annotate DEPENDENCIES/generic/include/boost/multiprecision/cpp_int/multiply.hpp @ 125:34e428693f5d vext

Vext -> Repoint

///////////////////////////////////////////////////////////////
//  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