add boost on mac

macx64/include/boost/multiprecision/cpp_int/bitwise.hpp

@@ -0,0 +1,842 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2012 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+// Comparison operators for cpp_int_backend:
+//
+#ifndef BOOST_MP_CPP_INT_BIT_HPP
+#define BOOST_MP_CPP_INT_BIT_HPP
+
+#ifdef _MSC_VER
+#pragma warning(push)
+#pragma warning(disable:4319)
+#endif
+
+namespace boost{ namespace multiprecision{ namespace backends{
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+void is_valid_bitwise_op(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::int_<checked>&)
+{
+   if(result.sign() || o.sign())
+      BOOST_THROW_EXCEPTION(std::range_error("Bitwise operations on negative values results in undefined behavior."));
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+void is_valid_bitwise_op(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& , const mpl::int_<unchecked>&){}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_int_check_type Checked1, class Allocator1>
+void is_valid_bitwise_op(
+      const cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1>& result, const mpl::int_<checked>&)
+{
+   if(result.sign())
+      BOOST_THROW_EXCEPTION(std::range_error("Bitwise operations on negative values results in undefined behavior."));
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_int_check_type Checked1, class Allocator1>
+void is_valid_bitwise_op(
+   const cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1>&, const mpl::int_<checked>&){}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+void is_valid_bitwise_op(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>&, const mpl::int_<unchecked>&){}
+
+template <class CppInt1, class CppInt2, class Op>
+void bitwise_op(
+   CppInt1& result,
+   const CppInt2& o,
+   Op op, const mpl::true_&) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<CppInt1>::value))
+{
+   //
+   // There are 4 cases:
+   // * Both positive.
+   // * result negative, o positive.
+   // * o negative, result positive.
+   // * Both negative.
+   //
+   // When one arg is negative we convert to 2's complement form "on the fly",
+   // and then convert back to signed-magnitude form at the end.
+   //
+   // Note however, that if the type is checked, then bitwise ops on negative values
+   // are not permitted and an exception will result.
+   //
+   is_valid_bitwise_op(result, o, typename CppInt1::checked_type());
+   //
+   // First figure out how big the result needs to be and set up some data:
+   //
+   unsigned rs = result.size();
+   unsigned os = o.size();
+   unsigned m, x;
+   minmax(rs, os, m, x);
+   result.resize(x, x);
+   typename CppInt1::limb_pointer pr = result.limbs();
+   typename CppInt2::const_limb_pointer po = o.limbs();
+   for(unsigned i = rs; i < x; ++i)
+      pr[i] = 0;
+
+   limb_type next_limb = 0;
+
+   if(!result.sign())
+   {
+      if(!o.sign())
+      {
+         for(unsigned i = 0; i < os; ++i)
+            pr[i] = op(pr[i], po[i]);
+         for(unsigned i = os; i < x; ++i)
+            pr[i] = op(pr[i], limb_type(0));
+      }
+      else
+      {
+         // "o" is negative:
+         double_limb_type carry = 1;
+         for(unsigned i = 0; i < os; ++i)
+         {
+            carry += static_cast<double_limb_type>(~po[i]);
+            pr[i] = op(pr[i], static_cast<limb_type>(carry));
+            carry >>= CppInt1::limb_bits;
+         }
+         for(unsigned i = os; i < x; ++i)
+         {
+            carry += static_cast<double_limb_type>(~limb_type(0));
+            pr[i] = op(pr[i], static_cast<limb_type>(carry));
+            carry >>= CppInt1::limb_bits;
+         }
+         // Set the overflow into the "extra" limb:
+         carry += static_cast<double_limb_type>(~limb_type(0));
+         next_limb = op(limb_type(0), static_cast<limb_type>(carry));
+      }
+   }
+   else
+   {
+      if(!o.sign())
+      {
+         // "result" is negative:
+         double_limb_type carry = 1;
+         for(unsigned i = 0; i < os; ++i)
+         {
+            carry += static_cast<double_limb_type>(~pr[i]);
+            pr[i] = op(static_cast<limb_type>(carry), po[i]);
+            carry >>= CppInt1::limb_bits;
+         }
+         for(unsigned i = os; i < x; ++i)
+         {
+            carry += static_cast<double_limb_type>(~pr[i]);
+            pr[i] = op(static_cast<limb_type>(carry), limb_type(0));
+            carry >>= CppInt1::limb_bits;
+         }
+         // Set the overflow into the "extra" limb:
+         carry += static_cast<double_limb_type>(~limb_type(0));
+         next_limb = op(static_cast<limb_type>(carry), limb_type(0));
+      }
+      else
+      {
+         // both are negative:
+         double_limb_type r_carry = 1;
+         double_limb_type o_carry = 1;
+         for(unsigned i = 0; i < os; ++i)
+         {
+            r_carry += static_cast<double_limb_type>(~pr[i]);
+            o_carry += static_cast<double_limb_type>(~po[i]);
+            pr[i] = op(static_cast<limb_type>(r_carry), static_cast<limb_type>(o_carry));
+            r_carry >>= CppInt1::limb_bits;
+            o_carry >>= CppInt1::limb_bits;
+         }
+         for(unsigned i = os; i < x; ++i)
+         {
+            r_carry += static_cast<double_limb_type>(~pr[i]);
+            o_carry += static_cast<double_limb_type>(~limb_type(0));
+            pr[i] = op(static_cast<limb_type>(r_carry), static_cast<limb_type>(o_carry));
+            r_carry >>= CppInt1::limb_bits;
+            o_carry >>= CppInt1::limb_bits;
+         }
+         // Set the overflow into the "extra" limb:
+         r_carry += static_cast<double_limb_type>(~limb_type(0));
+         o_carry += static_cast<double_limb_type>(~limb_type(0));
+         next_limb = op(static_cast<limb_type>(r_carry), static_cast<limb_type>(o_carry));
+      }
+   }
+   //
+   // See if the result is negative or not:
+   //
+   if(static_cast<signed_limb_type>(next_limb) < 0)
+   {
+      double_limb_type carry = 1;
+      for(unsigned i = 0; i < x; ++i)
+      {
+         carry += static_cast<double_limb_type>(~pr[i]);
+         pr[i] = static_cast<limb_type>(carry);
+         carry >>= CppInt1::limb_bits;
+      }
+      if(carry)
+      {
+         result.resize(x + 1, x);
+         if(result.size() > x)
+            result.limbs()[x] = static_cast<limb_type>(carry);
+      }
+      result.sign(true);
+   }
+   else
+      result.sign(false);
+
+   result.normalize();
+}
+
+template <class CppInt1, class CppInt2, class Op>
+void bitwise_op(
+   CppInt1& result,
+   const CppInt2& o,
+   Op op, const mpl::false_&) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<CppInt1>::value))
+{
+   //
+   // Both arguments are unsigned types, very simple case handled as a special case.
+   //
+   // First figure out how big the result needs to be and set up some data:
+   //
+   unsigned rs = result.size();
+   unsigned os = o.size();
+   unsigned m, x;
+   minmax(rs, os, m, x);
+   result.resize(x, x);
+   typename CppInt1::limb_pointer pr = result.limbs();
+   typename CppInt2::const_limb_pointer po = o.limbs();
+   for(unsigned i = rs; i < x; ++i)
+      pr[i] = 0;
+
+   for(unsigned i = 0; i < os; ++i)
+      pr[i] = op(pr[i], po[i]);
+   for(unsigned i = os; i < x; ++i)
+      pr[i] = op(pr[i], limb_type(0));
+
+   result.normalize();
+}
+
+struct bit_and{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a & b; } };
+struct bit_or { limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a | b; } };
+struct bit_xor{ limb_type operator()(limb_type a, limb_type b)const BOOST_NOEXCEPT { return a ^ b; } };
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value >::type
+   eval_bitwise_and(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   bitwise_op(result, o, bit_and(), 
+      mpl::bool_<std::numeric_limits<number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> > >::is_signed || std::numeric_limits<number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> > >::is_signed>());
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value >::type
+   eval_bitwise_or(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   bitwise_op(result, o, bit_or(),
+      mpl::bool_<std::numeric_limits<number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> > >::is_signed || std::numeric_limits<number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> > >::is_signed>());
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value >::type
+   eval_bitwise_xor(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   bitwise_op(result, o, bit_xor(),
+      mpl::bool_<std::numeric_limits<number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> > >::is_signed || std::numeric_limits<number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> > >::is_signed>());
+}
+//
+// Again for operands which are single limbs:
+//
+template <unsigned MinBits1, unsigned MaxBits1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1> >::value>::type
+   eval_bitwise_and(
+      cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1>& result,
+      limb_type l) BOOST_NOEXCEPT
+{
+   result.limbs()[0] &= l;
+   result.resize(1, 1);
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1> >::value>::type
+   eval_bitwise_or(
+      cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1>& result,
+      limb_type l) BOOST_NOEXCEPT
+{
+   result.limbs()[0] |= l;
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1> >::value>::type
+   eval_bitwise_xor(
+      cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1>& result,
+      limb_type l) BOOST_NOEXCEPT
+{
+   result.limbs()[0] ^= l;
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+BOOST_MP_FORCEINLINE typename enable_if_c<is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value >::type
+   eval_complement(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   BOOST_STATIC_ASSERT_MSG(((Checked1 != checked) || (Checked2 != checked)), "Attempt to take the complement of a signed type results in undefined behavior.");
+   // Increment and negate:
+   result = o;
+   eval_increment(result);
+   result.negate();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value >::type
+   eval_complement(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   unsigned os = o.size();
+   result.resize(UINT_MAX, os);
+   for(unsigned i = 0; i < os; ++i)
+      result.limbs()[i] = ~o.limbs()[i];
+   for(unsigned i = os; i < result.size(); ++i)
+      result.limbs()[i] = ~static_cast<limb_type>(0);
+   result.normalize();
+}
+
+template <class Int>
+inline void left_shift_byte(Int& result, double_limb_type s)
+{
+   limb_type offset = static_cast<limb_type>(s / Int::limb_bits);
+   limb_type shift = static_cast<limb_type>(s % Int::limb_bits);
+   unsigned ors = result.size();
+   if((ors == 1) && (!*result.limbs()))
+      return; // shifting zero yields zero.
+   unsigned rs = ors;
+   if(shift && (result.limbs()[ors - 1] >> (Int::limb_bits - shift)))
+      ++rs; // Most significant limb will overflow when shifted
+   rs += offset;
+   result.resize(rs, rs);
+   rs = result.size();
+
+   typename Int::limb_pointer pr = result.limbs();
+
+   if(rs != ors)
+      pr[rs - 1] = 0u;
+   std::size_t bytes = static_cast<std::size_t>(s / CHAR_BIT);
+   std::size_t len = (std::min)(ors * sizeof(limb_type), rs * sizeof(limb_type) - bytes);
+   if(bytes >= rs * sizeof(limb_type))
+      result = static_cast<limb_type>(0u);
+   else
+   {
+      unsigned char* pc = reinterpret_cast<unsigned char*>(pr);
+      std::memmove(pc + bytes, pc, len);
+      std::memset(pc, 0, bytes);
+   }
+}
+
+template <class Int>
+inline void left_shift_limb(Int& result, double_limb_type s)
+{
+   limb_type offset = static_cast<limb_type>(s / Int::limb_bits);
+   limb_type shift = static_cast<limb_type>(s % Int::limb_bits);
+
+   unsigned ors = result.size();
+   if((ors == 1) && (!*result.limbs()))
+      return; // shifting zero yields zero.
+   unsigned rs = ors;
+   if(shift && (result.limbs()[ors - 1] >> (Int::limb_bits - shift)))
+      ++rs; // Most significant limb will overflow when shifted
+   rs += offset;
+   result.resize(rs, rs);
+
+   typename Int::limb_pointer pr = result.limbs();
+
+   if(offset > rs)
+   {
+      // The result is shifted past the end of the result:
+      result = static_cast<limb_type>(0);
+      return;
+   }
+
+   unsigned i = rs - result.size();
+   for(; i < ors; ++i)
+      pr[rs - 1 - i] = pr[ors - 1 - i];
+   for(; i < rs; ++i)
+      pr[rs - 1 - i] = 0;
+}
+
+template <class Int>
+inline void left_shift_generic(Int& result, double_limb_type s)
+{
+   limb_type offset = static_cast<limb_type>(s / Int::limb_bits);
+   limb_type shift = static_cast<limb_type>(s % Int::limb_bits);
+
+   unsigned ors = result.size();
+   if((ors == 1) && (!*result.limbs()))
+      return; // shifting zero yields zero.
+   unsigned rs = ors;
+   if(shift && (result.limbs()[ors - 1] >> (Int::limb_bits - shift)))
+      ++rs; // Most significant limb will overflow when shifted
+   rs += offset;
+   result.resize(rs, rs);
+   bool truncated = result.size() != rs;
+
+   typename Int::limb_pointer pr = result.limbs();
+
+   if(offset > rs)
+   {
+      // The result is shifted past the end of the result:
+      result = static_cast<limb_type>(0);
+      return;
+   }
+
+   unsigned i = rs - result.size();
+   // This code only works when shift is non-zero, otherwise we invoke undefined behaviour!
+   BOOST_ASSERT(shift);
+   if(!truncated)
+   {
+      if(rs > ors + offset)
+      {
+         pr[rs - 1 - i] = pr[ors - 1 - i] >> (Int::limb_bits - shift);
+         --rs;
+      }
+      else
+      {
+         pr[rs - 1 - i] = pr[ors - 1 - i] << shift;
+         if(ors > 1)
+            pr[rs - 1 - i] |= pr[ors - 2 - i] >> (Int::limb_bits - shift);
+         ++i;
+      }
+   }
+   for(; rs - i >= 2 + offset; ++i)
+   {
+      pr[rs - 1 - i] = pr[rs - 1 - i - offset] << shift;
+      pr[rs - 1 - i] |= pr[rs - 2 - i - offset] >> (Int::limb_bits - shift);
+   }
+   if(rs - i >= 1 + offset)
+   {
+      pr[rs - 1 - i] = pr[rs - 1 - i - offset] << shift;
+      ++i;
+   }
+   for(; i < rs; ++i)
+      pr[rs - 1 - i] = 0;
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
+   eval_left_shift(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      double_limb_type s) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   is_valid_bitwise_op(result, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+   if(!s)
+      return;
+
+#if BOOST_ENDIAN_LITTLE_BYTE && defined(BOOST_MP_USE_LIMB_SHIFT)
+   static const limb_type limb_shift_mask = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits - 1;
+   static const limb_type byte_shift_mask = CHAR_BIT - 1;
+   if((s & limb_shift_mask) == 0)
+   {
+      left_shift_limb(result, s);
+   }
+   else if((s & byte_shift_mask) == 0)
+   {
+      left_shift_byte(result, s);
+   }
+#elif BOOST_ENDIAN_LITTLE_BYTE
+   static const limb_type byte_shift_mask = CHAR_BIT - 1;
+   if((s & byte_shift_mask) == 0)
+   {
+      left_shift_byte(result, s);
+   }
+#else
+   static const limb_type limb_shift_mask = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits - 1;
+   if((s & limb_shift_mask) == 0)
+   {
+      left_shift_limb(result, s);
+   }
+#endif
+   else
+   {
+      left_shift_generic(result, s);
+   }
+   //
+   // We may have shifted off the end and have leading zeros:
+   //
+   result.normalize();
+}
+
+template <class Int>
+inline void right_shift_byte(Int& result, double_limb_type s)
+{
+   limb_type offset = static_cast<limb_type>(s / Int::limb_bits);
+   limb_type shift;
+   BOOST_ASSERT((s % CHAR_BIT) == 0);
+   unsigned ors = result.size();
+   unsigned rs = ors;
+   if(offset >= rs)
+   {
+      result = limb_type(0);
+      return;
+   }
+   rs -= offset;
+   typename Int::limb_pointer pr = result.limbs();
+   unsigned char* pc = reinterpret_cast<unsigned char*>(pr);
+   shift = static_cast<limb_type>(s / CHAR_BIT);
+   std::memmove(pc, pc + shift, ors * sizeof(pr[0]) - shift);
+   shift = (sizeof(limb_type) - shift % sizeof(limb_type)) * CHAR_BIT;
+   if(shift < Int::limb_bits)
+   {
+      pr[ors - offset - 1] &= (static_cast<limb_type>(1u) << shift) - 1;
+      if(!pr[ors - offset - 1] && (rs > 1))
+         --rs;
+   }
+   result.resize(rs, rs);
+}
+
+template <class Int>
+inline void right_shift_limb(Int& result, double_limb_type s)
+{
+   limb_type offset = static_cast<limb_type>(s / Int::limb_bits);
+   BOOST_ASSERT((s % Int::limb_bits) == 0);
+   unsigned ors = result.size();
+   unsigned rs = ors;
+   if(offset >= rs)
+   {
+      result = limb_type(0);
+      return;
+   }
+   rs -= offset;
+   typename Int::limb_pointer pr = result.limbs();
+   unsigned i = 0;
+   for(; i < rs; ++i)
+      pr[i] = pr[i + offset];
+   result.resize(rs, rs);
+}
+
+template <class Int>
+inline void right_shift_generic(Int& result, double_limb_type s)
+{
+   limb_type offset = static_cast<limb_type>(s / Int::limb_bits);
+   limb_type shift = static_cast<limb_type>(s % Int::limb_bits);
+   unsigned ors = result.size();
+   unsigned rs = ors;
+   if(offset >= rs)
+   {
+      result = limb_type(0);
+      return;
+   }
+   rs -= offset;
+   typename Int::limb_pointer pr = result.limbs();
+   if((pr[ors - 1] >> shift) == 0)
+   {
+      if(--rs == 0)
+      {
+         result = limb_type(0);
+         return;
+      }
+   }
+   unsigned i = 0;
+
+   // This code only works for non-zero shift, otherwise we invoke undefined behaviour!
+   BOOST_ASSERT(shift);
+   for(; i + offset + 1 < ors; ++i)
+   {
+      pr[i] = pr[i + offset] >> shift;
+      pr[i] |= pr[i + offset + 1] << (Int::limb_bits - shift);
+   }
+   pr[i] = pr[i + offset] >> shift;
+   result.resize(rs, rs);
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_int_check_type Checked1, class Allocator1>
+inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1> >::value>::type
+   eval_right_shift(
+      cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1>& result,
+      double_limb_type s) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1> >::value))
+{
+   is_valid_bitwise_op(result, typename cpp_int_backend<MinBits1, MaxBits1, unsigned_magnitude, Checked1, Allocator1>::checked_type());
+   if(!s)
+      return;
+
+#if BOOST_ENDIAN_LITTLE_BYTE && defined(BOOST_MP_USE_LIMB_SHIFT)
+   static const limb_type limb_shift_mask = cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1>::limb_bits - 1;
+   static const limb_type byte_shift_mask = CHAR_BIT - 1;
+   if((s & limb_shift_mask) == 0)
+      right_shift_limb(result, s);
+   else if((s & byte_shift_mask) == 0)
+      right_shift_byte(result, s);
+#elif BOOST_ENDIAN_LITTLE_BYTE
+   static const limb_type byte_shift_mask = CHAR_BIT - 1;
+   if((s & byte_shift_mask) == 0)
+      right_shift_byte(result, s);
+#else
+   static const limb_type limb_shift_mask = cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1>::limb_bits - 1;
+   if((s & limb_shift_mask) == 0)
+      right_shift_limb(result, s);
+#endif
+   else
+      right_shift_generic(result, s);
+}
+template <unsigned MinBits1, unsigned MaxBits1, cpp_int_check_type Checked1, class Allocator1>
+inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1> >::value>::type
+   eval_right_shift(
+      cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1>& result,
+      double_limb_type s) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1> >::value))
+{
+   is_valid_bitwise_op(result, typename cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1>::checked_type());
+   if(!s)
+      return;
+
+   bool is_neg = result.sign();
+   if(is_neg)
+      eval_increment(result);
+
+#if BOOST_ENDIAN_LITTLE_BYTE && defined(BOOST_MP_USE_LIMB_SHIFT)
+   static const limb_type limb_shift_mask = cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1>::limb_bits - 1;
+   static const limb_type byte_shift_mask = CHAR_BIT - 1;
+   if((s & limb_shift_mask) == 0)
+      right_shift_limb(result, s);
+   else if((s & byte_shift_mask) == 0)
+      right_shift_byte(result, s);
+#elif BOOST_ENDIAN_LITTLE_BYTE
+   static const limb_type byte_shift_mask = CHAR_BIT - 1;
+   if((s & byte_shift_mask) == 0)
+      right_shift_byte(result, s);
+#else
+   static const limb_type limb_shift_mask = cpp_int_backend<MinBits1, MaxBits1, signed_magnitude, Checked1, Allocator1>::limb_bits - 1;
+   if((s & limb_shift_mask) == 0)
+      right_shift_limb(result, s);
+#endif
+   else
+      right_shift_generic(result, s);
+   if(is_neg)
+      eval_decrement(result);
+}
+
+//
+// Over again for trivial cpp_int's:
+//
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class T>
+BOOST_MP_FORCEINLINE typename enable_if<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> > >::type
+   eval_left_shift(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, T s) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   is_valid_bitwise_op(result, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+   *result.limbs() = detail::checked_left_shift(*result.limbs(), s, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+   result.normalize();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class T>
+BOOST_MP_FORCEINLINE typename enable_if<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> > >::type
+   eval_right_shift(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, T s) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   // Nothing to check here... just make sure we don't invoke undefined behavior:
+   is_valid_bitwise_op(result, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+   *result.limbs() = (static_cast<unsigned>(s) >= sizeof(*result.limbs()) * CHAR_BIT) ? 0 : (result.sign() ? ((--*result.limbs()) >> s) + 1 : *result.limbs() >> s);
+   if(result.sign() && (*result.limbs() == 0))
+      result = static_cast<signed_limb_type>(-1);
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value || is_signed_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value)
+         >::type
+   eval_complement(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   BOOST_STATIC_ASSERT_MSG(((Checked1 != checked) || (Checked2 != checked)), "Attempt to take the complement of a signed type results in undefined behavior.");
+   //
+   // If we're not checked then emulate 2's complement behavior:
+   //
+   if(o.sign())
+   {
+      *result.limbs() = *o.limbs() - 1;
+      result.sign(false);
+   }
+   else
+   {
+      *result.limbs() = 1 + *o.limbs();
+      result.sign(true);
+   }
+   result.normalize();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         >::type
+   eval_complement(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() = ~*o.limbs();
+   result.normalize();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         >::type
+   eval_bitwise_and(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() &= *o.limbs();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value || is_signed_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value)
+         >::type
+   eval_bitwise_and(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   is_valid_bitwise_op(result, o, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+
+   using default_ops::eval_bit_test;
+   using default_ops::eval_increment;
+
+   if(result.sign() || o.sign())
+   {
+      static const unsigned m = static_unsigned_max<static_unsigned_max<MinBits1, MinBits2>::value, static_unsigned_max<MaxBits1, MaxBits2>::value>::value;
+      cpp_int_backend<m + 1, m + 1, unsigned_magnitude, unchecked, void> t1(result);
+      cpp_int_backend<m + 1, m + 1, unsigned_magnitude, unchecked, void> t2(o);
+      eval_bitwise_and(t1, t2);
+      bool s = eval_bit_test(t1, m + 1);
+      if(s)
+      {
+         eval_complement(t1, t1);
+         eval_increment(t1);
+      }
+      result = t1;
+      result.sign(s);
+   }
+   else
+   {
+      *result.limbs() &= *o.limbs();
+   }
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         >::type
+   eval_bitwise_or(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() |= *o.limbs();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value || is_signed_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value)
+         >::type
+   eval_bitwise_or(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   is_valid_bitwise_op(result, o, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+
+   using default_ops::eval_bit_test;
+   using default_ops::eval_increment;
+
+   if(result.sign() || o.sign())
+   {
+      static const unsigned m = static_unsigned_max<static_unsigned_max<MinBits1, MinBits2>::value, static_unsigned_max<MaxBits1, MaxBits2>::value>::value;
+      cpp_int_backend<m + 1, m + 1, unsigned_magnitude, unchecked, void> t1(result);
+      cpp_int_backend<m + 1, m + 1, unsigned_magnitude, unchecked, void> t2(o);
+      eval_bitwise_or(t1, t2);
+      bool s = eval_bit_test(t1, m + 1);
+      if(s)
+      {
+         eval_complement(t1, t1);
+         eval_increment(t1);
+      }
+      result = t1;
+      result.sign(s);
+   }
+   else
+   {
+      *result.limbs() |= *o.limbs();
+      result.normalize();
+   }
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_unsigned_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         >::type
+   eval_bitwise_xor(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() ^= *o.limbs();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
+inline typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value || is_signed_number<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value)
+         >::type
+   eval_bitwise_xor(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   is_valid_bitwise_op(result, o, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+
+   using default_ops::eval_bit_test;
+   using default_ops::eval_increment;
+
+   if(result.sign() || o.sign())
+   {
+      static const unsigned m = static_unsigned_max<static_unsigned_max<MinBits1, MinBits2>::value, static_unsigned_max<MaxBits1, MaxBits2>::value>::value;
+      cpp_int_backend<m + 1, m + 1, unsigned_magnitude, unchecked, void> t1(result);
+      cpp_int_backend<m + 1, m + 1, unsigned_magnitude, unchecked, void> t2(o);
+      eval_bitwise_xor(t1, t2);
+      bool s = eval_bit_test(t1, m + 1);
+      if(s)
+      {
+         eval_complement(t1, t1);
+         eval_increment(t1);
+      }
+      result = t1;
+      result.sign(s);
+   }
+   else
+   {
+      *result.limbs() ^= *o.limbs();
+   }
+}
+
+}}} // namespaces
+
+#ifdef _MSC_VER
+#pragma warning(pop)
+#endif
+
+#endif