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libcarla/include/system/boost/multiprecision/cpp_int/misc.hpp

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2024-10-18 13:19:59 +08:00
///////////////////////////////////////////////////////////////
// Copyright 2012-2020 John Maddock.
// Copyright 2020 Madhur Chauhan.
// Copyright 2021 Matt Borland.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Comparison operators for cpp_int_backend:
//
#ifndef BOOST_MP_CPP_INT_MISC_HPP
#define BOOST_MP_CPP_INT_MISC_HPP
#include <boost/multiprecision/detail/standalone_config.hpp>
#include <boost/multiprecision/detail/number_base.hpp>
#include <boost/multiprecision/cpp_int/cpp_int_config.hpp>
#include <boost/multiprecision/detail/float128_functions.hpp>
#include <boost/multiprecision/detail/assert.hpp>
#include <boost/multiprecision/detail/constexpr.hpp>
#include <boost/multiprecision/detail/bitscan.hpp> // lsb etc
#include <boost/multiprecision/detail/hash.hpp>
#include <boost/multiprecision/detail/no_exceptions_support.hpp>
#include <numeric> // std::gcd
#include <type_traits>
#include <stdexcept>
#include <cmath>
#ifndef BOOST_MP_STANDALONE
#include <boost/integer/common_factor_rt.hpp>
#endif
#ifdef BOOST_MP_MATH_AVAILABLE
#include <boost/math/special_functions/next.hpp>
#endif
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 4702)
#pragma warning(disable : 4127) // conditional expression is constant
#pragma warning(disable : 4146) // unary minus operator applied to unsigned type, result still unsigned
#endif
// Forward decleration of gcd and lcm functions
namespace boost { namespace multiprecision { namespace detail {
template <typename T>
inline BOOST_CXX14_CONSTEXPR T constexpr_gcd(T a, T b) noexcept;
template <typename T>
inline BOOST_CXX14_CONSTEXPR T constexpr_lcm(T a, T b) noexcept;
}}} // namespace boost::multiprecision::detail
namespace boost { namespace multiprecision { namespace backends {
template <class T, bool has_limits = std::numeric_limits<T>::is_specialized>
struct numeric_limits_workaround : public std::numeric_limits<T>
{
};
template <class R>
struct numeric_limits_workaround<R, false>
{
static constexpr unsigned digits = ~static_cast<R>(0) < 0 ? sizeof(R) * CHAR_BIT - 1 : sizeof(R) * CHAR_BIT;
static constexpr R (min)(){ return (static_cast<R>(-1) < 0) ? static_cast<R>(1) << digits : 0; }
static constexpr R (max)() { return (static_cast<R>(-1) < 0) ? ~(static_cast<R>(1) << digits) : ~static_cast<R>(0); }
};
template <class R, class CppInt>
BOOST_MP_CXX14_CONSTEXPR void check_in_range(const CppInt& val, const std::integral_constant<int, checked>&)
{
using cast_type = typename boost::multiprecision::detail::canonical<R, CppInt>::type;
if (val.sign())
{
BOOST_IF_CONSTEXPR (boost::multiprecision::detail::is_signed<R>::value == false)
BOOST_MP_THROW_EXCEPTION(std::range_error("Attempt to assign a negative value to an unsigned type."));
if (val.compare(static_cast<cast_type>((numeric_limits_workaround<R>::min)())) < 0)
BOOST_MP_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
}
else
{
if (val.compare(static_cast<cast_type>((numeric_limits_workaround<R>::max)())) > 0)
BOOST_MP_THROW_EXCEPTION(std::overflow_error("Could not convert to the target type - -value is out of range."));
}
}
template <class R, class CppInt>
inline BOOST_MP_CXX14_CONSTEXPR void check_in_range(const CppInt& /*val*/, const std::integral_constant<int, unchecked>&) noexcept {}
inline BOOST_MP_CXX14_CONSTEXPR void check_is_negative(const std::integral_constant<bool, true>&) noexcept {}
inline void check_is_negative(const std::integral_constant<bool, false>&)
{
BOOST_MP_THROW_EXCEPTION(std::range_error("Attempt to assign a negative value to an unsigned type."));
}
template <class Integer>
inline BOOST_MP_CXX14_CONSTEXPR Integer negate_integer(Integer i, const std::integral_constant<bool, true>&) noexcept
{
return -i;
}
template <class Integer>
inline BOOST_MP_CXX14_CONSTEXPR Integer negate_integer(Integer i, const std::integral_constant<bool, false>&) noexcept
{
return ~(i - 1);
}
template <class R, std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<R>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, void>::type
eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& backend)
{
using checked_type = std::integral_constant<int, Checked1>;
check_in_range<R>(backend, checked_type());
BOOST_IF_CONSTEXPR(numeric_limits_workaround<R>::digits < cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits)
{
if ((backend.sign() && boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value) && (1 + static_cast<boost::multiprecision::limb_type>((std::numeric_limits<R>::max)()) <= backend.limbs()[0]))
{
*result = (numeric_limits_workaround<R>::min)();
return;
}
else if (boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value && !backend.sign() && static_cast<boost::multiprecision::limb_type>((std::numeric_limits<R>::max)()) <= backend.limbs()[0])
{
*result = (numeric_limits_workaround<R>::max)();
return;
}
else
*result = static_cast<R>(backend.limbs()[0]);
}
else
*result = static_cast<R>(backend.limbs()[0]);
BOOST_IF_CONSTEXPR(numeric_limits_workaround<R>::digits > cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits)
{
std::size_t shift = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
std::size_t i = 1u;
while ((i < backend.size()) && (shift < static_cast<unsigned>(numeric_limits_workaround<R>::digits - cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits)))
{
*result += static_cast<R>(backend.limbs()[i]) << shift;
shift += cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
++i;
}
//
// We have one more limb to extract, but may not need all the bits, so treat this as a special case:
//
if (i < backend.size())
{
const limb_type mask = ((numeric_limits_workaround<R>::digits - shift) == cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits) ? ~static_cast<limb_type>(0) : static_cast<limb_type>(static_cast<limb_type>(1u) << (numeric_limits_workaround<R>::digits - shift)) - 1u;
const limb_type limb_at_index_masked = static_cast<limb_type>(backend.limbs()[i] & mask);
*result = static_cast<R>(*result + static_cast<R>(static_cast<R>(limb_at_index_masked) << shift));
if ((backend.limbs()[i] & static_cast<limb_type>(~mask)) || (i + 1 < backend.size()))
{
// Overflow:
if (backend.sign())
{
check_is_negative(boost::multiprecision::detail::is_signed<R>());
*result = (numeric_limits_workaround<R>::min)();
}
else if (boost::multiprecision::detail::is_signed<R>::value)
*result = (numeric_limits_workaround<R>::max)();
return;
}
}
}
else if (backend.size() > 1)
{
// Overflow:
if (backend.sign())
{
check_is_negative(boost::multiprecision::detail::is_signed<R>());
*result = (numeric_limits_workaround<R>::min)();
}
else if (boost::multiprecision::detail::is_signed<R>::value)
*result = (numeric_limits_workaround<R>::max)();
return;
}
if (backend.sign())
{
check_is_negative(std::integral_constant<bool, boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value>());
*result = negate_integer(*result, std::integral_constant<bool, boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value>());
}
}
template <class R, std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_floating_point<R>::value && !is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, void>::type
eval_convert_to(R* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& backend) noexcept(boost::multiprecision::detail::is_arithmetic<R>::value)
{
BOOST_MP_FLOAT128_USING using std::ldexp;
if (eval_is_zero(backend))
{
*result = 0.0f;
return;
}
#ifdef BOOST_HAS_FLOAT128
std::ptrdiff_t bits_to_keep = static_cast<std::ptrdiff_t>(std::is_same<R, float128_type>::value ? 113 : std::numeric_limits<R>::digits);
#else
std::ptrdiff_t bits_to_keep = static_cast<std::ptrdiff_t>(std::numeric_limits<R>::digits);
#endif
std::ptrdiff_t bits = static_cast<std::ptrdiff_t>(eval_msb_imp(backend) + 1);
if (bits > bits_to_keep)
{
// Extract the bits we need, and then manually round the result:
*result = 0.0f;
typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::const_limb_pointer p = backend.limbs();
limb_type mask = ~static_cast<limb_type>(0u);
std::size_t index = backend.size() - 1;
std::size_t shift = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits * index;
while (bits_to_keep > 0)
{
if (bits_to_keep < (std::ptrdiff_t)cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits)
{
if(index != backend.size() - 1)
{
const std::ptrdiff_t left_shift_amount = static_cast<std::ptrdiff_t>(static_cast<std::ptrdiff_t>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits) - bits_to_keep);
mask <<= left_shift_amount;
}
else
{
std::ptrdiff_t bits_in_first_limb = static_cast<std::ptrdiff_t>(bits % static_cast<std::ptrdiff_t>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits));
if (bits_in_first_limb == 0)
bits_in_first_limb = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
if (bits_in_first_limb > bits_to_keep)
mask <<= bits_in_first_limb - bits_to_keep;
}
}
*result += ldexp(static_cast<R>(p[index] & mask), static_cast<int>(shift));
shift -= cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
const bool bits_has_non_zero_remainder = (bits % static_cast<std::ptrdiff_t>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits) != 0);
bits_to_keep -= ((index == backend.size() - 1) && bits_has_non_zero_remainder)
? bits % static_cast<std::ptrdiff_t>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits)
: static_cast<std::ptrdiff_t>(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits);
--index;
}
// Perform rounding:
bits -= 1 + std::numeric_limits<R>::digits;
if (eval_bit_test(backend, static_cast<unsigned>(bits)))
{
if ((eval_lsb_imp(backend) < static_cast<std::size_t>(bits)) || eval_bit_test(backend, static_cast<std::size_t>(bits + 1)))
{
#ifdef BOOST_MP_MATH_AVAILABLE
*result = boost::math::float_next(*result);
#else
*result = std::nextafter(*result, *result * 2);
#endif
}
}
}
else
{
typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::const_limb_pointer p = backend.limbs();
std::size_t shift = cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
*result = static_cast<R>(*p);
for (std::size_t i = 1; i < backend.size(); ++i)
{
*result += static_cast<R>(ldexp(static_cast<long double>(p[i]), static_cast<int>(shift)));
shift += cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
}
}
if (backend.sign())
*result = -*result;
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, bool>::type
eval_is_zero(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) noexcept
{
return (val.size() == 1) && (val.limbs()[0] == 0);
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, int>::type
eval_get_sign(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) noexcept
{
return eval_is_zero(val) ? 0 : val.sign() ? -1 : 1;
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
eval_abs(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
{
result = val;
result.sign(false);
}
//
// Get the location of the least-significant-bit:
//
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, std::size_t>::type
eval_lsb_imp(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
{
//
// Find the index of the least significant limb that is non-zero:
//
std::size_t index = 0;
while (!a.limbs()[index] && (index < a.size()))
++index;
//
// Find the index of the least significant bit within that limb:
//
std::size_t result = boost::multiprecision::detail::find_lsb(a.limbs()[index]);
return result + index * cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, std::size_t>::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_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
if (a.sign())
{
BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
}
return eval_lsb_imp(a);
}
//
// Get the location of the most-significant-bit:
//
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, std::size_t>::type
eval_msb_imp(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& a)
{
//
// Find the index of the most significant bit that is non-zero:
//
return (a.size() - 1) * cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits + boost::multiprecision::detail::find_msb(a.limbs()[a.size() - 1]);
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, std::size_t>::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_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
if (a.sign())
{
BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
}
return eval_msb_imp(a);
}
#ifdef BOOST_GCC
//
// We really shouldn't need to be disabling this warning, but it really does appear to be
// spurious. The warning appears only when in release mode, and asserts are on.
//
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Warray-bounds"
#endif
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, bool>::type
eval_bit_test(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, std::size_t index) noexcept
{
std::size_t offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
std::size_t shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
if (offset >= val.size())
return false;
return val.limbs()[offset] & mask ? true : false;
}
#ifdef BOOST_GCC
#pragma GCC diagnostic pop
#endif
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
eval_bit_set(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, std::size_t index)
{
std::size_t offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
std::size_t shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
if (offset >= val.size())
{
std::size_t os = val.size();
val.resize(offset + 1, offset + 1);
if (offset >= val.size())
return; // fixed precision overflow
for (std::size_t i = os; i <= offset; ++i)
val.limbs()[i] = 0;
}
val.limbs()[offset] |= mask;
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
eval_bit_unset(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, std::size_t index) noexcept
{
std::size_t offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
std::size_t shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
if (offset >= val.size())
return;
val.limbs()[offset] &= ~mask;
val.normalize();
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
eval_bit_flip(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val, std::size_t index)
{
std::size_t offset = index / cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
std::size_t shift = index % cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::limb_bits;
limb_type mask = shift ? limb_type(1u) << shift : limb_type(1u);
if (offset >= val.size())
{
std::size_t os = val.size();
val.resize(offset + 1, offset + 1);
if (offset >= val.size())
return; // fixed precision overflow
for (std::size_t i = os; i <= offset; ++i)
val.limbs()[i] = 0;
}
val.limbs()[offset] ^= mask;
val.normalize();
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
eval_qr(
const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& y,
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
{
divide_unsigned_helper(&q, x, y, r);
q.sign(x.sign() != y.sign());
r.sign(x.sign());
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value>::type
eval_qr(
const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& x,
limb_type y,
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& q,
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& r) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
{
divide_unsigned_helper(&q, x, y, r);
q.sign(x.sign());
r.sign(x.sign());
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::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) noexcept((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 <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::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>& a, Integer mod)
{
BOOST_IF_CONSTEXPR (sizeof(Integer) <= sizeof(limb_type))
{
if (mod <= (std::numeric_limits<limb_type>::max)())
{
const std::ptrdiff_t n = a.size();
const double_limb_type two_n_mod = static_cast<limb_type>(1u) + (~static_cast<limb_type>(0u) - mod) % mod;
limb_type res = a.limbs()[n - 1] % mod;
for (std::ptrdiff_t i = n - 2; i >= 0; --i)
res = static_cast<limb_type>((res * two_n_mod + a.limbs()[i]) % mod);
return res;
}
else
return default_ops::eval_integer_modulus(a, mod);
}
else
{
return default_ops::eval_integer_modulus(a, mod);
}
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_signed<Integer>::value && boost::multiprecision::detail::is_integral<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));
}
BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR limb_type eval_gcd(limb_type u, limb_type v)
{
// boundary cases
if (!u || !v)
return u | v;
#if (defined(__cpp_lib_gcd_lcm) && (__cpp_lib_gcd_lcm >= 201606L))
return std::gcd(u, v);
#else
std::size_t shift = boost::multiprecision::detail::find_lsb(u | v);
u >>= boost::multiprecision::detail::find_lsb(u);
do
{
v >>= boost::multiprecision::detail::find_lsb(v);
if (u > v)
std_constexpr::swap(u, v);
v -= u;
} while (v);
return u << shift;
#endif
}
inline BOOST_MP_CXX14_CONSTEXPR double_limb_type eval_gcd(double_limb_type u, double_limb_type v)
{
#if (defined(__cpp_lib_gcd_lcm) && (__cpp_lib_gcd_lcm >= 201606L)) && (!defined(BOOST_HAS_INT128) || !defined(__STRICT_ANSI__))
return std::gcd(u, v);
#else
if (u == 0)
return v;
std::size_t shift = boost::multiprecision::detail::find_lsb(u | v);
u >>= boost::multiprecision::detail::find_lsb(u);
do
{
v >>= boost::multiprecision::detail::find_lsb(v);
if (u > v)
std_constexpr::swap(u, v);
v -= u;
} while (v);
return u << shift;
#endif
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!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 b)
{
int s = eval_get_sign(a);
if (!b || !s)
{
result = a;
*result.limbs() |= b;
}
else
{
eval_modulus(result, a, b);
limb_type& res = *result.limbs();
res = eval_gcd(res, b);
}
result.sign(false);
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!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,
double_limb_type b)
{
int s = eval_get_sign(a);
if (!b || !s)
{
if (!s)
result = b;
else
result = a;
return;
}
double_limb_type res = 0;
if(a.sign() == 0)
res = eval_integer_modulus(a, b);
else
{
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(a);
t.negate();
res = eval_integer_modulus(t, b);
}
res = eval_gcd(res, b);
result = res;
result.sign(false);
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!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,
signed_double_limb_type v)
{
eval_gcd(result, a, static_cast<double_limb_type>(v < 0 ? -v : v));
}
//
// These 2 overloads take care of gcd against an (unsigned) short etc:
//
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::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 <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Integer>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_signed<Integer>::value && boost::multiprecision::detail::is_integral<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));
}
//
// What follows is Lehmer's GCD algorithm:
// Essentially this uses the leading digit(s) of U and V
// only to run a "simulated" Euclid algorithm. It stops
// when the calculated quotient differs from what would have been
// the true quotient. At that point the cosequences are used to
// calculate the new U and V. A nice lucid description appears
// in "An Analysis of Lehmer's Euclidean GCD Algorithm",
// by Jonathan Sorenson. https://www.researchgate.net/publication/2424634_An_Analysis_of_Lehmer%27s_Euclidean_GCD_Algorithm
// DOI: 10.1145/220346.220378.
//
// There are two versions of this algorithm here, and both are "double digit"
// variations: which is to say if there are k bits per limb, then they extract
// 2k bits into a double_limb_type and then run the algorithm on that. The first
// version is a straightforward version of the algorithm, and is designed for
// situations where double_limb_type is a native integer (for example where
// limb_type is a 32-bit integer on a 64-bit machine). For 32-bit limbs it
// reduces the size of U by about 30 bits per call. The second is a more complex
// version for situations where double_limb_type is a synthetic type: for example
// __int128. For 64 bit limbs it reduces the size of U by about 62 bits per call.
//
// The complexity of the algorithm given by Sorenson is roughly O(ln^2(N)) for
// two N bit numbers.
//
// The original double-digit version of the algorithm is described in:
//
// "A Double Digit Lehmer-Euclid Algorithm for Finding the GCD of Long Integers",
// Tudor Jebelean, J Symbolic Computation, 1995 (19), 145.
//
#ifndef BOOST_HAS_INT128
//
// When double_limb_type is a native integer type then we should just use it and not worry about the consequences.
// This can eliminate approximately a full limb with each call.
//
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Storage>
void eval_gcd_lehmer(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& U, cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& V, std::size_t lu, Storage& storage)
{
//
// Extract the leading 2 * bits_per_limb bits from U and V:
//
std::size_t h = lu % bits_per_limb;
double_limb_type u = (static_cast<double_limb_type>((U.limbs()[U.size() - 1])) << bits_per_limb) | U.limbs()[U.size() - 2];
double_limb_type v = (static_cast<double_limb_type>((V.size() < U.size() ? 0 : V.limbs()[V.size() - 1])) << bits_per_limb) | V.limbs()[U.size() - 2];
if (h)
{
u <<= bits_per_limb - h;
u |= U.limbs()[U.size() - 3] >> h;
v <<= bits_per_limb - h;
v |= V.limbs()[U.size() - 3] >> h;
}
//
// Co-sequences x an y: we need only the last 3 values of these,
// the first 2 values are known correct, the third gets checked
// in each loop operation, and we terminate when they go wrong.
//
// x[i+0] is positive for even i.
// y[i+0] is positive for odd i.
//
// However we track only absolute values here:
//
double_limb_type x[3] = {1, 0};
double_limb_type y[3] = {0, 1};
std::size_t i = 0;
#ifdef BOOST_MP_GCD_DEBUG
cpp_int UU, VV;
UU = U;
VV = V;
#endif
while (true)
{
double_limb_type q = u / v;
x[2] = x[0] + q * x[1];
y[2] = y[0] + q * y[1];
double_limb_type tu = u;
u = v;
v = tu - q * v;
++i;
//
// We must make sure that y[2] occupies a single limb otherwise
// the multiprecision multiplications below would be much more expensive.
// This can sometimes lose us one iteration, but is worth it for improved
// calculation efficiency.
//
if (y[2] >> bits_per_limb)
break;
//
// These are Jebelean's exact termination conditions:
//
if ((i & 1u) == 0)
{
BOOST_MP_ASSERT(u > v);
if ((v < x[2]) || ((u - v) < (y[2] + y[1])))
break;
}
else
{
BOOST_MP_ASSERT(u > v);
if ((v < y[2]) || ((u - v) < (x[2] + x[1])))
break;
}
#ifdef BOOST_MP_GCD_DEBUG
BOOST_MP_ASSERT(q == UU / VV);
UU %= VV;
UU.swap(VV);
#endif
x[0] = x[1];
x[1] = x[2];
y[0] = y[1];
y[1] = y[2];
}
if (i == 1)
{
// No change to U and V we've stalled!
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
eval_modulus(t, U, V);
U.swap(V);
V.swap(t);
return;
}
//
// Update U and V.
// We have:
//
// U = x[0]U + y[0]V and
// V = x[1]U + y[1]V.
//
// But since we track only absolute values of x and y
// we have to take account of the implied signs and perform
// the appropriate subtraction depending on the whether i is
// even or odd:
//
std::size_t ts = U.size() + 1;
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t1(storage, ts), t2(storage, ts), t3(storage, ts);
eval_multiply(t1, U, static_cast<limb_type>(x[0]));
eval_multiply(t2, V, static_cast<limb_type>(y[0]));
eval_multiply(t3, U, static_cast<limb_type>(x[1]));
if ((i & 1u) == 0)
{
if (x[0] == 0)
U = t2;
else
{
BOOST_MP_ASSERT(t2.compare(t1) >= 0);
eval_subtract(U, t2, t1);
BOOST_MP_ASSERT(U.sign() == false);
}
}
else
{
BOOST_MP_ASSERT(t1.compare(t2) >= 0);
eval_subtract(U, t1, t2);
BOOST_MP_ASSERT(U.sign() == false);
}
eval_multiply(t2, V, static_cast<limb_type>(y[1]));
if (i & 1u)
{
if (x[1] == 0)
V = t2;
else
{
BOOST_MP_ASSERT(t2.compare(t3) >= 0);
eval_subtract(V, t2, t3);
BOOST_MP_ASSERT(V.sign() == false);
}
}
else
{
BOOST_MP_ASSERT(t3.compare(t2) >= 0);
eval_subtract(V, t3, t2);
BOOST_MP_ASSERT(V.sign() == false);
}
BOOST_MP_ASSERT(U.compare(V) >= 0);
BOOST_MP_ASSERT(lu > eval_msb(U));
#ifdef BOOST_MP_GCD_DEBUG
BOOST_MP_ASSERT(UU == U);
BOOST_MP_ASSERT(VV == V);
extern std::size_t total_lehmer_gcd_calls;
extern std::size_t total_lehmer_gcd_bits_saved;
extern std::size_t total_lehmer_gcd_cycles;
++total_lehmer_gcd_calls;
total_lehmer_gcd_bits_saved += lu - eval_msb(U);
total_lehmer_gcd_cycles += i;
#endif
if (lu < 2048)
{
//
// Since we have stripped all common powers of 2 from U and V at the start
// if either are even at this point, we can remove stray powers of 2 now.
// Note that it is not possible for *both* U and V to be even at this point.
//
// This has an adverse effect on performance for high bit counts, but has
// a significant positive effect for smaller counts.
//
if ((U.limbs()[0] & 1u) == 0)
{
eval_right_shift(U, eval_lsb(U));
if (U.compare(V) < 0)
U.swap(V);
}
else if ((V.limbs()[0] & 1u) == 0)
{
eval_right_shift(V, eval_lsb(V));
}
}
storage.deallocate(ts * 3);
}
#else
//
// This branch is taken when double_limb_type is a synthetic type with no native hardware support.
// For example __int128. The assumption is that add/subtract/multiply of double_limb_type are efficient,
// but that division is very slow.
//
// We begin with a specialized routine for division.
// We know that most of the time this is called the result will be 1.
// For small limb counts, this almost doubles the performance of Lehmer's routine!
//
BOOST_FORCEINLINE void divide_subtract(double_limb_type& q, double_limb_type& u, const double_limb_type& v)
{
BOOST_MP_ASSERT(q == 1); // precondition on entry.
u -= v;
while (u >= v)
{
u -= v;
if (++q > 30)
{
double_limb_type t = u / v;
u -= t * v;
q += t;
}
}
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1, class Storage>
void eval_gcd_lehmer(cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& U, cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& V, std::size_t lu, Storage& storage)
{
//
// Extract the leading 2*bits_per_limb bits from U and V:
//
std::size_t h = lu % bits_per_limb;
double_limb_type u, v;
if (h)
{
u = (static_cast<double_limb_type>((U.limbs()[U.size() - 1])) << bits_per_limb) | U.limbs()[U.size() - 2];
v = (static_cast<double_limb_type>((V.size() < U.size() ? 0 : V.limbs()[V.size() - 1])) << bits_per_limb) | V.limbs()[U.size() - 2];
u <<= bits_per_limb - h;
u |= U.limbs()[U.size() - 3] >> h;
v <<= bits_per_limb - h;
v |= V.limbs()[U.size() - 3] >> h;
}
else
{
u = (static_cast<double_limb_type>(U.limbs()[U.size() - 1]) << bits_per_limb) | U.limbs()[U.size() - 2];
v = (static_cast<double_limb_type>(V.limbs()[U.size() - 1]) << bits_per_limb) | V.limbs()[U.size() - 2];
}
//
// Cosequences are stored as limb_types, we take care not to overflow these:
//
// x[i+0] is positive for even i.
// y[i+0] is positive for odd i.
//
// However we track only absolute values here:
//
limb_type x[3] = { 1, 0 };
limb_type y[3] = { 0, 1 };
std::size_t i = 0;
#ifdef BOOST_MP_GCD_DEBUG
cpp_int UU, VV;
UU = U;
VV = V;
#endif
//
// We begine by running a single digit version of Lehmer's algorithm, we still have
// to track u and v at double precision, but this adds only a tiny performance penalty.
// What we gain is fast division, and fast termination testing.
// When you see static_cast<limb_type>(u >> bits_per_limb) here, this is really just
// a direct access to the upper bits_per_limb of the double limb type. For __int128
// this is simple a load of the upper 64 bits and the "shift" is optimised away.
//
double_limb_type old_u, old_v;
while (true)
{
limb_type q = static_cast<limb_type>(u >> bits_per_limb) / static_cast<limb_type>(v >> bits_per_limb);
x[2] = x[0] + q * x[1];
y[2] = y[0] + q * y[1];
double_limb_type tu = u;
old_u = u;
old_v = v;
u = v;
double_limb_type t = q * v;
if (tu < t)
{
++i;
break;
}
v = tu - t;
++i;
BOOST_MP_ASSERT((u <= v) || (t / q == old_v));
if (u <= v)
{
// We've gone terribly wrong, probably numeric overflow:
break;
}
if ((i & 1u) == 0)
{
if ((static_cast<limb_type>(v >> bits_per_limb) < x[2]) || ((static_cast<limb_type>(u >> bits_per_limb) - static_cast<limb_type>(v >> bits_per_limb)) < (y[2] + y[1])))
break;
}
else
{
if ((static_cast<limb_type>(v >> bits_per_limb) < y[2]) || ((static_cast<limb_type>(u >> bits_per_limb) - static_cast<limb_type>(v >> bits_per_limb)) < (x[2] + x[1])))
break;
}
#ifdef BOOST_MP_GCD_DEBUG
BOOST_MP_ASSERT(q == UU / VV);
UU %= VV;
UU.swap(VV);
#endif
x[0] = x[1];
x[1] = x[2];
y[0] = y[1];
y[1] = y[2];
}
//
// We get here when the single digit algorithm has gone wrong, back up i, u and v:
//
--i;
u = old_u;
v = old_v;
//
// Now run the full double-digit algorithm:
//
while (true)
{
double_limb_type q = 1u;
double_limb_type tt = u;
divide_subtract(q, u, v);
std::swap(u, v);
tt = y[0] + q * static_cast<double_limb_type>(y[1]);
//
// If calculation of y[2] would overflow a single limb, then we *must* terminate.
// Note that x[2] < y[2] so there is no need to check that as well:
//
if (tt >> bits_per_limb)
{
++i;
break;
}
x[2] = static_cast<limb_type>(x[0] + static_cast<double_limb_type>(q * x[1]));
y[2] = static_cast<limb_type>(tt);
++i;
if ((i & 1u) == 0)
{
BOOST_MP_ASSERT(u > v);
if ((v < x[2]) || ((u - v) < (static_cast<double_limb_type>(y[2]) + y[1])))
break;
}
else
{
BOOST_MP_ASSERT(u > v);
if ((v < y[2]) || ((u - v) < (static_cast<double_limb_type>(x[2]) + x[1])))
break;
}
#ifdef BOOST_MP_GCD_DEBUG
BOOST_MP_ASSERT(q == UU / VV);
UU %= VV;
UU.swap(VV);
#endif
x[0] = x[1];
x[1] = x[2];
y[0] = y[1];
y[1] = y[2];
}
if (i == 1)
{
// No change to U and V we've stalled!
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t;
eval_modulus(t, U, V);
U.swap(V);
V.swap(t);
return;
}
//
// Update U and V.
// We have:
//
// U = x[0]U + y[0]V and
// V = x[1]U + y[1]V.
//
// But since we track only absolute values of x and y
// we have to take account of the implied signs and perform
// the appropriate subtraction depending on the whether i is
// even or odd:
//
std::size_t ts = U.size() + 1;
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t1(storage, ts), t2(storage, ts), t3(storage, ts);
eval_multiply(t1, U, x[0]);
eval_multiply(t2, V, y[0]);
eval_multiply(t3, U, x[1]);
if ((i & 1u) == 0)
{
if (x[0] == 0)
U = t2;
else
{
BOOST_MP_ASSERT(t2.compare(t1) >= 0);
eval_subtract(U, t2, t1);
BOOST_MP_ASSERT(U.sign() == false);
}
}
else
{
BOOST_MP_ASSERT(t1.compare(t2) >= 0);
eval_subtract(U, t1, t2);
BOOST_MP_ASSERT(U.sign() == false);
}
eval_multiply(t2, V, y[1]);
if (i & 1u)
{
if (x[1] == 0)
V = t2;
else
{
BOOST_MP_ASSERT(t2.compare(t3) >= 0);
eval_subtract(V, t2, t3);
BOOST_MP_ASSERT(V.sign() == false);
}
}
else
{
BOOST_MP_ASSERT(t3.compare(t2) >= 0);
eval_subtract(V, t3, t2);
BOOST_MP_ASSERT(V.sign() == false);
}
BOOST_MP_ASSERT(U.compare(V) >= 0);
BOOST_MP_ASSERT(lu > eval_msb(U));
#ifdef BOOST_MP_GCD_DEBUG
BOOST_MP_ASSERT(UU == U);
BOOST_MP_ASSERT(VV == V);
extern std::size_t total_lehmer_gcd_calls;
extern std::size_t total_lehmer_gcd_bits_saved;
extern std::size_t total_lehmer_gcd_cycles;
++total_lehmer_gcd_calls;
total_lehmer_gcd_bits_saved += lu - eval_msb(U);
total_lehmer_gcd_cycles += i;
#endif
if (lu < 2048)
{
//
// Since we have stripped all common powers of 2 from U and V at the start
// if either are even at this point, we can remove stray powers of 2 now.
// Note that it is not possible for *both* U and V to be even at this point.
//
// This has an adverse effect on performance for high bit counts, but has
// a significant positive effect for smaller counts.
//
if ((U.limbs()[0] & 1u) == 0)
{
eval_right_shift(U, eval_lsb(U));
if (U.compare(V) < 0)
U.swap(V);
}
else if ((V.limbs()[0] & 1u) == 0)
{
eval_right_shift(V, eval_lsb(V));
}
}
storage.deallocate(ts * 3);
}
#endif
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!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_get_sign;
using default_ops::eval_is_zero;
using default_ops::eval_lsb;
if (a.size() == 1)
{
eval_gcd(result, b, *a.limbs());
return;
}
if (b.size() == 1)
{
eval_gcd(result, a, *b.limbs());
return;
}
std::size_t temp_size = (std::max)(a.size(), b.size()) + 1;
typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::scoped_shared_storage storage(a, temp_size * 6);
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> U(storage, temp_size);
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> V(storage, temp_size);
cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> t(storage, temp_size);
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;
}
//
// Remove common factors of 2:
//
std::size_t us = eval_lsb(U);
std::size_t vs = eval_lsb(V);
std::size_t shift = (std::min)(us, vs);
if (us)
eval_right_shift(U, us);
if (vs)
eval_right_shift(V, vs);
if (U.compare(V) < 0)
U.swap(V);
while (!eval_is_zero(V))
{
if (U.size() <= 2)
{
//
// Special case: if V has no more than 2 limbs
// then we can reduce U and V to a pair of integers and perform
// direct integer gcd:
//
if (U.size() == 1)
U = eval_gcd(*V.limbs(), *U.limbs());
else
{
double_limb_type i = U.limbs()[0] | (static_cast<double_limb_type>(U.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
double_limb_type j = (V.size() == 1) ? *V.limbs() : V.limbs()[0] | (static_cast<double_limb_type>(V.limbs()[1]) << sizeof(limb_type) * CHAR_BIT);
U = eval_gcd(i, j);
}
break;
}
std::size_t lu = eval_msb(U) + 1;
std::size_t lv = eval_msb(V) + 1;
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
if (!BOOST_MP_IS_CONST_EVALUATED(lu) && (lu - lv <= bits_per_limb / 2))
#else
if (lu - lv <= bits_per_limb / 2)
#endif
{
eval_gcd_lehmer(U, V, lu, storage);
}
else
{
eval_modulus(t, U, V);
U.swap(V);
V.swap(t);
}
}
result = U;
if (shift)
eval_left_shift(result, shift);
}
//
// Now again for trivial backends:
//
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<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) noexcept
{
*result.limbs() = boost::multiprecision::detail::constexpr_gcd(*a.limbs(), *b.limbs());
result.sign(false);
}
// This one is only enabled for unchecked cpp_int's, for checked int's we need the checking in the default version:
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
BOOST_MP_FORCEINLINE BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<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) noexcept((is_non_throwing_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value))
{
*result.limbs() = boost::multiprecision::detail::constexpr_lcm(*a.limbs(), *b.limbs());
result.normalize(); // result may overflow the specified number of bits
result.sign(false);
}
inline void conversion_overflow(const std::integral_constant<int, checked>&)
{
BOOST_MP_THROW_EXCEPTION(std::overflow_error("Overflow in conversion to narrower type"));
}
inline BOOST_MP_CXX14_CONSTEXPR void conversion_overflow(const std::integral_constant<int, unchecked>&) {}
#if defined(__clang__) && defined(__MINGW32__)
//
// clang-11 on Mingw segfaults on conversion of __int128 -> float.
// See: https://bugs.llvm.org/show_bug.cgi?id=48941
// These workarounds pass everything through an intermediate uint64_t.
//
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
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 && std::is_same<typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type, double_limb_type>::value>::type
eval_convert_to(float* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val)
{
float f = static_cast<std::uint64_t>((*val.limbs()) >> 64);
*result = std::ldexp(f, 64);
*result += static_cast<std::uint64_t>((*val.limbs()));
if(val.sign())
*result = -*result;
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
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 && std::is_same<typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type, double_limb_type>::value>::type
eval_convert_to(double* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val)
{
float f = static_cast<std::uint64_t>((*val.limbs()) >> 64);
*result = std::ldexp(f, 64);
*result += static_cast<std::uint64_t>((*val.limbs()));
if(val.sign())
*result = -*result;
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
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 && std::is_same<typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type, double_limb_type>::value>::type
eval_convert_to(long double* result, const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val)
{
float f = static_cast<std::uint64_t>((*val.limbs()) >> 64);
*result = std::ldexp(f, 64);
*result += static_cast<std::uint64_t>((*val.limbs()));
if(val.sign())
*result = -*result;
}
#endif
template <class R, std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
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 && std::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)
{
BOOST_IF_CONSTEXPR(std::numeric_limits<R>::is_specialized)
{
using common_type = typename std::common_type<R, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type>::type;
if (static_cast<common_type>(*val.limbs()) > static_cast<common_type>((std::numeric_limits<R>::max)()))
{
if (val.isneg())
{
check_is_negative(std::integral_constant < bool, (boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value) || (number_category<R>::value == number_kind_floating_point) > ());
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 = boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value ? (std::numeric_limits<R>::max)() : static_cast<R>(*val.limbs());
}
}
else
{
*result = static_cast<R>(*val.limbs());
if (val.isneg())
{
check_is_negative(std::integral_constant < bool, (boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value) || (number_category<R>::value == number_kind_floating_point) > ());
*result = negate_integer(*result, std::integral_constant < bool, is_signed_number<R>::value || (number_category<R>::value == number_kind_floating_point) > ());
}
}
}
else
{
*result = static_cast<R>(*val.limbs());
if (val.isneg())
{
check_is_negative(std::integral_constant<bool, (boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value) || (number_category<R>::value == number_kind_floating_point) > ());
*result = negate_integer(*result, std::integral_constant<bool, is_signed_number<R>::value || (number_category<R>::value == number_kind_floating_point) > ());
}
}
}
template <class R, std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
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 && std::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)
{
BOOST_IF_CONSTEXPR(std::numeric_limits<R>::is_specialized)
{
using common_type = typename std::common_type<R, typename cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>::local_limb_type>::type;
if(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 = boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value ? (std::numeric_limits<R>::max)() : static_cast<R>(*val.limbs());
}
else
*result = static_cast<R>(*val.limbs());
}
else
*result = static_cast<R>(*val.limbs());
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, std::size_t>::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_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
if (a.sign())
{
BOOST_MP_THROW_EXCEPTION(std::domain_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 <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, std::size_t>::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 <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<is_trivial_cpp_int<cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1> >::value, std::size_t>::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_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
if (a.sign())
{
BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
}
return eval_msb_imp(a);
}
template <std::size_t MinBits1, std::size_t MaxBits1, cpp_integer_type SignType1, cpp_int_check_type Checked1, class Allocator1>
inline BOOST_MP_CXX14_CONSTEXPR std::size_t hash_value(const cpp_int_backend<MinBits1, MaxBits1, SignType1, Checked1, Allocator1>& val) noexcept
{
std::size_t result = 0;
for (std::size_t i = 0; i < val.size(); ++i)
{
boost::multiprecision::detail::hash_combine(result, val.limbs()[i]);
}
boost::multiprecision::detail::hash_combine(result, val.sign());
return result;
}
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
} // Namespace backends
namespace detail {
#ifndef BOOST_MP_STANDALONE
template <typename T>
inline BOOST_CXX14_CONSTEXPR T constexpr_gcd(T a, T b) noexcept
{
return boost::integer::gcd(a, b);
}
template <typename T>
inline BOOST_CXX14_CONSTEXPR T constexpr_lcm(T a, T b) noexcept
{
return boost::integer::lcm(a, b);
}
#else
template <typename T>
inline BOOST_CXX14_CONSTEXPR T constexpr_gcd(T a, T b) noexcept
{
return boost::multiprecision::backends::eval_gcd(a, b);
}
template <typename T>
inline BOOST_CXX14_CONSTEXPR T constexpr_lcm(T a, T b) noexcept
{
const T ab_gcd = boost::multiprecision::detail::constexpr_gcd(a, b);
return (a * b) / ab_gcd;
}
#endif // BOOST_MP_STANDALONE
}
}} // Namespace boost::multiprecision
#endif
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