         }
+         template <class T, class U>
+         inline constexpr void constexpr_swap(T&a, U& b...) BOOST_GCD_NOEXCEPT(T)
+         {
+            T t(static_cast<T&&>(a));
+            a = static_cast<T&&>(b);
+            b = static_cast<T&&>(t);
+         }
+#else
+         template <class T>
+         inline T constexpr_min(T const& a, T const& b) BOOST_GCD_NOEXCEPT(T)
+         {
+            return a < b ? a : b;
+         }
+         template <class T>
+         inline void constexpr_swap(T&a, T& b) BOOST_GCD_NOEXCEPT(T)
+         {
+            using std::swap;
+            swap(a, b);
+         }
+#endif
+
+      template <class T, bool a = 
+#ifndef BOOST_NO_CXX11_HDR_TYPE_TRAITS
+         std::is_unsigned<T>::value || 
+#endif
+         (std::numeric_limits<T>::is_specialized && !std::numeric_limits<T>::is_signed)>
+      struct gcd_traits_abs_defaults
+      {
+         inline static BOOST_CXX14_CONSTEXPR const T& abs(const T& val) BOOST_GCD_NOEXCEPT(T) { return val; }
+      };
+      template <class T>
+      struct gcd_traits_abs_defaults<T, false>
+      {
+         inline static T BOOST_CXX14_CONSTEXPR abs(const T& val) BOOST_GCD_NOEXCEPT(T)
+         {
+            // This sucks, but std::abs is not constexpr :(
+            return val < 0 ? -val : val;
+         }
+      };
+
+      enum method_type
+      {
+         method_euclid = 0,
+         method_binary = 1,
+         method_mixed = 2,
+      };
+
+      struct any_convert
+      {
+         template <class T>
+         any_convert(const T&);
+      };
+
+      struct unlikely_size
+      {
+         char buf[9973];
+      };
+
+      unlikely_size operator <<= (any_convert, any_convert);
+      unlikely_size operator >>= (any_convert, any_convert);
+
+      template <class T>
+      struct gcd_traits_defaults : public gcd_traits_abs_defaults<T>
+      {
+         BOOST_FORCEINLINE static BOOST_CXX14_CONSTEXPR unsigned make_odd(T& val) BOOST_GCD_NOEXCEPT(T)
+         {
+            unsigned r = 0;
+            while(0 == (val & 1u))
+            {
+#ifdef _MSC_VER  // VC++ can't handle operator >>= in constexpr code for some reason
+               val = val >> 1;
+#else
+               val >>= 1;
+#endif
+               ++r;
+            }
+            return r;
+         }
+         inline static BOOST_CXX14_CONSTEXPR bool less(const T& a, const T& b) BOOST_GCD_NOEXCEPT(T)
+         {
+            return a < b;
+         }
+
+         static T& get_value();
+
+#ifndef BOOST_NO_SFINAE
+         static const bool has_operator_left_shift_equal = sizeof(get_value() <<= 2) != sizeof(unlikely_size);
+         static const bool has_operator_right_shift_equal = sizeof(get_value() >>= 2) != sizeof(unlikely_size);
+#else
+         static const bool has_operator_left_shift_equal = true;
+         static const bool has_operator_right_shift_equal = true;
+#endif
+         static const method_type method = std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer && has_operator_left_shift_equal && has_operator_right_shift_equal ? method_mixed : method_euclid;
+      };
+      //
+      // Default gcd_traits just inherits from defaults:
+      //
+      template <class T>
+      struct gcd_traits : public gcd_traits_defaults<T> {};
+
+#ifdef BOOST_NO_CXX14_CONSTEXPR
+      //
+      // Some platforms have fast bitscan operations, that allow us to implement
+      // make_odd much more efficiently, unfortunately we can't use these if we want
+      // the functions to be constexpr as the compiler intrinsics aren't constexpr.
+      //
+#if (defined(BOOST_MSVC) || (defined(__clang__) && defined(__c2__)) || (defined(BOOST_INTEL) && defined(_MSC_VER))) && (defined(_M_IX86) || defined(_M_X64))
+#pragma intrinsic(_BitScanForward,)
+      template <>
+      struct gcd_traits<unsigned long> : public gcd_traits_defaults<unsigned long>
+      {
+         BOOST_FORCEINLINE static unsigned find_lsb(unsigned long val) BOOST_NOEXCEPT
+         {
+            unsigned long result;
+            _BitScanForward(&result, val);
+            return result;
+         }
+         BOOST_FORCEINLINE static unsigned make_odd(unsigned long& val) BOOST_NOEXCEPT
+         {
+            unsigned result = find_lsb(val);
+            val >>= result;
+            return result;
+         }
+      };
+
+#ifdef _M_X64
+#pragma intrinsic(_BitScanForward64)
+      template <>
+      struct gcd_traits<unsigned __int64> : public gcd_traits_defaults<unsigned __int64>
+      {
+         BOOST_FORCEINLINE static unsigned find_lsb(unsigned __int64 mask) BOOST_NOEXCEPT
+         {
+            unsigned long result;
+            _BitScanForward64(&result, mask);
+            return result;
+         }
+         BOOST_FORCEINLINE static unsigned make_odd(unsigned __int64& val) BOOST_NOEXCEPT
+         {
+            unsigned result = find_lsb(val);
+            val >>= result;
+            return result;
+         }
+      };
+#endif
+      //
+      // Other integer type are trivial adaptations of the above,
+      // this works for signed types too, as by the time these functions
+      // are called, all values are > 0.
+      //
+      template <> struct gcd_traits<long> : public gcd_traits_defaults<long> 
+      { BOOST_FORCEINLINE static unsigned make_odd(long& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+      template <> struct gcd_traits<unsigned int> : public gcd_traits_defaults<unsigned int> 
+      { BOOST_FORCEINLINE static unsigned make_odd(unsigned int& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+      template <> struct gcd_traits<int> : public gcd_traits_defaults<int> 
+      { BOOST_FORCEINLINE static unsigned make_odd(int& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+      template <> struct gcd_traits<unsigned short> : public gcd_traits_defaults<unsigned short> 
+      { BOOST_FORCEINLINE static unsigned make_odd(unsigned short& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+      template <> struct gcd_traits<short> : public gcd_traits_defaults<short> 
+      { BOOST_FORCEINLINE static unsigned make_odd(short& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+      template <> struct gcd_traits<unsigned char> : public gcd_traits_defaults<unsigned char> 
+      { BOOST_FORCEINLINE static unsigned make_odd(unsigned char& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+      template <> struct gcd_traits<signed char> : public gcd_traits_defaults<signed char> 
+      { BOOST_FORCEINLINE static signed make_odd(signed char& val)BOOST_NOEXCEPT{ signed result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+      template <> struct gcd_traits<char> : public gcd_traits_defaults<char> 
+      { BOOST_FORCEINLINE static unsigned make_odd(char& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+#ifndef BOOST_NO_INTRINSIC_WCHAR_T
+      template <> struct gcd_traits<wchar_t> : public gcd_traits_defaults<wchar_t> 
+      { BOOST_FORCEINLINE static unsigned make_odd(wchar_t& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; } };
+#endif
+#ifdef _M_X64
+      template <> struct gcd_traits<__int64> : public gcd_traits_defaults<__int64> 
+      { BOOST_FORCEINLINE static unsigned make_odd(__int64& val)BOOST_NOEXCEPT{ unsigned result = gcd_traits<unsigned __int64>::find_lsb(val); val >>= result; return result; } };
+#endif
+
+#elif defined(BOOST_GCC) || defined(__clang__) || (defined(BOOST_INTEL) && defined(__GNUC__))
+
+      template <>
+      struct gcd_traits<unsigned> : public gcd_traits_defaults<unsigned>
+      {
+         BOOST_FORCEINLINE static unsigned find_lsb(unsigned mask)BOOST_NOEXCEPT
+         {
+            return __builtin_ctz(mask);
+         }
+         BOOST_FORCEINLINE static unsigned make_odd(unsigned& val)BOOST_NOEXCEPT
+         {
+            unsigned result = find_lsb(val);
+            val >>= result;
+            return result;
+         }
+      };
+      template <>
+      struct gcd_traits<unsigned long> : public gcd_traits_defaults<unsigned long>
+      {
+         BOOST_FORCEINLINE static unsigned find_lsb(unsigned long mask)BOOST_NOEXCEPT
+         {
+            return __builtin_ctzl(mask);
+         }
+         BOOST_FORCEINLINE static unsigned make_odd(unsigned long& val)BOOST_NOEXCEPT
+         {
+            unsigned result = find_lsb(val);
+            val >>= result;
+            return result;
+         }
+      };
+      template <>
+      struct gcd_traits<boost::ulong_long_type> : public gcd_traits_defaults<boost::ulong_long_type>
+      {
+         BOOST_FORCEINLINE static unsigned find_lsb(boost::ulong_long_type mask)BOOST_NOEXCEPT
+         {
+            return __builtin_ctzll(mask);
+         }
+         BOOST_FORCEINLINE static unsigned make_odd(boost::ulong_long_type& val)BOOST_NOEXCEPT
+         {
+            unsigned result = find_lsb(val);
+            val >>= result;
+            return result;
+         }
+      };
+      //
+      // Other integer type are trivial adaptations of the above,
+      // this works for signed types too, as by the time these functions
+      // are called, all values are > 0.
+      //
+      template <> struct gcd_traits<boost::long_long_type> : public gcd_traits_defaults<boost::long_long_type>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(boost::long_long_type& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<boost::ulong_long_type>::find_lsb(val); val >>= result; return result; }
+      };
+      template <> struct gcd_traits<long> : public gcd_traits_defaults<long>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(long& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; }
+      };
+      template <> struct gcd_traits<int> : public gcd_traits_defaults<int>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(int& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<unsigned long>::find_lsb(val); val >>= result; return result; }
+      };
+      template <> struct gcd_traits<unsigned short> : public gcd_traits_defaults<unsigned short>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(unsigned short& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<unsigned>::find_lsb(val); val >>= result; return result; }
+      };
+      template <> struct gcd_traits<short> : public gcd_traits_defaults<short>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(short& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<unsigned>::find_lsb(val); val >>= result; return result; }
+      };
+      template <> struct gcd_traits<unsigned char> : public gcd_traits_defaults<unsigned char>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(unsigned char& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<unsigned>::find_lsb(val); val >>= result; return result; }
+      };
+      template <> struct gcd_traits<signed char> : public gcd_traits_defaults<signed char>
+      {
+         BOOST_FORCEINLINE static signed make_odd(signed char& val)BOOST_NOEXCEPT { signed result = gcd_traits<unsigned>::find_lsb(val); val >>= result; return result; }
+      };
+      template <> struct gcd_traits<char> : public gcd_traits_defaults<char>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(char& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<unsigned>::find_lsb(val); val >>= result; return result; }
+      };
+#ifndef BOOST_NO_INTRINSIC_WCHAR_T
+      template <> struct gcd_traits<wchar_t> : public gcd_traits_defaults<wchar_t>
+      {
+         BOOST_FORCEINLINE static unsigned make_odd(wchar_t& val)BOOST_NOEXCEPT { unsigned result = gcd_traits<unsigned>::find_lsb(val); val >>= result; return result; }
+      };
+#endif
+#endif
+#endif // BOOST_NO_CXX14_CONSTEXPR
+   //
+   // The Mixed Binary Euclid Algorithm
+   // Sidi Mohamed Sedjelmaci
+   // Electronic Notes in Discrete Mathematics 35 (2009) 169-176
+   //
+   template <class T>
+   BOOST_CXX14_CONSTEXPR T mixed_binary_gcd(T u, T v) BOOST_GCD_NOEXCEPT(T)
+   {
+      if(gcd_traits<T>::less(u, v))
+         constexpr_swap(u, v);
+
+      unsigned shifts = 0;
+
+      if(!u)
+         return v;
+      if(!v)
+         return u;
+
+      shifts = constexpr_min(gcd_traits<T>::make_odd(u), gcd_traits<T>::make_odd(v));
+
+      while(gcd_traits<T>::less(1, v))
+      {
+         u %= v;
+         v -= u;
+         if(!u)
+            return v << shifts;
+         if(!v)
+            return u << shifts;
+         gcd_traits<T>::make_odd(u);
+         gcd_traits<T>::make_odd(v);
+         if(gcd_traits<T>::less(u, v))
+            constexpr_swap(u, v);
+      }
+      return (v == 1 ? v : u) << shifts;
+   }
+
+    /** Stein gcd (aka 'binary gcd')
+     * 
+     * From Mathematics to Generic Programming, Alexander Stepanov, Daniel Rose
+     */
+    template <typename SteinDomain>
+    BOOST_CXX14_CONSTEXPR SteinDomain Stein_gcd(SteinDomain m, SteinDomain n) BOOST_GCD_NOEXCEPT(SteinDomain)
+    {
+        BOOST_ASSERT(m >= 0);
+        BOOST_ASSERT(n >= 0);
+        if (m == SteinDomain(0))
+            return n;
+        if (n == SteinDomain(0))
+            return m;
+        // m > 0 && n > 0
+        int d_m = gcd_traits<SteinDomain>::make_odd(m);
+        int d_n = gcd_traits<SteinDomain>::make_odd(n);
+        // odd(m) && odd(n)
+        while (m != n)
+        {
+            if (n > m)
+               constexpr_swap(n, m);
+            m -= n;
+            gcd_traits<SteinDomain>::make_odd(m);
+        }
+        // m == n
+        m <<= constexpr_min(d_m, d_n);
+        return m;
+    }
+
+    
+    /** Euclidean algorithm
+     * 
+     * From Mathematics to Generic Programming, Alexander Stepanov, Daniel Rose
+     * 
+     */
+    template <typename EuclideanDomain>
+    inline BOOST_CXX14_CONSTEXPR EuclideanDomain Euclid_gcd(EuclideanDomain a, EuclideanDomain b) BOOST_GCD_NOEXCEPT(EuclideanDomain)
+    {
+        while (b != EuclideanDomain(0))
+        {
+            a %= b;
+            constexpr_swap(a, b);
+        }
+        return a;
+    }
+
+
+    template <typename T>
+    inline BOOST_CXX14_CONSTEXPR BOOST_DEDUCED_TYPENAME enable_if_c<gcd_traits<T>::method == method_mixed, T>::type
+       optimal_gcd_select(T const &a, T const &b) BOOST_GCD_NOEXCEPT(T)
+    {
+       return gcd_detail::mixed_binary_gcd(a, b);
+    }
+
+    template <typename T>
+    inline BOOST_CXX14_CONSTEXPR BOOST_DEDUCED_TYPENAME enable_if_c<gcd_traits<T>::method == method_binary, T>::type
+       optimal_gcd_select(T const &a, T const &b) BOOST_GCD_NOEXCEPT(T)
+    {
+       return gcd_detail::Stein_gcd(a, b);
+    }
+
+    template <typename T>
+    inline BOOST_CXX14_CONSTEXPR BOOST_DEDUCED_TYPENAME enable_if_c<gcd_traits<T>::method == method_euclid, T>::type
+       optimal_gcd_select(T const &a, T const &b) BOOST_GCD_NOEXCEPT(T)
+    {
+       return gcd_detail::Euclid_gcd(a, b);
+    }
+
+    template <class T>
+    inline BOOST_CXX14_CONSTEXPR T lcm_imp(const T& a, const T& b) BOOST_GCD_NOEXCEPT(T)
+    {
+       T temp = boost::integer::gcd_detail::optimal_gcd_select(a, b);
+#if BOOST_WORKAROUND(BOOST_GCC_VERSION, < 40500)
+       return (temp != T(0)) ? T(a / temp * b) : T(0);
+#else
+       return temp != T(0) ? T(a / temp * b) : T(0);
+#endif
+    }
+
+} // namespace detail
+
+
+template <typename Integer>
+inline BOOST_CXX14_CONSTEXPR Integer gcd(Integer const &a, Integer const &b) BOOST_GCD_NOEXCEPT(Integer)
 {
-namespace integer
+    if(a == (std::numeric_limits<Integer>::min)())
+       return a == static_cast<Integer>(0) ? b : gcd(static_cast<Integer>(a % b), b);
+    else if (b == (std::numeric_limits<Integer>::min)())
+       return b == static_cast<Integer>(0) ? a : gcd(a, static_cast<Integer>(b % a));
+    return gcd_detail::optimal_gcd_select(static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(a)), static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(b)));
+}
+
+template <typename Integer>
+inline BOOST_CXX14_CONSTEXPR Integer lcm(Integer const &a, Integer const &b) BOOST_GCD_NOEXCEPT(Integer)
 {
+   return gcd_detail::lcm_imp(static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(a)), static_cast<Integer>(gcd_detail::gcd_traits<Integer>::abs(b)));
+}
+#ifndef BOOST_NO_CXX11_VARIADIC_TEMPLATES
+template <typename Integer, typename... Args>
+inline BOOST_CXX14_CONSTEXPR Integer gcd(Integer const &a, Integer const &b, Args const&... args) BOOST_GCD_NOEXCEPT(Integer)
+{
+   Integer t = gcd(b, args...);
+   return t == 1 ? 1 : gcd(a, t);
+}
 
-//  Forward declarations for function templates  -----------------------------//
+template <typename Integer, typename... Args>
+inline BOOST_CXX14_CONSTEXPR Integer lcm(Integer const &a, Integer const &b, Args const&... args) BOOST_GCD_NOEXCEPT(Integer)
+{
+   return lcm(a, lcm(b, args...));
+}
+#endif
+//
+// Special handling for rationals:
+//
+template <typename Integer>
+inline typename boost::enable_if_c<std::numeric_limits<Integer>::is_specialized, boost::rational<Integer> >::type gcd(boost::rational<Integer> const &a, boost::rational<Integer> const &b)
+{
+   return boost::rational<Integer>(static_cast<Integer>(gcd(a.numerator(), b.numerator())), static_cast<Integer>(lcm(a.denominator(), b.denominator())));
+}
 
-template < typename IntegerType >
-BOOST_CXX14_CONSTEXPR IntegerType  gcd( IntegerType const &a, IntegerType const &b )BOOST_INT_NOEXCEPT(IntegerType);
-
-template < typename IntegerType >
-BOOST_CXX14_CONSTEXPR IntegerType  lcm( IntegerType const &a, IntegerType const &b )BOOST_INT_NOEXCEPT(IntegerType);
-
-
-//  Greatest common divisor evaluator class declaration  ---------------------//
+template <typename Integer>
+inline typename boost::enable_if_c<std::numeric_limits<Integer>::is_specialized, boost::rational<Integer> >::type lcm(boost::rational<Integer> const &a, boost::rational<Integer> const &b)
+{
+   return boost::rational<Integer>(static_cast<Integer>(lcm(a.numerator(), b.numerator())), static_cast<Integer>(gcd(a.denominator(), b.denominator())));
+}
+/**
+ * Knuth, The Art of Computer Programming: Volume 2, Third edition, 1998
+ * Chapter 4.5.2, Algorithm C: Greatest common divisor of n integers.
+ *
+ * Knuth counts down from n to zero but we naturally go from first to last.
+ * We also return the termination position because it might be useful to know.
+ * 
+ * Partly by quirk, partly by design, this algorithm is defined for n = 1, 
+ * because the gcd of {x} is x. It is not defined for n = 0.
+ * 
+ * @tparam  I   Input iterator.
+ * @return  The gcd of the range and the iterator position at termination.
+ */
+template <typename I>
+std::pair<typename std::iterator_traits<I>::value_type, I>
+gcd_range(I first, I last) BOOST_GCD_NOEXCEPT(I)
+{
+    BOOST_ASSERT(first != last);
+    typedef typename std::iterator_traits<I>::value_type T;
+    
+    T d = *first++;
+    while (d != T(1) && first != last)
+    {
+        d = gcd(d, *first);
+        first++;
+    }
+    return std::make_pair(d, first);
+}
+template <typename I>
+std::pair<typename std::iterator_traits<I>::value_type, I>
+lcm_range(I first, I last) BOOST_GCD_NOEXCEPT(I)
+{
+    BOOST_ASSERT(first != last);
+    typedef typename std::iterator_traits<I>::value_type T;
+    
+    T d = *first++;
+    while (d != T(1) && first != last)
+    {
+        d = lcm(d, *first);
+        first++;
+    }
+    return std::make_pair(d, first);
+}
 
 template < typename IntegerType >
 class gcd_evaluator
+#ifdef BOOST_NO_CXX11_HDR_FUNCTIONAL
+   : public std::binary_function<IntegerType, IntegerType, IntegerType>
+#endif
 {
 public:
-    // Types
-    typedef IntegerType  result_type, first_argument_type, second_argument_type;
-
-    // Function object interface
-    BOOST_CXX14_CONSTEXPR result_type  operator ()( first_argument_type const &a,
-     second_argument_type const &b )const BOOST_INT_NOEXCEPT(IntegerType) ;
-
-};  // boost::integer::gcd_evaluator
-
-
-//  Least common multiple evaluator class declaration  -----------------------//
+#ifndef BOOST_NO_CXX11_HDR_FUNCTIONAL
+   typedef IntegerType first_argument_type;
+   typedef IntegerType second_argument_type;
+   typedef IntegerType result_type;
+#endif
+   IntegerType operator()(IntegerType const &a, IntegerType const &b)const
+   {
+      return boost::integer::gcd(a, b);
+   }
+};
 
 template < typename IntegerType >
 class lcm_evaluator
+#ifdef BOOST_NO_CXX11_HDR_FUNCTIONAL
+   : public std::binary_function<IntegerType, IntegerType, IntegerType>
+#endif
 {
 public:
-    // Types
-    typedef IntegerType  result_type, first_argument_type, second_argument_type;
-
-    // Function object interface
-    BOOST_CXX14_CONSTEXPR result_type  operator ()( first_argument_type const &a,
-     second_argument_type const &b )const BOOST_INT_NOEXCEPT(IntegerType) ;
-
-};  // boost::integer::lcm_evaluator
-
-
-//  Implementation details  --------------------------------------------------//
-
-namespace detail
-{
-    // Greatest common divisor for rings (including unsigned integers)
-    template < typename RingType >
-    BOOST_CXX14_CONSTEXPR RingType
-    gcd_euclidean
-    (
-        RingType a,
-        RingType b
-    )BOOST_INT_NOEXCEPT(RingType)
-    {
-        // Avoid repeated construction
-        #ifndef __BORLANDC__
-        RingType const  zero = static_cast<RingType>( 0 );
-        #else
-        RingType  zero = static_cast<RingType>( 0 );
-        #endif
-
-        // Reduce by GCD-remainder property [GCD(a,b) == GCD(b,a MOD b)]
-        while ( true )
-        {
-            if ( a == zero )
-                return b;
-            b %= a;
-
-            if ( b == zero )
-                return a;
-            a %= b;
-        }
-    }
-
-    // Greatest common divisor for (signed) integers
-    template < typename IntegerType >
-    inline
-    BOOST_CXX14_CONSTEXPR IntegerType
-    gcd_integer
-    (
-        IntegerType const &  a,
-        IntegerType const &  b
-    )BOOST_INT_NOEXCEPT(IntegerType)
-    {
-        // Avoid repeated construction
-        IntegerType const  zero = static_cast<IntegerType>( 0 );
-        IntegerType const  result = gcd_euclidean( a, b );
-
-        return ( result < zero ) ? static_cast<IntegerType>(-result) : result;
-    }
-
-    // Greatest common divisor for unsigned binary integers
-    template < typename BuiltInUnsigned >
-    BOOST_CXX14_CONSTEXPR BuiltInUnsigned
-    gcd_binary
-    (
-        BuiltInUnsigned  u,
-        BuiltInUnsigned  v
-    )BOOST_INT_NOEXCEPT(BuiltInUnsigned)
-    {
-        if ( u && v )
-        {
-            // Shift out common factors of 2
-            unsigned  shifts = 0;
-
-            while ( !(u & 1u) && !(v & 1u) )
-            {
-                ++shifts;
-                u >>= 1;
-                v >>= 1;
-            }
-
-            // Start with the still-even one, if any
-            BuiltInUnsigned  r[] = { u, v };
-            unsigned         which = static_cast<bool>( u & 1u );
-
-            // Whittle down the values via their differences
-            do
-            {
-#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
-                while ( !(r[ which ] & 1u) )
-                {
-                    r[ which ] = (r[which] >> 1);
-                }
-#else
-                // Remove factors of two from the even one
-                while ( !(r[ which ] & 1u) )
-                {
-                    r[ which ] >>= 1;
-                }
+#ifndef BOOST_NO_CXX11_HDR_FUNCTIONAL
+   typedef IntegerType first_argument_type;
+   typedef IntegerType second_argument_type;
+   typedef IntegerType result_type;
 #endif
-
-                // Replace the larger of the two with their difference
-                if ( r[!which] > r[which] )
-                {
-                    which ^= 1u;
-                }
-
-                r[ which ] -= r[ !which ];
-            }
-            while ( r[which] );
-
-            // Shift-in the common factor of 2 to the residues' GCD
-            return r[ !which ] << shifts;
-        }
-        else
-        {
-            // At least one input is zero, return the other
-            // (adding since zero is the additive identity)
-            // or zero if both are zero.
-            return u + v;
-        }
-    }
-
-    // Least common multiple for rings (including unsigned integers)
-    template < typename RingType >
-    inline
-    BOOST_CXX14_CONSTEXPR RingType
-    lcm_euclidean
-    (
-        RingType const &  a,
-        RingType const &  b
-    )BOOST_INT_NOEXCEPT(RingType)
-    {
-        RingType const  zero = static_cast<RingType>( 0 );
-        RingType const  temp = gcd_euclidean( a, b );
-
-        return ( temp != zero ) ? ( a / temp * b ) : zero;
-    }
-
-    // Least common multiple for (signed) integers
-    template < typename IntegerType >
-    inline BOOST_CXX14_CONSTEXPR
-    IntegerType
-    lcm_integer
-    (
-        IntegerType const &  a,
-        IntegerType const &  b
-    )BOOST_INT_NOEXCEPT(IntegerType)
-    {
-        // Avoid repeated construction
-        IntegerType const  zero = static_cast<IntegerType>( 0 );
-        IntegerType const  result = lcm_euclidean( a, b );
-
-        return ( result < zero ) ? static_cast<IntegerType>(-result) : result;
-    }
-
-    // Function objects to find the best way of computing GCD or LCM
-#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-    template < typename T, bool IsSpecialized, bool IsSigned >
-    struct gcd_optimal_evaluator_helper_t
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            return gcd_euclidean( a, b );
-        }
-    };
-
-    template < typename T >
-    struct gcd_optimal_evaluator_helper_t< T, true, true >
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            return gcd_integer( a, b );
-        }
-    };
-
-    template < typename T >
-    struct gcd_optimal_evaluator
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            typedef ::std::numeric_limits<T>  limits_type;
-
-            typedef gcd_optimal_evaluator_helper_t<T,
-             limits_type::is_specialized, limits_type::is_signed>  helper_type;
-
-            helper_type  solver;
-
-            return solver( a, b );
-        }
-    };
-#else // BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-    template < typename T >
-    struct gcd_optimal_evaluator
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            return gcd_integer( a, b );
-        }
-    };
-#endif
-
-    // Specialize for the built-in integers
-#define BOOST_PRIVATE_GCD_UF( Ut )                  \
-    template < >  struct gcd_optimal_evaluator<Ut>  \
-    {  BOOST_CXX14_CONSTEXPR Ut  operator ()( Ut a, Ut b ) const BOOST_INT_NOEXCEPT(Ut)   { return gcd_binary( a, b ); }  }
-
-    BOOST_PRIVATE_GCD_UF( unsigned char );
-    BOOST_PRIVATE_GCD_UF( unsigned short );
-    BOOST_PRIVATE_GCD_UF( unsigned );
-    BOOST_PRIVATE_GCD_UF( unsigned long );
-
-#ifdef BOOST_HAS_LONG_LONG
-    BOOST_PRIVATE_GCD_UF( boost::ulong_long_type );
-#elif defined(BOOST_HAS_MS_INT64)
-    BOOST_PRIVATE_GCD_UF( unsigned __int64 );
-#endif
-
-#if CHAR_MIN == 0
-    BOOST_PRIVATE_GCD_UF( char ); // char is unsigned
-#endif
-
-#undef BOOST_PRIVATE_GCD_UF
-
-#define BOOST_PRIVATE_GCD_SF( St, Ut )                            \
-    template < >  struct gcd_optimal_evaluator<St>                \
-    {  BOOST_CXX14_CONSTEXPR St  operator ()( St a, St b ) const BOOST_INT_NOEXCEPT(St)   { Ut const  a_abs =   \
-    static_cast<Ut>( a < 0 ? -a : +a ), b_abs = static_cast<Ut>(  \
-    b < 0 ? -b : +b ); return static_cast<St>(                    \
-    gcd_optimal_evaluator<Ut>()(a_abs, b_abs) ); }  }
-
-    BOOST_PRIVATE_GCD_SF( signed char, unsigned char );
-    BOOST_PRIVATE_GCD_SF( short, unsigned short );
-    BOOST_PRIVATE_GCD_SF( int, unsigned );
-    BOOST_PRIVATE_GCD_SF( long, unsigned long );
-
-#if CHAR_MIN < 0
-    BOOST_PRIVATE_GCD_SF( char, unsigned char ); // char is signed
-#endif
-
-#ifdef BOOST_HAS_LONG_LONG
-    BOOST_PRIVATE_GCD_SF( boost::long_long_type, boost::ulong_long_type );
-#elif defined(BOOST_HAS_MS_INT64)
-    BOOST_PRIVATE_GCD_SF( __int64, unsigned __int64 );
-#endif
-
-#undef BOOST_PRIVATE_GCD_SF
-
-#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-    template < typename T, bool IsSpecialized, bool IsSigned >
-    struct lcm_optimal_evaluator_helper_t
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            return lcm_euclidean( a, b );
-        }
-    };
-
-    template < typename T >
-    struct lcm_optimal_evaluator_helper_t< T, true, true >
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            return lcm_integer( a, b );
-        }
-    };
-
-    template < typename T >
-    struct lcm_optimal_evaluator
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            typedef ::std::numeric_limits<T>  limits_type;
-
-            typedef lcm_optimal_evaluator_helper_t<T,
-             limits_type::is_specialized, limits_type::is_signed>  helper_type;
-
-            helper_type  solver;
-
-            return solver( a, b );
-        }
-    };
-#else // BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
-    template < typename T >
-    struct lcm_optimal_evaluator
-    {
-        BOOST_CXX14_CONSTEXPR T  operator ()( T const &a, T const &b )BOOST_INT_NOEXCEPT(T)
-        {
-            return lcm_integer( a, b );
-        }
-    };
-#endif
-
-    // Functions to find the GCD or LCM in the best way
-    template < typename T >
-    inline BOOST_CXX14_CONSTEXPR
-    T
-    gcd_optimal
-    (
-        T const &  a,
-        T const &  b
-    )BOOST_INT_NOEXCEPT(T)
-    {
-        gcd_optimal_evaluator<T>  solver;
-
-        return solver( a, b );
-    }
-
-    template < typename T >
-    inline BOOST_CXX14_CONSTEXPR
-    T
-    lcm_optimal
-    (
-        T const &  a,
-        T const &  b
-    )BOOST_INT_NOEXCEPT(T)
-    {
-        lcm_optimal_evaluator<T>  solver;
-
-        return solver( a, b );
-    }
-
-}  // namespace detail
-
-
-//  Greatest common divisor evaluator member function definition  ------------//
-
-template < typename IntegerType >
-inline BOOST_CXX14_CONSTEXPR
-typename gcd_evaluator<IntegerType>::result_type
-gcd_evaluator<IntegerType>::operator ()
-(
-    first_argument_type const &   a,
-    second_argument_type const &  b
-) const BOOST_INT_NOEXCEPT(IntegerType) 
-{
-    return detail::gcd_optimal( a, b );
-}
-
-
-//  Least common multiple evaluator member function definition  --------------//
-
-template < typename IntegerType >
-inline BOOST_CXX14_CONSTEXPR
-typename lcm_evaluator<IntegerType>::result_type
-lcm_evaluator<IntegerType>::operator ()
-(
-    first_argument_type const &   a,
-    second_argument_type const &  b
-) const BOOST_INT_NOEXCEPT(IntegerType) 
-{
-    return detail::lcm_optimal( a, b );
-}
-
-
-//  Greatest common divisor and least common multiple function definitions  --//
-
-template < typename IntegerType >
-inline BOOST_CXX14_CONSTEXPR
-IntegerType
-gcd
-(
-    IntegerType const &  a,
-    IntegerType const &  b
-) BOOST_INT_NOEXCEPT(IntegerType)
-{
-    gcd_evaluator<IntegerType>  solver;
-
-    return solver( a, b );
-}
-
-template < typename IntegerType >
-inline BOOST_CXX14_CONSTEXPR
-IntegerType
-lcm
-(
-    IntegerType const &  a,
-    IntegerType const &  b
-) BOOST_INT_NOEXCEPT(IntegerType)
-{
-    lcm_evaluator<IntegerType>  solver;
-
-    return solver( a, b );
-}
-
+   IntegerType operator()(IntegerType const &a, IntegerType const &b)const
+   {
+      return boost::integer::lcm(a, b);
+   }
+};
 
 }  // namespace integer
 }  // namespace boost
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index ea29336..691b703 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -20,6 +20,7 @@ test-suite integer
         [ compile static_min_max_include_test.cpp ]
         [ compile integer_fwd_include_test.cpp ]
 		[ compile gcd_constexpr14_test.cpp ]
+		[ compile gcd_noexcept_test.cpp ]
         [ compile-fail fail_int_exact.cpp ]
         [ compile-fail fail_int_fast.cpp ]
         [ compile-fail fail_int_least.cpp ]
diff --git a/test/common_factor_test.cpp b/test/common_factor_test.cpp
index 81ffc47..9457e1a 100644
--- a/test/common_factor_test.cpp
+++ b/test/common_factor_test.cpp
@@ -15,14 +15,17 @@
 //  02 Nov 2006  Change to Boost.Test's unit test system (Daryle Walker)
 //  07 Nov 2001  Initial version (Daryle Walker)
 
-#define BOOST_TEST_MAIN  "Boost.Math GCD & LCM unit tests"
+#define BOOST_TEST_MAIN  "Boost.integer GCD & LCM unit tests"
 
-#include <boost/integer/common_factor.hpp>
-
-#include <boost/config.hpp>                // for BOOST_MSVC, etc.
+#include <boost/config.hpp>              // for BOOST_MSVC, etc.
 #include <boost/detail/workaround.hpp>
+#include <boost/integer/common_factor.hpp>  // for boost::integer::gcd, etc.
+#include <boost/mpl/list.hpp>            // for boost::mpl::list
 #include <boost/operators.hpp>
 #include <boost/core/lightweight_test.hpp>
+#include <boost/multiprecision/cpp_int.hpp>
+#include <boost/random.hpp>
+#include <boost/rational.hpp>
 
 #include <istream>  // for std::basic_istream
 #include <limits>   // for std::numeric_limits
@@ -109,6 +112,25 @@ MyUnsigned1  dummy2;
 MyInt2       dummy3;
 MyUnsigned2  dummy4;
 
+// Various types to test with each GCD/LCM
+typedef ::boost::mpl::list<signed char, short, int, long,
+#if BOOST_WORKAROUND(BOOST_MSVC, <= 1500)
+#elif defined(BOOST_HAS_LONG_LONG)
+ boost::long_long_type,
+#elif defined(BOOST_HAS_MS_INT64)
+ __int64,
+#endif
+ MyInt1, boost::multiprecision::cpp_int>  signed_test_types;
+typedef ::boost::mpl::list<unsigned char, unsigned short, unsigned,
+ unsigned long,
+#if BOOST_WORKAROUND(BOOST_MSVC, <= 1500)
+#elif defined(BOOST_HAS_LONG_LONG)
+ boost::ulong_long_type,
+#elif defined(BOOST_HAS_MS_INT64)
+ unsigned __int64,
+#endif
+ MyUnsigned1, MyUnsigned2 /*, boost::multiprecision::uint256_t*/>  unsigned_test_types;
+
 }  // namespace
 
 #define BOOST_NO_MACRO_EXPAND /**/
@@ -246,7 +268,12 @@ inline ostream& operator<<(ostream& os, unsigned __int64 i)
 // GCD on signed integer types
 template< class T > void gcd_int_test() // signed_test_types
 {
+#ifndef BOOST_MSVC
     using boost::integer::gcd;
+    using boost::integer::gcd_evaluator;
+#else
+    using namespace boost::integer;
+#endif
 
     // Originally from Boost.Rational tests
     BOOST_TEST_EQ( gcd<T>(  1,  -1), static_cast<T>( 1) );
@@ -265,12 +292,33 @@ template< class T > void gcd_int_test() // signed_test_types
     BOOST_TEST_EQ( gcd<T>(  3,   7), static_cast<T>( 1) );
     BOOST_TEST_EQ( gcd<T>(  8,   9), static_cast<T>( 1) );
     BOOST_TEST_EQ( gcd<T>(  7,  49), static_cast<T>( 7) );
+    // Again with function object:
+    BOOST_TEST_EQ(gcd_evaluator<T>()(1, -1), static_cast<T>(1));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(-1, 1), static_cast<T>(1));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(1, 1), static_cast<T>(1));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(-1, -1), static_cast<T>(1));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(0, 0), static_cast<T>(0));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(7, 0), static_cast<T>(7));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(0, 9), static_cast<T>(9));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(-7, 0), static_cast<T>(7));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(0, -9), static_cast<T>(9));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(42, 30), static_cast<T>(6));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(6, -9), static_cast<T>(3));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(-10, -10), static_cast<T>(10));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(-25, -10), static_cast<T>(5));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(3, 7), static_cast<T>(1));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(8, 9), static_cast<T>(1));
+    BOOST_TEST_EQ(gcd_evaluator<T>()(7, 49), static_cast<T>(7));
 }
 
 // GCD on unmarked signed integer type
 void gcd_unmarked_int_test()
 {
+#ifndef BOOST_MSVC
     using boost::integer::gcd;
+#else
+    using namespace boost::integer;
+#endif
 
     // The regular signed-integer GCD function performs the unsigned version,
     // then does an absolute-value on the result.  Signed types that are not
@@ -297,7 +345,11 @@ void gcd_unmarked_int_test()
 // GCD on unsigned integer types
 template< class T > void gcd_unsigned_test() // unsigned_test_types
 {
+#ifndef BOOST_MSVC
     using boost::integer::gcd;
+#else
+    using namespace boost::integer;
+#endif
 
     // Note that unmarked types (i.e. have no std::numeric_limits
     // specialization) are treated like non/unsigned types
@@ -314,29 +366,53 @@ template< class T > void gcd_unsigned_test() // unsigned_test_types
 // GCD at compile-time
 void gcd_static_test()
 {
+#ifndef BOOST_MSVC
     using boost::integer::static_gcd;
+#else
+    using namespace boost::integer;
+#endif
 
-    BOOST_TEST_EQ( (static_gcd< 1,  1>::value), 1 );
-    BOOST_TEST_EQ( (static_gcd< 0,  0>::value), 0 );
-    BOOST_TEST_EQ( (static_gcd< 7,  0>::value), 7 );
-    BOOST_TEST_EQ( (static_gcd< 0,  9>::value), 9 );
-    BOOST_TEST_EQ( (static_gcd<42, 30>::value), 6 );
-    BOOST_TEST_EQ( (static_gcd< 3,  7>::value), 1 );
-    BOOST_TEST_EQ( (static_gcd< 8,  9>::value), 1 );
-    BOOST_TEST_EQ( (static_gcd< 7, 49>::value), 7 );
+    // Can't use "BOOST_TEST_EQ", otherwise the "value" member will be
+    // disqualified as compile-time-only constant, needing explicit definition
+    BOOST_TEST( (static_gcd< 1,  1>::value) == 1 );
+    BOOST_TEST( (static_gcd< 0,  0>::value) == 0 );
+    BOOST_TEST( (static_gcd< 7,  0>::value) == 7 );
+    BOOST_TEST( (static_gcd< 0,  9>::value) == 9 );
+    BOOST_TEST( (static_gcd<42, 30>::value) == 6 );
+    BOOST_TEST( (static_gcd< 3,  7>::value) == 1 );
+    BOOST_TEST( (static_gcd< 8,  9>::value) == 1 );
+    BOOST_TEST( (static_gcd< 7, 49>::value) == 7 );
 }
 
-// TODO: non-built-in signed and unsigned integer tests, with and without
-// numeric_limits specialization; polynominal tests; note any changes if
-// built-ins switch to binary-GCD algorithm
+void gcd_method_test()
+{
+   // Verify that the 3 different methods all yield the same result:
+   boost::random::mt19937 gen;
+   boost::random::uniform_int_distribution<int> d(0, ((std::numeric_limits<int>::max)() / 2));
 
+   for (unsigned int i = 0; i < 10000; ++i)
+   {
+      int v1 = d(gen);
+      int v2 = d(gen);
+      int g = boost::integer::gcd_detail::Euclid_gcd(v1, v2);
+      BOOST_TEST(v1 % g == 0);
+      BOOST_TEST(v2 % g == 0);
+      BOOST_TEST_EQ(g, boost::integer::gcd_detail::mixed_binary_gcd(v1, v2));
+      BOOST_TEST_EQ(g, boost::integer::gcd_detail::Stein_gcd(v1, v2));
+   }
+}
 
 // LCM tests
 
 // LCM on signed integer types
 template< class T > void lcm_int_test() // signed_test_types
 {
+#ifndef BOOST_MSVC
     using boost::integer::lcm;
+    using boost::integer::lcm_evaluator;
+#else
+    using namespace boost::integer;
+#endif
 
     // Originally from Boost.Rational tests
     BOOST_TEST_EQ( lcm<T>(  1,  -1), static_cast<T>( 1) );
@@ -355,12 +431,33 @@ template< class T > void lcm_int_test() // signed_test_types
     BOOST_TEST_EQ( lcm<T>(  3,   7), static_cast<T>(21) );
     BOOST_TEST_EQ( lcm<T>(  8,   9), static_cast<T>(72) );
     BOOST_TEST_EQ( lcm<T>(  7,  49), static_cast<T>(49) );
+    // Again with function object:
+    BOOST_TEST_EQ(lcm_evaluator<T>()(1, -1), static_cast<T>(1));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(-1, 1), static_cast<T>(1));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(1, 1), static_cast<T>(1));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(-1, -1), static_cast<T>(1));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(0, 0), static_cast<T>(0));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(6, 0), static_cast<T>(0));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(0, 7), static_cast<T>(0));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(-5, 0), static_cast<T>(0));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(0, -4), static_cast<T>(0));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(18, 30), static_cast<T>(90));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(-6, 9), static_cast<T>(18));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(-10, -10), static_cast<T>(10));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(25, -10), static_cast<T>(50));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(3, 7), static_cast<T>(21));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(8, 9), static_cast<T>(72));
+    BOOST_TEST_EQ(lcm_evaluator<T>()(7, 49), static_cast<T>(49));
 }
 
 // LCM on unmarked signed integer type
 void lcm_unmarked_int_test()
 {
+#ifndef BOOST_MSVC
     using boost::integer::lcm;
+#else
+    using namespace boost::integer;
+#endif
 
     // The regular signed-integer LCM function performs the unsigned version,
     // then does an absolute-value on the result.  Signed types that are not
@@ -387,7 +484,11 @@ void lcm_unmarked_int_test()
 // LCM on unsigned integer types
 template< class T > void lcm_unsigned_test() // unsigned_test_types
 {
+#ifndef BOOST_MSVC
     using boost::integer::lcm;
+#else
+    using namespace boost::integer;
+#endif
 
     // Note that unmarked types (i.e. have no std::numeric_limits
     // specialization) are treated like non/unsigned types
@@ -404,23 +505,46 @@ template< class T > void lcm_unsigned_test() // unsigned_test_types
 // LCM at compile-time
 void lcm_static_test()
 {
+#ifndef BOOST_MSVC
     using boost::integer::static_lcm;
+#else
+    using namespace boost::integer;
+#endif
 
-    BOOST_TEST_EQ( (static_lcm< 1,  1>::value),  1 );
-    BOOST_TEST_EQ( (static_lcm< 0,  0>::value),  0 );
-    BOOST_TEST_EQ( (static_lcm< 6,  0>::value),  0 );
-    BOOST_TEST_EQ( (static_lcm< 0,  7>::value),  0 );
-    BOOST_TEST_EQ( (static_lcm<18, 30>::value), 90 );
-    BOOST_TEST_EQ( (static_lcm< 3,  7>::value), 21 );
-    BOOST_TEST_EQ( (static_lcm< 8,  9>::value), 72 );
-    BOOST_TEST_EQ( (static_lcm< 7, 49>::value), 49 );
+    // Can't use "BOOST_TEST_EQ", otherwise the "value" member will be
+    // disqualified as compile-time-only constant, needing explicit definition
+    BOOST_TEST( (static_lcm< 1,  1>::value) ==  1 );
+    BOOST_TEST( (static_lcm< 0,  0>::value) ==  0 );
+    BOOST_TEST( (static_lcm< 6,  0>::value) ==  0 );
+    BOOST_TEST( (static_lcm< 0,  7>::value) ==  0 );
+    BOOST_TEST( (static_lcm<18, 30>::value) == 90 );
+    BOOST_TEST( (static_lcm< 3,  7>::value) == 21 );
+    BOOST_TEST( (static_lcm< 8,  9>::value) == 72 );
+    BOOST_TEST( (static_lcm< 7, 49>::value) == 49 );
 }
 
-// TODO: see GCD to-do
+void variadics()
+{
+   unsigned i[] = { 44, 56, 76, 88 };
+   BOOST_TEST_EQ(boost::integer::gcd_range(i, i + 4).first, 4);
+   BOOST_TEST_EQ(boost::integer::gcd_range(i, i + 4).second, i + 4);
+   BOOST_TEST_EQ(boost::integer::lcm_range(i, i + 4).first, 11704);
+   BOOST_TEST_EQ(boost::integer::lcm_range(i, i + 4).second, i + 4);
+#ifndef BOOST_NO_CXX11_VARIADIC_TEMPLATES
+   BOOST_TEST_EQ(boost::integer::gcd(i[0], i[1], i[2], i[3]), 4);
+   BOOST_TEST_EQ(boost::integer::lcm(i[0], i[1], i[2], i[3]), 11704);
+#endif
+}
 
-// main
-
-// Various types to test with each GCD/LCM
+// Test case from Boost.Rational, need to make sure we don't break the rational lib:
+template <class T> void gcd_and_lcm_on_rationals()
+{
+   typedef boost::rational<T> rational;
+   BOOST_TEST_EQ(boost::integer::gcd(rational(1, 4), rational(1, 3)),
+      rational(1, 12));
+   BOOST_TEST_EQ(boost::integer::lcm(rational(1, 4), rational(1, 3)),
+      rational(1));
+}
 
 #define TEST_SIGNED_( test ) \
     test<signed char>(); \
@@ -459,15 +583,18 @@ void lcm_static_test()
 
 int main()
 {
-    TEST_SIGNED( gcd_int_test )
-    gcd_unmarked_int_test();
-    TEST_UNSIGNED( gcd_unsigned_test )
-    gcd_static_test();
+   TEST_SIGNED(gcd_int_test)
+   gcd_unmarked_int_test();
+   TEST_UNSIGNED(gcd_unsigned_test)
+   gcd_static_test();
+   gcd_method_test();
 
-    TEST_SIGNED( lcm_int_test )
-    lcm_unmarked_int_test();
-    TEST_UNSIGNED( lcm_unsigned_test )
-    lcm_static_test();
+   TEST_SIGNED(lcm_int_test)
+   lcm_unmarked_int_test();
+   TEST_UNSIGNED(lcm_unsigned_test)
+   lcm_static_test();
+   variadics();
+   TEST_SIGNED(gcd_and_lcm_on_rationals)
 
-    return boost::report_errors();
+   return boost::report_errors();
 }
diff --git a/test/gcd_constexpr14_test.cpp b/test/gcd_constexpr14_test.cpp
index 6e4bf30..05bef34 100644
--- a/test/gcd_constexpr14_test.cpp
+++ b/test/gcd_constexpr14_test.cpp
@@ -8,7 +8,7 @@
 
 #ifndef BOOST_NO_CXX14_CONSTEXPR
 
-void test_constexpr()
+void test_constexpr1()
 {
    constexpr const boost::int64_t i = 347 * 463 * 727;
    constexpr const boost::int64_t j = 191 * 347 * 281;
@@ -16,30 +16,51 @@ void test_constexpr()
    constexpr const boost::int64_t k = boost::integer::gcd(i, j);
    constexpr const boost::int64_t l = boost::integer::lcm(i, j);
 
-   static_assert(k == 347, "Expected result not found in constexpr gcd.");
-   static_assert(l == 6268802158037, "Expected result not found in constexpr lcm.");
+   static_assert(k == 347, "Expected result not integer in constexpr gcd.");
+   static_assert(l == 6268802158037, "Expected result not integer in constexpr lcm.");
 }
 
-#endif
-
-#ifndef BOOST_NO_CXX11_NOEXCEPT
-
-void test_noexcept()
+void test_constexpr2()
 {
-   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned char>(2), static_cast<unsigned char>(4))), "Expected a noexcept function.");
-#ifndef _MSC_VER
-   // This generates an internal compiler error if enabled as well as the following test:
-   static_assert(noexcept(boost::integer::gcd(static_cast<char>(2), static_cast<char>(4))), "Expected a noexcept function.");
-#endif
-   static_assert(noexcept(boost::integer::gcd(static_cast<signed char>(2), static_cast<signed char>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<short>(2), static_cast<short>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned short>(2), static_cast<unsigned short>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<int>(2), static_cast<int>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned int>(2), static_cast<unsigned int>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<long>(2), static_cast<long>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned long>(2), static_cast<unsigned long>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<long long>(2), static_cast<long long>(4))), "Expected a noexcept function.");
-   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned long long>(2), static_cast<unsigned long long>(4))), "Expected a noexcept function.");
+   constexpr const boost::uint64_t i = 347 * 463 * 727;
+   constexpr const boost::uint64_t j = 191 * 347 * 281;
+
+   constexpr const boost::uint64_t k = boost::integer::gcd(i, j);
+   constexpr const boost::uint64_t l = boost::integer::lcm(i, j);
+
+   static_assert(k == 347, "Expected result not integer in constexpr gcd.");
+   static_assert(l == 6268802158037, "Expected result not integer in constexpr lcm.");
 }
 
+void test_constexpr3()
+{
+   constexpr const boost::uint64_t i = 347 * 463 * 727;
+   constexpr const boost::uint64_t j = 191 * 347 * 281;
+
+   constexpr const boost::uint64_t k = boost::integer::gcd_detail::Euclid_gcd(i, j);
+
+   static_assert(k == 347, "Expected result not integer in constexpr gcd.");
+}
+
+void test_constexpr4()
+{
+   constexpr const boost::uint64_t i = 347 * 463 * 727;
+   constexpr const boost::uint64_t j = 191 * 347 * 281;
+
+   constexpr const boost::uint64_t k = boost::integer::gcd_detail::mixed_binary_gcd(i, j);
+
+   static_assert(k == 347, "Expected result not integer in constexpr gcd.");
+}
+
+void test_constexpr5()
+{
+   constexpr const boost::uint64_t i = 347 * 463 * 727;
+   constexpr const boost::uint64_t j = 191 * 347 * 281;
+
+   constexpr const boost::uint64_t k = boost::integer::gcd_detail::Stein_gcd(i, j);
+
+   static_assert(k == 347, "Expected result not integer in constexpr gcd.");
+}
 #endif
+
+
diff --git a/test/gcd_noexcept_test.cpp b/test/gcd_noexcept_test.cpp
new file mode 100644
index 0000000..9100744
--- /dev/null
+++ b/test/gcd_noexcept_test.cpp
@@ -0,0 +1,35 @@
+
+//  (C) Copyright John Maddock 2017.
+//  Distributed under the Boost Software License, Version 1.0. (See
+//  accompanying file LICENSE_1_0.txt or copy at
+//  http://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/integer/common_factor.hpp>
+
+#if !defined(BOOST_NO_CXX11_NOEXCEPT) && !defined(BOOST_NO_CXX11_HDR_TYPE_TRAITS)
+//
+// These tests don't pass with GCC-4.x:
+//
+#if !defined(BOOST_GCC) || (BOOST_GCC >= 50000)
+
+void test_noexcept(unsigned char a, unsigned char b)
+{
+   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned char>(a), static_cast<unsigned char>(b))), "Expected a noexcept function.");
+#ifndef _MSC_VER
+   // This generates an internal compiler error if enabled as well as the following test:
+   static_assert(noexcept(boost::integer::gcd(static_cast<char>(a), static_cast<char>(b))), "Expected a noexcept function.");
+#endif
+   static_assert(noexcept(boost::integer::gcd(static_cast<signed char>(a), static_cast<signed char>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<short>(a), static_cast<short>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned short>(a), static_cast<unsigned short>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<int>(a), static_cast<int>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned int>(a), static_cast<unsigned int>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<long>(a), static_cast<long>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned long>(a), static_cast<unsigned long>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<long long>(a), static_cast<long long>(b))), "Expected a noexcept function.");
+   static_assert(noexcept(boost::integer::gcd(static_cast<unsigned long long>(a), static_cast<unsigned long long>(b))), "Expected a noexcept function.");
+}
+
+#endif
+#endif
+