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657 lines
29 KiB
C++
657 lines
29 KiB
C++
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///////////////////////////////////////////////////////////////
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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_MISC_HPP
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#define BOOST_MP_CPP_INT_MISC_HPP
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#include <boost/multiprecision/detail/bitscan.hpp> // lsb etc
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#include <boost/integer/common_factor_rt.hpp> // gcd/lcm
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#include <boost/functional/hash_fwd.hpp>
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4702)
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#pragma warning(disable:4127) // conditional expression is constant
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#pragma warning(disable:4146) // unary minus operator applied to unsigned type, result still unsigned
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#endif
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namespace boost{ namespace multiprecision{ namespace backends{
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template <class R, class CppInt>
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void check_in_range(const CppInt& val, const mpl::int_<checked>&)
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{
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typedef typename boost::multiprecision::detail::canonical<R, CppInt>::type cast_type;
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if(val.sign())
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{
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if(val.compare(static_cast<cast_type>((std::numeric_limits<R>::min)())) < 0)
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BOOST_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
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}
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else
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{
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if(val.compare(static_cast<cast_type>((std::numeric_limits<R>::max)())) > 0)
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BOOST_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
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}
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}
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template <class R, class CppInt>
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inline void check_in_range(const CppInt& /*val*/, const mpl::int_<unchecked>&) BOOST_NOEXCEPT {}
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inline void check_is_negative(const mpl::true_&) BOOST_NOEXCEPT {}
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inline void check_is_negative(const mpl::false_&)
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{
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BOOST_THROW_EXCEPTION(std::range_error("Attempt to assign a negative value to an unsigned type."));
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}
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template <class Integer>
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inline Integer negate_integer(Integer i, const mpl::true_&) BOOST_NOEXCEPT
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{
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return -i;
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}
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template <class Integer>
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inline Integer negate_integer(Integer i, const mpl::false_&) BOOST_NOEXCEPT
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{
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return ~(i-1);
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}
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template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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inline typename enable_if_c<is_integral<R>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, void>::type
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eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& backend) 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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typedef mpl::int_<Checked1> checked_type;
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check_in_range<R>(backend, checked_type());
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*result = static_cast<R>(backend.limbs()[0]);
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unsigned shift = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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for(unsigned i = 1; (i < backend.size()) && (shift < static_cast<unsigned>(std::numeric_limits<R>::digits)); ++i)
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{
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*result += static_cast<R>(backend.limbs()[i]) << shift;
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shift += cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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}
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if(backend.sign())
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{
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check_is_negative(boost::is_signed<R>());
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*result = negate_integer(*result, boost::is_signed<R>());
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}
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}
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template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
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inline typename enable_if_c<is_floating_point<R>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, void>::type
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eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& backend) BOOST_MP_NOEXCEPT_IF(is_arithmetic<R>::value)
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{
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typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::const_limb_pointer p = backend.limbs();
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unsigned shift = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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*result = static_cast<R>(*p);
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for(unsigned i = 1; i < backend.size(); ++i)
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{
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*result += static_cast<R>(std::ldexp(static_cast<long double>(p[i]), shift));
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shift += cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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}
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if(backend.sign())
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*result = -*result;
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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, bool>::type
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eval_is_zero(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) BOOST_NOEXCEPT
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{
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return (val.size() == 1) && (val.limbs()[0] == 0);
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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, int>::type
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eval_get_sign(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) BOOST_NOEXCEPT
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{
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return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1;
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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_abs(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& 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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result = val;
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result.sign(false);
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}
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//
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// Get the location of the least-significant-bit:
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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 typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
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eval_lsb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
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{
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using default_ops::eval_get_sign;
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if(eval_get_sign(a) == 0)
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{
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BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
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}
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if(a.sign())
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{
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BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
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}
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//
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// Find the index of the least significant limb that is non-zero:
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//
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unsigned index = 0;
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while(!a.limbs()[index] && (index < a.size()))
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++index;
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//
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// Find the index of the least significant bit within that limb:
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//
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unsigned result = boost::multiprecision::detail::find_lsb(a.limbs()[index]);
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return result + index * cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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}
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//
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// Get the location of the most-significant-bit:
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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 typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
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eval_msb_imp(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
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{
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//
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// Find the index of the most significant bit that is non-zero:
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//
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return (a.size() - 1) * cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits + boost::multiprecision::detail::find_msb(a.limbs()[a.size() - 1]);
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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 typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
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eval_msb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
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{
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using default_ops::eval_get_sign;
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if(eval_get_sign(a) == 0)
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{
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BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
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}
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if(a.sign())
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{
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BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
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}
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return eval_msb_imp(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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inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, bool>::type
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eval_bit_test(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index) BOOST_NOEXCEPT
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{
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unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
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if(offset >= val.size())
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return false;
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return val.limbs()[offset] & mask ? true : false;
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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 typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_bit_set(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index)
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{
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unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
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if(offset >= val.size())
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{
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unsigned os = val.size();
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val.resize(offset + 1, offset + 1);
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if(offset >= val.size())
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return; // fixed precision overflow
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for(unsigned i = os; i <= offset; ++i)
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val.limbs()[i] = 0;
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}
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val.limbs()[offset] |= mask;
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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 typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_bit_unset(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index) BOOST_NOEXCEPT
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{
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unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
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if(offset >= val.size())
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return;
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val.limbs()[offset] &= ~mask;
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val.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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inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_bit_flip(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, unsigned index)
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{
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unsigned offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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unsigned shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
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limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
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if(offset >= val.size())
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{
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unsigned os = val.size();
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val.resize(offset + 1, offset + 1);
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if(offset >= val.size())
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return; // fixed precision overflow
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for(unsigned i = os; i <= offset; ++i)
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val.limbs()[i] = 0;
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}
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val.limbs()[offset] ^= mask;
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val.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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inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_qr(
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const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
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const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& y,
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) 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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divide_unsigned_helper(&q, x, y, r);
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q.sign(x.sign() != y.sign());
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r.sign(x.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>
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inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
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eval_qr(
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const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
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limb_type y,
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
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cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) 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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divide_unsigned_helper(&q, x, y, r);
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q.sign(x.sign());
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r.sign(x.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, class U>
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|
inline typename enable_if_c<is_integral<U>::value>::type eval_qr(
|
||
|
|
const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
|
||
|
|
U y,
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) BOOST_MP_NOEXCEPT_IF((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
|
||
|
|
{
|
||
|
|
using default_ops::eval_qr;
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
|
||
|
|
t = y;
|
||
|
|
eval_qr(x, t, q, r);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
|
||
|
|
inline typename enable_if_c<is_unsigned<Integer>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, Integer>::type
|
||
|
|
eval_integer_modulus(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x, Integer val)
|
||
|
|
{
|
||
|
|
if((sizeof(Integer) <= sizeof(limb_type)) || (val <= (std::numeric_limits<limb_type>::max)()))
|
||
|
|
{
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> d;
|
||
|
|
divide_unsigned_helper(static_cast<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>*>(0), x, static_cast<limb_type>(val), d);
|
||
|
|
return d.limbs()[0];
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return default_ops::eval_integer_modulus(x, val);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
|
||
|
|
BOOST_MP_FORCEINLINE typename enable_if_c<is_signed<Integer>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, Integer>::type
|
||
|
|
eval_integer_modulus(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x, Integer val)
|
||
|
|
{
|
||
|
|
return eval_integer_modulus(x, boost::multiprecision::detail::unsigned_abs(val));
|
||
|
|
}
|
||
|
|
|
||
|
|
inline limb_type integer_gcd_reduce(limb_type u, limb_type v)
|
||
|
|
{
|
||
|
|
do
|
||
|
|
{
|
||
|
|
if(u > v)
|
||
|
|
std::swap(u, v);
|
||
|
|
if(u == v)
|
||
|
|
break;
|
||
|
|
v -= u;
|
||
|
|
v >>= boost::multiprecision::detail::find_lsb(v);
|
||
|
|
} while(true);
|
||
|
|
return u;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline double_limb_type integer_gcd_reduce(double_limb_type u, double_limb_type v)
|
||
|
|
{
|
||
|
|
do
|
||
|
|
{
|
||
|
|
if(u > v)
|
||
|
|
std::swap(u, v);
|
||
|
|
if(u == v)
|
||
|
|
break;
|
||
|
|
if(v <= ~static_cast<limb_type>(0))
|
||
|
|
{
|
||
|
|
u = integer_gcd_reduce(static_cast<limb_type>(v), static_cast<limb_type>(u));
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
v -= u;
|
||
|
|
#ifdef __MSVC_RUNTIME_CHECKS
|
||
|
|
while((v & 1u) == 0)
|
||
|
|
#else
|
||
|
|
while((static_cast<unsigned>(v) & 1u) == 0)
|
||
|
|
#endif
|
||
|
|
v >>= 1;
|
||
|
|
} while(true);
|
||
|
|
return u;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
|
||
|
|
eval_gcd(
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
|
||
|
|
const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
|
||
|
|
limb_type v)
|
||
|
|
{
|
||
|
|
using default_ops::eval_lsb;
|
||
|
|
using default_ops::eval_is_zero;
|
||
|
|
using default_ops::eval_get_sign;
|
||
|
|
|
||
|
|
int shift;
|
||
|
|
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> u(a);
|
||
|
|
|
||
|
|
int s = eval_get_sign(u);
|
||
|
|
|
||
|
|
/* GCD(0,x) := x */
|
||
|
|
if(s < 0)
|
||
|
|
{
|
||
|
|
u.negate();
|
||
|
|
}
|
||
|
|
else if(s == 0)
|
||
|
|
{
|
||
|
|
result = v;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if(v == 0)
|
||
|
|
{
|
||
|
|
result = u;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Let shift := lg K, where K is the greatest power of 2
|
||
|
|
dividing both u and v. */
|
||
|
|
|
||
|
|
unsigned us = eval_lsb(u);
|
||
|
|
unsigned vs = boost::multiprecision::detail::find_lsb(v);
|
||
|
|
shift = (std::min)(us, vs);
|
||
|
|
eval_right_shift(u, us);
|
||
|
|
if(vs)
|
||
|
|
v >>= vs;
|
||
|
|
|
||
|
|
do
|
||
|
|
{
|
||
|
|
/* Now u and v are both odd, so diff(u, v) is even.
|
||
|
|
Let u = min(u, v), v = diff(u, v)/2. */
|
||
|
|
if(u.size() <= 2)
|
||
|
|
{
|
||
|
|
if(u.size() == 1)
|
||
|
|
v = integer_gcd_reduce(*u.limbs(), v);
|
||
|
|
else
|
||
|
|
{
|
||
|
|
double_limb_type i;
|
||
|
|
i = u.limbs()[0] | (static_cast<double_limb_type>(u.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
|
||
|
|
v = static_cast<limb_type>(integer_gcd_reduce(i, static_cast<double_limb_type>(v)));
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
eval_subtract(u, v);
|
||
|
|
us = eval_lsb(u);
|
||
|
|
eval_right_shift(u, us);
|
||
|
|
}
|
||
|
|
while(true);
|
||
|
|
|
||
|
|
result = v;
|
||
|
|
eval_left_shift(result, shift);
|
||
|
|
}
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
|
||
|
|
inline typename enable_if_c<is_unsigned<Integer>::value && (sizeof(Integer) <= sizeof(limb_type)) && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
|
||
|
|
eval_gcd(
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
|
||
|
|
const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
|
||
|
|
const Integer& v)
|
||
|
|
{
|
||
|
|
eval_gcd(result, a, static_cast<limb_type>(v));
|
||
|
|
}
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
|
||
|
|
inline typename enable_if_c<is_signed<Integer>::value && (sizeof(Integer) <= sizeof(limb_type)) && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
|
||
|
|
eval_gcd(
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result,
|
||
|
|
const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a,
|
||
|
|
const Integer& v)
|
||
|
|
{
|
||
|
|
eval_gcd(result, a, static_cast<limb_type>(v < 0 ? -v : v));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline typename enable_if_c<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
|
||
|
|
eval_gcd(
|
||
|
|
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)
|
||
|
|
{
|
||
|
|
using default_ops::eval_lsb;
|
||
|
|
using default_ops::eval_is_zero;
|
||
|
|
using default_ops::eval_get_sign;
|
||
|
|
|
||
|
|
if(a.size() == 1)
|
||
|
|
{
|
||
|
|
eval_gcd(result, b, *a.limbs());
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if(b.size() == 1)
|
||
|
|
{
|
||
|
|
eval_gcd(result, a, *b.limbs());
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
int shift;
|
||
|
|
|
||
|
|
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> u(a), v(b);
|
||
|
|
|
||
|
|
int s = eval_get_sign(u);
|
||
|
|
|
||
|
|
/* GCD(0,x) := x */
|
||
|
|
if(s < 0)
|
||
|
|
{
|
||
|
|
u.negate();
|
||
|
|
}
|
||
|
|
else if(s == 0)
|
||
|
|
{
|
||
|
|
result = v;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
s = eval_get_sign(v);
|
||
|
|
if(s < 0)
|
||
|
|
{
|
||
|
|
v.negate();
|
||
|
|
}
|
||
|
|
else if(s == 0)
|
||
|
|
{
|
||
|
|
result = u;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Let shift := lg K, where K is the greatest power of 2
|
||
|
|
dividing both u and v. */
|
||
|
|
|
||
|
|
unsigned us = eval_lsb(u);
|
||
|
|
unsigned vs = eval_lsb(v);
|
||
|
|
shift = (std::min)(us, vs);
|
||
|
|
eval_right_shift(u, us);
|
||
|
|
eval_right_shift(v, vs);
|
||
|
|
|
||
|
|
do
|
||
|
|
{
|
||
|
|
/* Now u and v are both odd, so diff(u, v) is even.
|
||
|
|
Let u = min(u, v), v = diff(u, v)/2. */
|
||
|
|
s = u.compare(v);
|
||
|
|
if(s > 0)
|
||
|
|
u.swap(v);
|
||
|
|
if(s == 0)
|
||
|
|
break;
|
||
|
|
if(v.size() <= 2)
|
||
|
|
{
|
||
|
|
if(v.size() == 1)
|
||
|
|
u = integer_gcd_reduce(*v.limbs(), *u.limbs());
|
||
|
|
else
|
||
|
|
{
|
||
|
|
double_limb_type i, j;
|
||
|
|
i = v.limbs()[0] | (static_cast<double_limb_type>(v.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
|
||
|
|
j = (u.size() == 1) ? *u.limbs() : u.limbs()[0] | (static_cast<double_limb_type>(u.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
|
||
|
|
u = integer_gcd_reduce(i, j);
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
eval_subtract(v, u);
|
||
|
|
vs = eval_lsb(v);
|
||
|
|
eval_right_shift(v, vs);
|
||
|
|
}
|
||
|
|
while(true);
|
||
|
|
|
||
|
|
result = u;
|
||
|
|
eval_left_shift(result, shift);
|
||
|
|
}
|
||
|
|
//
|
||
|
|
// Now again for trivial backends:
|
||
|
|
//
|
||
|
|
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_gcd(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
|
||
|
|
{
|
||
|
|
*result.limbs() = boost::integer::gcd(*a.limbs(), *b.limbs());
|
||
|
|
}
|
||
|
|
// This one is only enabled for unchecked cpp_int's, for checked int's we need the checking in the default version:
|
||
|
|
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 && (Checked1 == unchecked)>::type
|
||
|
|
eval_lcm(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() = boost::integer::lcm(*a.limbs(), *b.limbs());
|
||
|
|
result.normalize(); // result may overflow the specified number of bits
|
||
|
|
}
|
||
|
|
|
||
|
|
inline void conversion_overflow(const mpl::int_<checked>&)
|
||
|
|
{
|
||
|
|
BOOST_THROW_EXCEPTION(std::overflow_error("Overflow in conversion to narrower type"));
|
||
|
|
}
|
||
|
|
inline void conversion_overflow(const mpl::int_<unchecked>&){}
|
||
|
|
|
||
|
|
template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline typename enable_if_c<
|
||
|
|
is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
|
||
|
|
&& is_signed_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
|
||
|
|
&& boost::is_convertible<typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type, R>::value
|
||
|
|
>::type
|
||
|
|
eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val)
|
||
|
|
{
|
||
|
|
typedef typename common_type<R, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type>::type common_type;
|
||
|
|
if(std::numeric_limits<R>::is_specialized && (static_cast<common_type>(*val.limbs()) > static_cast<common_type>((std::numeric_limits<R>::max)())))
|
||
|
|
{
|
||
|
|
if(val.isneg())
|
||
|
|
{
|
||
|
|
if(static_cast<common_type>(*val.limbs()) > -static_cast<common_type>((std::numeric_limits<R>::min)()))
|
||
|
|
conversion_overflow(typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
|
||
|
|
*result = (std::numeric_limits<R>::min)();
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
conversion_overflow(typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
|
||
|
|
*result = (std::numeric_limits<R>::max)();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
*result = static_cast<R>(*val.limbs());
|
||
|
|
if(val.isneg())
|
||
|
|
{
|
||
|
|
check_is_negative(mpl::bool_<is_signed_number<R>::value || (number_category<R>::value == number_kind_floating_point)>());
|
||
|
|
*result = negate_integer(*result, mpl::bool_<is_signed_number<R>::value || (number_category<R>::value == number_kind_floating_point)>());
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class R, unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline typename enable_if_c<
|
||
|
|
is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
|
||
|
|
&& is_unsigned_number<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value
|
||
|
|
&& boost::is_convertible<typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type, R>::value
|
||
|
|
>::type
|
||
|
|
eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val)
|
||
|
|
{
|
||
|
|
typedef typename common_type<R, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type>::type common_type;
|
||
|
|
if(std::numeric_limits<R>::is_specialized && (static_cast<common_type>(*val.limbs()) > static_cast<common_type>((std::numeric_limits<R>::max)())))
|
||
|
|
{
|
||
|
|
conversion_overflow(typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::checked_type());
|
||
|
|
*result = (std::numeric_limits<R>::max)();
|
||
|
|
}
|
||
|
|
else
|
||
|
|
*result = static_cast<R>(*val.limbs());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline typename enable_if_c<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
|
||
|
|
eval_lsb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
|
||
|
|
{
|
||
|
|
using default_ops::eval_get_sign;
|
||
|
|
if(eval_get_sign(a) == 0)
|
||
|
|
{
|
||
|
|
BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
|
||
|
|
}
|
||
|
|
if(a.sign())
|
||
|
|
{
|
||
|
|
BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
|
||
|
|
}
|
||
|
|
//
|
||
|
|
// Find the index of the least significant bit within that limb:
|
||
|
|
//
|
||
|
|
return boost::multiprecision::detail::find_lsb(*a.limbs());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline typename enable_if_c<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
|
||
|
|
eval_msb_imp(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
|
||
|
|
{
|
||
|
|
//
|
||
|
|
// Find the index of the least significant bit within that limb:
|
||
|
|
//
|
||
|
|
return boost::multiprecision::detail::find_msb(*a.limbs());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline typename enable_if_c<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, unsigned>::type
|
||
|
|
eval_msb(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
|
||
|
|
{
|
||
|
|
using default_ops::eval_get_sign;
|
||
|
|
if(eval_get_sign(a) == 0)
|
||
|
|
{
|
||
|
|
BOOST_THROW_EXCEPTION(std::range_error("No bits were set in the operand."));
|
||
|
|
}
|
||
|
|
if(a.sign())
|
||
|
|
{
|
||
|
|
BOOST_THROW_EXCEPTION(std::range_error("Testing individual bits in negative values is not supported - results are undefined."));
|
||
|
|
}
|
||
|
|
return eval_msb_imp(a);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <unsigned MinBits1, unsigned MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
|
||
|
|
inline std::size_t hash_value(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) BOOST_NOEXCEPT
|
||
|
|
{
|
||
|
|
std::size_t result = 0;
|
||
|
|
for(unsigned i = 0; i < val.size(); ++i)
|
||
|
|
{
|
||
|
|
boost::hash_combine(result, val.limbs()[i]);
|
||
|
|
}
|
||
|
|
boost::hash_combine(result, val.sign());
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifdef BOOST_MSVC
|
||
|
|
#pragma warning(pop)
|
||
|
|
#endif
|
||
|
|
|
||
|
|
}}} // namespaces
|
||
|
|
|
||
|
|
#endif
|