1 files changed, 437 insertions, 0 deletions
diff --git a/boost/multiprecision/cpp_int/multiply.hpp b/boost/multiprecision/cpp_int/multiply.hpp
new file mode 100644
index 0000000000..fd569faa00
--- /dev/null
+++ b/boost/multiprecision/cpp_int/multiply.hpp
@@ -0,0 +1,437 @@
+///////////////////////////////////////////////////////////////
+//  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_MUL_HPP
+#define BOOST_MP_CPP_INT_MUL_HPP
+
+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>
+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 >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
+      const limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   if(!val)
+   {
+      result = static_cast<limb_type>(0);
+      return;
+   }
+   if((void*)&a != (void*)&result)
+      result.resize(a.size(), a.size());
+   double_limb_type carry = 0;
+   typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer p = result.limbs();
+   typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pe = result.limbs() + result.size();
+   typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
+   while(p != pe)
+   {
+      carry += static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(val);
+      *p = static_cast<limb_type>(carry);
+      carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
+      ++p, ++pa;
+   }
+   if(carry)
+   {
+      unsigned i = result.size();
+      result.resize(i + 1, i + 1);
+      if(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (result.size() > i))
+         result.limbs()[i] = static_cast<limb_type>(carry);
+   }
+   result.sign(a.sign());
+   if(!cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable)
+      result.normalize();
+}
+
+//
+// resize_for_carry forces a resize of the underlying buffer only if a previous request
+// for "required" elements could possibly have failed, *and* we have checking enabled.
+// This will cause an overflow error inside resize():
+//
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& /*result*/, unsigned /*required*/){}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, checked, void>& result, unsigned required)
+{
+   if(result.size() != required)
+      result.resize(required, required);
+}
+
+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, unsigned MinBits3, unsigned MaxBits3, cpp_integer_type SignType3, cpp_int_check_type Checked3, class Allocator3>
+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_trivial_cpp_int<cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3> >::value >::type
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
+      const cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   // Very simple long multiplication, only usable for small numbers of limb_type's
+   // but that's the typical use case for this type anyway:
+   //
+   // Special cases first:
+   //
+   unsigned as = a.size();
+   unsigned bs = b.size();
+   typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
+   typename cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>::const_limb_pointer pb = b.limbs();
+   if(as == 1)
+   {
+      bool s = b.sign() != a.sign();
+      if(bs == 1)
+      {
+         result = static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(*pb);
+      }
+      else
+      {
+         limb_type l = *pa;
+         eval_multiply(result, b, l);
+      }
+      result.sign(s);
+      return;
+   }
+   if(bs == 1)
+   {
+      bool s = b.sign() != a.sign();
+      limb_type l = *pb;
+      eval_multiply(result, a, l);
+      result.sign(s);
+      return;
+   }
+
+   if((void*)&result == (void*)&a)
+   {
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(a);
+      eval_multiply(result, t, b);
+      return;
+   }
+   if((void*)&result == (void*)&b)
+   {
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(b);
+      eval_multiply(result, a, t);
+      return;
+   }
+
+   result.resize(as + bs, as + bs - 1);
+   typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pr = result.limbs();
+
+   static const double_limb_type limb_max = ~static_cast<limb_type>(0u);
+   static const double_limb_type double_limb_max = ~static_cast<double_limb_type>(0u);
+   BOOST_STATIC_ASSERT(double_limb_max - 2 * limb_max >= limb_max * limb_max);
+
+   double_limb_type carry = 0;
+   std::memset(pr, 0, result.size() * sizeof(limb_type));
+   for(unsigned i = 0; i < as; ++i)
+   {
+      unsigned inner_limit = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable ? bs : (std::min)(result.size() - i, bs);
+      for(unsigned j = 0; j < inner_limit; ++j)
+      {
+         BOOST_ASSERT(i+j < result.size());
+         BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized 
+            || ((std::numeric_limits<double_limb_type>::max)() - carry 
+                  > 
+                static_cast<double_limb_type>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value) * static_cast<double_limb_type>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value)));
+         carry += static_cast<double_limb_type>(pa[i]) * static_cast<double_limb_type>(pb[j]);
+         BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized || ((std::numeric_limits<double_limb_type>::max)() - carry >= pr[i+j]));
+         carry += pr[i + j];
+         pr[i + j] = static_cast<limb_type>(carry);
+         carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
+         BOOST_ASSERT(carry <= (cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value));
+      }
+      resize_for_carry(result, as + bs);  // May throw if checking is enabled
+      if(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (i + bs < result.size()))
+         pr[i + bs] = static_cast<limb_type>(carry);
+      carry = 0;
+   }
+   result.normalize();
+   //
+   // Set the sign of the result:
+   //
+   result.sign(a.sign() != b.sign());
+}
+
+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_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+    eval_multiply(result, result, a);
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
+   eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+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_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
+      const double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   if(val <= (std::numeric_limits<limb_type>::max)())
+   {
+      eval_multiply(result, a, static_cast<limb_type>(val));
+   }
+   else
+   {
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
+      eval_multiply(result, a, t);
+   }
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
+   eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+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_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
+      const signed_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   if(val > 0)
+      eval_multiply(result, a, static_cast<limb_type>(val));
+   else
+   {
+      eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
+      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_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
+   eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const signed_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+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 >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
+      const signed_double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   if(val > 0)
+   {
+      if(val <= (std::numeric_limits<limb_type>::max)())
+      {
+         eval_multiply(result, a, static_cast<limb_type>(val));
+         return;
+      }
+   }
+   else if(val >= -static_cast<signed_double_limb_type>((std::numeric_limits<limb_type>::max)()))
+   {
+      eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
+      result.negate();
+      return;
+   }
+   cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
+   eval_multiply(result, a, t);
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
+   eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const signed_double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   eval_multiply(result, result, val);
+}
+
+//
+// Now over again for trivial cpp_int's:
+//
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+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<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+            || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
+         >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+   result.sign(result.sign() != o.sign());
+   result.normalize();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+         && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+         >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& o) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), 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>
+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<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
+         && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+            || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
+         >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
+      const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+   result.sign(a.sign() != b.sign());
+   result.normalize();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<
+         is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+         && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+         >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
+      const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& b) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
+{
+   *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
+   result.normalize();
+}
+
+//
+// Special routines for multiplying two integers to obtain a multiprecision result:
+//
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<
+            !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+         >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      signed_double_limb_type a, signed_double_limb_type b)
+{
+   static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
+   static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
+   bool s = false;
+   double_limb_type w, x, y, z;
+   if(a < 0)
+   {
+      a = -a;
+      s = true;
+   }
+   if(b < 0)
+   {
+      b = -b;
+      s = !s;
+   }
+   w = a & mask;
+   x = a >> limb_bits;
+   y = b & mask;
+   z = b >> limb_bits;
+
+   result.resize(4, 4);
+   limb_type* pr = result.limbs();
+
+   double_limb_type carry = w * y;
+   pr[0] = static_cast<limb_type>(carry);
+   carry >>= limb_bits;
+   carry += w * z + x * y;
+   pr[1] = static_cast<limb_type>(carry);
+   carry >>= limb_bits;
+   carry += x * z;
+   pr[2] = static_cast<limb_type>(carry);
+   pr[3] = static_cast<limb_type>(carry >> limb_bits);
+
+   result.sign(s);
+   result.normalize();
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
+BOOST_MP_FORCEINLINE typename enable_if_c<
+            !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
+         >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      double_limb_type a, double_limb_type b)
+{
+   static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
+   static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
+
+   double_limb_type w, x, y, z;
+   w = a & mask;
+   x = a >> limb_bits;
+   y = b & mask;
+   z = b >> limb_bits;
+
+   result.resize(4, 4);
+   limb_type* pr = result.limbs();
+
+   double_limb_type carry = w * y;
+   pr[0] = static_cast<limb_type>(carry);
+   carry >>= limb_bits;
+   carry += w * z;
+   pr[1] = static_cast<limb_type>(carry);
+   carry >>= limb_bits;
+   pr[2] = static_cast<limb_type>(carry);
+   carry = x * y + pr[1];
+   pr[1] = static_cast<limb_type>(carry);
+   carry >>= limb_bits;
+   carry += pr[2] + x * z;
+   pr[2] = static_cast<limb_type>(carry);
+   pr[3] = static_cast<limb_type>(carry >> limb_bits);
+
+   result.sign(false);
+   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>
+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
+            && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
+         >::type 
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& a, 
+      cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& b)
+{
+   typedef typename boost::multiprecision::detail::canonical<typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::local_limb_type, cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::type canonical_type;
+   eval_multiply(result, static_cast<canonical_type>(*a.limbs()), static_cast<canonical_type>(*b.limbs()));
+   result.sign(a.sign() != b.sign());
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class SI>
+BOOST_MP_FORCEINLINE typename enable_if_c<is_signed<SI>::value && (sizeof(SI) <= sizeof(signed_double_limb_type) / 2)>::type
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      SI a, SI b)
+{
+   result = static_cast<signed_double_limb_type>(a) * static_cast<signed_double_limb_type>(b);
+}
+
+template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class UI>
+BOOST_MP_FORCEINLINE typename enable_if_c<is_unsigned<UI>::value && (sizeof(UI) <= sizeof(signed_double_limb_type) / 2)>::type
+   eval_multiply(
+      cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
+      UI a, UI b)
+{
+   result = static_cast<double_limb_type>(a) * static_cast<double_limb_type>(b);
+}
+
+}}} // namespaces
+
+#endif