Chris@16: ///////////////////////////////////////////////////////////////
Chris@16: //  Copyright 2012 John Maddock. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
Chris@16: //
Chris@16: // Comparison operators for cpp_int_backend:
Chris@16: //
Chris@16: #ifndef BOOST_MP_CPP_INT_MUL_HPP
Chris@16: #define BOOST_MP_CPP_INT_MUL_HPP
Chris@16: 
Chris@16: namespace boost{ namespace multiprecision{ namespace backends{
Chris@16: 
Chris@16: 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>
Chris@16: 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 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
Chris@16:       const limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@16:    if(!val)
Chris@16:    {
Chris@16:       result = static_cast<limb_type>(0);
Chris@16:       return;
Chris@16:    }
Chris@16:    if((void*)&a != (void*)&result)
Chris@16:       result.resize(a.size(), a.size());
Chris@16:    double_limb_type carry = 0;
Chris@16:    typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer p = result.limbs();
Chris@16:    typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pe = result.limbs() + result.size();
Chris@16:    typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
Chris@16:    while(p != pe)
Chris@16:    {
Chris@16:       carry += static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(val);
Chris@16:       *p = static_cast<limb_type>(carry);
Chris@16:       carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:       ++p, ++pa;
Chris@16:    }
Chris@16:    if(carry)
Chris@16:    {
Chris@16:       unsigned i = result.size();
Chris@16:       result.resize(i + 1, i + 1);
Chris@16:       if(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (result.size() > i))
Chris@16:          result.limbs()[i] = static_cast<limb_type>(carry);
Chris@16:    }
Chris@16:    result.sign(a.sign());
Chris@16:    if(!cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable)
Chris@16:       result.normalize();
Chris@16: }
Chris@16: 
Chris@16: //
Chris@16: // resize_for_carry forces a resize of the underlying buffer only if a previous request
Chris@16: // for "required" elements could possibly have failed, *and* we have checking enabled.
Chris@16: // This will cause an overflow error inside resize():
Chris@16: //
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& /*result*/, unsigned /*required*/){}
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, checked, void>& result, unsigned required)
Chris@16: {
Chris@16:    if(result.size() != required)
Chris@16:       result.resize(required, required);
Chris@16: }
Chris@16: 
Chris@16: 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>
Chris@16: 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
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
Chris@16:       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))
Chris@16: {
Chris@16:    // Very simple long multiplication, only usable for small numbers of limb_type's
Chris@16:    // but that's the typical use case for this type anyway:
Chris@16:    //
Chris@16:    // Special cases first:
Chris@16:    //
Chris@16:    unsigned as = a.size();
Chris@16:    unsigned bs = b.size();
Chris@16:    typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
Chris@16:    typename cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>::const_limb_pointer pb = b.limbs();
Chris@16:    if(as == 1)
Chris@16:    {
Chris@16:       bool s = b.sign() != a.sign();
Chris@16:       if(bs == 1)
Chris@16:       {
Chris@16:          result = static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(*pb);
Chris@16:       }
Chris@16:       else
Chris@16:       {
Chris@16:          limb_type l = *pa;
Chris@16:          eval_multiply(result, b, l);
Chris@16:       }
Chris@16:       result.sign(s);
Chris@16:       return;
Chris@16:    }
Chris@16:    if(bs == 1)
Chris@16:    {
Chris@16:       bool s = b.sign() != a.sign();
Chris@16:       limb_type l = *pb;
Chris@16:       eval_multiply(result, a, l);
Chris@16:       result.sign(s);
Chris@16:       return;
Chris@16:    }
Chris@16: 
Chris@16:    if((void*)&result == (void*)&a)
Chris@16:    {
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(a);
Chris@16:       eval_multiply(result, t, b);
Chris@16:       return;
Chris@16:    }
Chris@16:    if((void*)&result == (void*)&b)
Chris@16:    {
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(b);
Chris@16:       eval_multiply(result, a, t);
Chris@16:       return;
Chris@16:    }
Chris@16: 
Chris@16:    result.resize(as + bs, as + bs - 1);
Chris@16:    typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pr = result.limbs();
Chris@16: 
Chris@16:    static const double_limb_type limb_max = ~static_cast<limb_type>(0u);
Chris@16:    static const double_limb_type double_limb_max = ~static_cast<double_limb_type>(0u);
Chris@16:    BOOST_STATIC_ASSERT(double_limb_max - 2 * limb_max >= limb_max * limb_max);
Chris@16: 
Chris@16:    double_limb_type carry = 0;
Chris@16:    std::memset(pr, 0, result.size() * sizeof(limb_type));
Chris@16:    for(unsigned i = 0; i < as; ++i)
Chris@16:    {
Chris@16:       unsigned inner_limit = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable ? bs : (std::min)(result.size() - i, bs);
Chris@16:       for(unsigned j = 0; j < inner_limit; ++j)
Chris@16:       {
Chris@16:          BOOST_ASSERT(i+j < result.size());
Chris@16:          BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized 
Chris@16:             || ((std::numeric_limits<double_limb_type>::max)() - carry 
Chris@16:                   > 
Chris@16:                 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)));
Chris@16:          carry += static_cast<double_limb_type>(pa[i]) * static_cast<double_limb_type>(pb[j]);
Chris@16:          BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized || ((std::numeric_limits<double_limb_type>::max)() - carry >= pr[i+j]));
Chris@16:          carry += pr[i + j];
Chris@16:          pr[i + j] = static_cast<limb_type>(carry);
Chris@16:          carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
Chris@16:          BOOST_ASSERT(carry <= (cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value));
Chris@16:       }
Chris@16:       resize_for_carry(result, as + bs);  // May throw if checking is enabled
Chris@16:       if(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (i + bs < result.size()))
Chris@16:          pr[i + bs] = static_cast<limb_type>(carry);
Chris@16:       carry = 0;
Chris@16:    }
Chris@16:    result.normalize();
Chris@16:    //
Chris@16:    // Set the sign of the result:
Chris@16:    //
Chris@16:    result.sign(a.sign() != b.sign());
Chris@16: }
Chris@16: 
Chris@16: 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>
Chris@16: 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 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       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))
Chris@16: {
Chris@16:     eval_multiply(result, result, a);
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
Chris@16:    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))
Chris@16: {
Chris@16:    eval_multiply(result, result, val);
Chris@16: }
Chris@16: 
Chris@16: 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>
Chris@16: 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 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
Chris@16:       const double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@16:    if(val <= (std::numeric_limits<limb_type>::max)())
Chris@16:    {
Chris@16:       eval_multiply(result, a, static_cast<limb_type>(val));
Chris@16:    }
Chris@16:    else
Chris@16:    {
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
Chris@16:       eval_multiply(result, a, t);
Chris@16:    }
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
Chris@16:    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))
Chris@16: {
Chris@16:    eval_multiply(result, result, val);
Chris@16: }
Chris@16: 
Chris@16: 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>
Chris@16: 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 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
Chris@16:       const signed_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@16:    if(val > 0)
Chris@16:       eval_multiply(result, a, static_cast<limb_type>(val));
Chris@16:    else
Chris@16:    {
Chris@101:       eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
Chris@16:       result.negate();
Chris@16:    }
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
Chris@16:    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))
Chris@16: {
Chris@16:    eval_multiply(result, result, val);
Chris@16: }
Chris@16: 
Chris@16: 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>
Chris@16: 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 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a, 
Chris@16:       const signed_double_limb_type& val) BOOST_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
Chris@16: {
Chris@16:    if(val > 0)
Chris@16:    {
Chris@16:       if(val <= (std::numeric_limits<limb_type>::max)())
Chris@16:       {
Chris@16:          eval_multiply(result, a, static_cast<limb_type>(val));
Chris@16:          return;
Chris@16:       }
Chris@16:    }
Chris@16:    else if(val >= -static_cast<signed_double_limb_type>((std::numeric_limits<limb_type>::max)()))
Chris@16:    {
Chris@101:       eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
Chris@16:       result.negate();
Chris@16:       return;
Chris@16:    }
Chris@16:    cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
Chris@16:    eval_multiply(result, a, t);
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type 
Chris@16:    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))
Chris@16: {
Chris@16:    eval_multiply(result, result, val);
Chris@16: }
Chris@16: 
Chris@16: //
Chris@16: // Now over again for trivial cpp_int's:
Chris@16: //
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<
Chris@16:          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
Chris@16:          && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:             || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
Chris@16:          >::type 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       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))
Chris@16: {
Chris@16:    *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
Chris@16:    result.sign(result.sign() != o.sign());
Chris@16:    result.normalize();
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<
Chris@16:          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          >::type 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       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))
Chris@16: {
Chris@16:    *result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
Chris@16:    result.normalize();
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<
Chris@16:          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          && is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
Chris@16:          && (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:             || is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
Chris@16:          >::type 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
Chris@16:       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))
Chris@16: {
Chris@16:    *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
Chris@16:    result.sign(a.sign() != b.sign());
Chris@16:    result.normalize();
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<
Chris@16:          is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          && is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          >::type 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
Chris@16:       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))
Chris@16: {
Chris@16:    *result.limbs() = detail::checked_multiply(*a.limbs(), *b.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
Chris@16:    result.normalize();
Chris@16: }
Chris@16: 
Chris@16: //
Chris@16: // Special routines for multiplying two integers to obtain a multiprecision result:
Chris@16: //
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<
Chris@16:             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          >::type 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       signed_double_limb_type a, signed_double_limb_type b)
Chris@16: {
Chris@16:    static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
Chris@16:    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
Chris@16:    bool s = false;
Chris@16:    double_limb_type w, x, y, z;
Chris@16:    if(a < 0)
Chris@16:    {
Chris@16:       a = -a;
Chris@16:       s = true;
Chris@16:    }
Chris@16:    if(b < 0)
Chris@16:    {
Chris@16:       b = -b;
Chris@16:       s = !s;
Chris@16:    }
Chris@16:    w = a & mask;
Chris@16:    x = a >> limb_bits;
Chris@16:    y = b & mask;
Chris@16:    z = b >> limb_bits;
Chris@16: 
Chris@16:    result.resize(4, 4);
Chris@16:    limb_type* pr = result.limbs();
Chris@16: 
Chris@16:    double_limb_type carry = w * y;
Chris@16:    pr[0] = static_cast<limb_type>(carry);
Chris@16:    carry >>= limb_bits;
Chris@16:    carry += w * z + x * y;
Chris@16:    pr[1] = static_cast<limb_type>(carry);
Chris@16:    carry >>= limb_bits;
Chris@16:    carry += x * z;
Chris@16:    pr[2] = static_cast<limb_type>(carry);
Chris@16:    pr[3] = static_cast<limb_type>(carry >> limb_bits);
Chris@16: 
Chris@16:    result.sign(s);
Chris@16:    result.normalize();
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<
Chris@16:             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value 
Chris@16:          >::type 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       double_limb_type a, double_limb_type b)
Chris@16: {
Chris@16:    static const signed_double_limb_type mask = ~static_cast<limb_type>(0);
Chris@16:    static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
Chris@16: 
Chris@16:    double_limb_type w, x, y, z;
Chris@16:    w = a & mask;
Chris@16:    x = a >> limb_bits;
Chris@16:    y = b & mask;
Chris@16:    z = b >> limb_bits;
Chris@16: 
Chris@16:    result.resize(4, 4);
Chris@16:    limb_type* pr = result.limbs();
Chris@16: 
Chris@16:    double_limb_type carry = w * y;
Chris@16:    pr[0] = static_cast<limb_type>(carry);
Chris@16:    carry >>= limb_bits;
Chris@16:    carry += w * z;
Chris@16:    pr[1] = static_cast<limb_type>(carry);
Chris@16:    carry >>= limb_bits;
Chris@16:    pr[2] = static_cast<limb_type>(carry);
Chris@16:    carry = x * y + pr[1];
Chris@16:    pr[1] = static_cast<limb_type>(carry);
Chris@16:    carry >>= limb_bits;
Chris@16:    carry += pr[2] + x * z;
Chris@16:    pr[2] = static_cast<limb_type>(carry);
Chris@16:    pr[3] = static_cast<limb_type>(carry >> limb_bits);
Chris@16: 
Chris@16:    result.sign(false);
Chris@16:    result.normalize();
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1,
Chris@16:           unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<
Chris@16:             !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
Chris@16:             && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
Chris@16:             && is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value
Chris@16:          >::type 
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& a, 
Chris@16:       cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> const& b)
Chris@16: {
Chris@16:    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;
Chris@16:    eval_multiply(result, static_cast<canonical_type>(*a.limbs()), static_cast<canonical_type>(*b.limbs()));
Chris@16:    result.sign(a.sign() != b.sign());
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class SI>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<is_signed<SI>::value && (sizeof(SI) <= sizeof(signed_double_limb_type) / 2)>::type
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       SI a, SI b)
Chris@16: {
Chris@16:    result = static_cast<signed_double_limb_type>(a) * static_cast<signed_double_limb_type>(b);
Chris@16: }
Chris@16: 
Chris@16: template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class UI>
Chris@16: BOOST_MP_FORCEINLINE typename enable_if_c<is_unsigned<UI>::value && (sizeof(UI) <= sizeof(signed_double_limb_type) / 2)>::type
Chris@16:    eval_multiply(
Chris@16:       cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, 
Chris@16:       UI a, UI b)
Chris@16: {
Chris@16:    result = static_cast<double_limb_type>(a) * static_cast<double_limb_type>(b);
Chris@16: }
Chris@16: 
Chris@16: }}} // namespaces
Chris@16: 
Chris@16: #endif