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491 lines
25 KiB
C++
491 lines
25 KiB
C++
///////////////////////////////////////////////////////////////
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// Copyright 2012 John Maddock. Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
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//
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// Comparison operators for cpp_int_backend:
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//
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#ifndef BOOST_MP_CPP_INT_MUL_HPP
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#define BOOST_MP_CPP_INT_MUL_HPP
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namespace boost{ namespace multiprecision{ namespace backends{
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#ifdef _MSC_VER
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#pragma warning(push)
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#pragma warning(disable:4127) // conditional expression is constant
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#endif
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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>
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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
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
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const limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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if(!val)
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{
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result = static_cast<limb_type>(0);
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return;
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}
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if((void*)&a != (void*)&result)
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result.resize(a.size(), a.size());
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double_limb_type carry = 0;
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typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer p = result.limbs();
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typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pe = result.limbs() + result.size();
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typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
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while(p != pe)
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{
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carry += static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(val);
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#ifdef __MSVC_RUNTIME_CHECKS
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*p = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
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#else
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*p = static_cast<limb_type>(carry);
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#endif
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carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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++p, ++pa;
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}
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if(carry)
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{
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unsigned i = result.size();
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result.resize(i + 1, i + 1);
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if(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (result.size() > i))
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result.limbs()[i] = static_cast<limb_type>(carry);
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}
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result.sign(a.sign());
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if(!cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable)
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result.normalize();
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}
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//
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// resize_for_carry forces a resize of the underlying buffer only if a previous request
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// for "required" elements could possibly have failed, *and* we have checking enabled.
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// This will cause an overflow error inside resize():
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//
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& /*result*/, unsigned /*required*/){}
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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inline void resize_for_carry(cpp_int_backend<MinBits1, MaxBits1, SignType1, checked, void>& result, unsigned required)
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{
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if(result.size() != required)
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result.resize(required, required);
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}
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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>
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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
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
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const cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>& b) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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// Very simple long multiplication, only usable for small numbers of limb_type's
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// but that's the typical use case for this type anyway:
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//
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// Special cases first:
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//
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unsigned as = a.size();
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unsigned bs = b.size();
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typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::const_limb_pointer pa = a.limbs();
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typename cpp_int_backend<MinBits3, MaxBits3, SignType3, Checked3, Allocator3>::const_limb_pointer pb = b.limbs();
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if(as == 1)
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{
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bool s = b.sign() != a.sign();
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if(bs == 1)
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{
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result = static_cast<double_limb_type>(*pa) * static_cast<double_limb_type>(*pb);
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}
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else
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{
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limb_type l = *pa;
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eval_multiply(result, b, l);
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}
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result.sign(s);
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return;
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}
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if(bs == 1)
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{
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bool s = b.sign() != a.sign();
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limb_type l = *pb;
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eval_multiply(result, a, l);
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result.sign(s);
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return;
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}
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if((void*)&result == (void*)&a)
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{
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(a);
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eval_multiply(result, t, b);
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return;
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}
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if((void*)&result == (void*)&b)
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{
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(b);
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eval_multiply(result, a, t);
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return;
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}
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result.resize(as + bs, as + bs - 1);
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typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_pointer pr = result.limbs();
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static const double_limb_type limb_max = ~static_cast<limb_type>(0u);
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static const double_limb_type double_limb_max = ~static_cast<double_limb_type>(0u);
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BOOST_STATIC_ASSERT(double_limb_max - 2 * limb_max >= limb_max * limb_max);
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double_limb_type carry = 0;
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std::memset(pr, 0, result.size() * sizeof(limb_type));
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for(unsigned i = 0; i < as; ++i)
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{
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unsigned inner_limit = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable ? bs : (std::min)(result.size() - i, bs);
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for(unsigned j = 0; j < inner_limit; ++j)
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{
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BOOST_ASSERT(i+j < result.size());
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#if (!defined(__GLIBCXX__) && !defined(__GLIBCPP__)) || !BOOST_WORKAROUND(BOOST_GCC_VERSION, <= 50100)
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BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized
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|| ((std::numeric_limits<double_limb_type>::max)() - carry
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>
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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)));
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#endif
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carry += static_cast<double_limb_type>(pa[i]) * static_cast<double_limb_type>(pb[j]);
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BOOST_ASSERT(!std::numeric_limits<double_limb_type>::is_specialized || ((std::numeric_limits<double_limb_type>::max)() - carry >= pr[i+j]));
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carry += pr[i + j];
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#ifdef __MSVC_RUNTIME_CHECKS
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pr[i + j] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
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#else
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pr[i + j] = static_cast<limb_type>(carry);
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#endif
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carry >>= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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BOOST_ASSERT(carry <= (cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::max_limb_value));
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}
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resize_for_carry(result, as + bs); // May throw if checking is enabled
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if(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::variable || (i + bs < result.size()))
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pr[i + bs] = static_cast<limb_type>(carry);
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carry = 0;
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}
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result.normalize();
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//
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// Set the sign of the result:
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//
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result.sign(a.sign() != b.sign());
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}
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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>
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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
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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eval_multiply(result, result, a);
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}
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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eval_multiply(result, result, val);
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}
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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>
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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
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
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const double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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if(val <= (std::numeric_limits<limb_type>::max)())
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{
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eval_multiply(result, a, static_cast<limb_type>(val));
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}
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else
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{
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#if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
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#else
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
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t = val;
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#endif
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eval_multiply(result, a, t);
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}
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}
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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eval_multiply(result, result, val);
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}
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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>
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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
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
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const signed_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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if(val > 0)
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eval_multiply(result, a, static_cast<limb_type>(val));
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else
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{
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eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
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result.negate();
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}
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}
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const signed_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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eval_multiply(result, result, val);
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}
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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>
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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
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& a,
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const signed_double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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if(val > 0)
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{
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if(val <= (std::numeric_limits<limb_type>::max)())
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{
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eval_multiply(result, a, static_cast<limb_type>(val));
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return;
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}
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}
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else if(val >= -static_cast<signed_double_limb_type>((std::numeric_limits<limb_type>::max)()))
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{
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eval_multiply(result, a, static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(val)));
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result.negate();
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return;
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}
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#if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(val);
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#else
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
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t = val;
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#endif
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eval_multiply(result, a, t);
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}
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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BOOST_MP_FORCEINLINE typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_multiply(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const signed_double_limb_type& val) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
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{
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eval_multiply(result, result, val);
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}
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//
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// Now over again for trivial cpp_int's:
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//
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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BOOST_MP_FORCEINLINE typename enable_if_c<
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is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
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&& is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
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&& (is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
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|| is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value)
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>::type
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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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))
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{
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*result.limbs() = detail::checked_multiply(*result.limbs(), *o.limbs(), typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
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result.sign(result.sign() != o.sign());
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result.normalize();
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}
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template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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BOOST_MP_FORCEINLINE typename enable_if_c<
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is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
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&& is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
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>::type
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eval_multiply(
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
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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))
|
|
{
|
|
*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_MP_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_MP_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;
|
|
#ifdef __MSVC_RUNTIME_CHECKS
|
|
pr[0] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
carry >>= limb_bits;
|
|
carry += w * z + x * y;
|
|
pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
carry >>= limb_bits;
|
|
carry += x * z;
|
|
pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
pr[3] = static_cast<limb_type>(carry >> limb_bits);
|
|
#else
|
|
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);
|
|
#endif
|
|
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;
|
|
#ifdef __MSVC_RUNTIME_CHECKS
|
|
pr[0] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
carry >>= limb_bits;
|
|
carry += w * z;
|
|
pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
carry >>= limb_bits;
|
|
pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
carry = x * y + pr[1];
|
|
pr[1] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
carry >>= limb_bits;
|
|
carry += pr[2] + x * z;
|
|
pr[2] = static_cast<limb_type>(carry & ~static_cast<limb_type>(0));
|
|
pr[3] = static_cast<limb_type>(carry >> limb_bits);
|
|
#else
|
|
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);
|
|
#endif
|
|
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);
|
|
}
|
|
|
|
#ifdef _MSC_VER
|
|
#pragma warning(pop)
|
|
#endif
|
|
|
|
}}} // namespaces
|
|
|
|
#endif
|