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WSJT-X/boost/multiprecision/cpp_int.hpp
Bill Somerville 4ebe6417a5 Squashed 'boost/' content from commit b4feb19f2 
git-subtree-dir: boost
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2018-06-09 21:48:32 +01:00

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//////////////////3/////////////////////////////////////////////
// Copyright 2012 John Maddock. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
#ifndef BOOST_MP_CPP_INT_HPP
#define BOOST_MP_CPP_INT_HPP
#include <iostream>
#include <iomanip>
#include <boost/cstdint.hpp>
#include <boost/multiprecision/number.hpp>
#include <boost/multiprecision/detail/integer_ops.hpp>
#include <boost/array.hpp>
#include <boost/type_traits/is_integral.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/multiprecision/cpp_int/cpp_int_config.hpp>
#include <boost/multiprecision/rational_adaptor.hpp>
#include <boost/multiprecision/traits/is_byte_container.hpp>
#include <boost/detail/endian.hpp>
#include <boost/integer/static_min_max.hpp>
#include <boost/type_traits/common_type.hpp>
#include <boost/type_traits/make_signed.hpp>
#include <boost/multiprecision/cpp_int/checked.hpp>
#ifdef BOOST_MP_USER_DEFINED_LITERALS
#include <boost/multiprecision/cpp_int/value_pack.hpp>
#endif
namespace boost{
namespace multiprecision{
namespace backends{
using boost::enable_if;
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4307) // integral constant overflow (oveflow is in a branch not taken when it would overflow)
#pragma warning(disable:4127) // conditional expression is constant
#pragma warning(disable:4702) // Unreachable code (reachability depends on template params)
#endif
template <unsigned MinBits = 0, unsigned MaxBits = 0, boost::multiprecision::cpp_integer_type SignType = signed_magnitude, cpp_int_check_type Checked = unchecked, class Allocator = typename mpl::if_c<MinBits && (MinBits == MaxBits), void, std::allocator<limb_type> >::type >
struct cpp_int_backend;
} // namespace backends
namespace detail {
template <unsigned MinBits, unsigned MaxBits, boost::multiprecision::cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct is_byte_container<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> > : public boost::false_type {};
} // namespace detail
namespace backends{
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator, bool trivial = false>
struct cpp_int_base;
//
// Traits class determines the maximum and minimum precision values:
//
template <class T> struct max_precision;
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct max_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
{
static const unsigned value = is_void<Allocator>::value ?
static_unsigned_max<MinBits, MaxBits>::value
: (((MaxBits >= MinBits) && MaxBits) ? MaxBits : UINT_MAX);
};
template <class T> struct min_precision;
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct min_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
{
static const unsigned value = (is_void<Allocator>::value ? static_unsigned_max<MinBits, MaxBits>::value : MinBits);
};
//
// Traits class determines whether the number of bits precision requested could fit in a native type,
// we call this a "trivial" cpp_int:
//
template <class T>
struct is_trivial_cpp_int
{
static const bool value = false;
};
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct is_trivial_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
{
typedef cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> self;
static const bool value = is_void<Allocator>::value && (max_precision<self>::value <= (sizeof(double_limb_type) * CHAR_BIT) - (SignType == signed_packed ? 1 : 0));
};
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct is_trivial_cpp_int<cpp_int_base<MinBits, MaxBits, SignType, Checked, Allocator, true> >
{
static const bool value = true;
};
} // namespace backends
//
// Traits class to determine whether a cpp_int_backend is signed or not:
//
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct is_unsigned_number<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
: public mpl::bool_<(SignType == unsigned_magnitude) || (SignType == unsigned_packed)>{};
namespace backends{
//
// Traits class determines whether T should be implicitly convertible to U, or
// whether the constructor should be made explicit. The latter happens if we
// are losing the sign, or have fewer digits precision in the target type:
//
template <class T, class U>
struct is_implicit_cpp_int_conversion;
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
struct is_implicit_cpp_int_conversion<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >
{
typedef cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> t1;
typedef cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> t2;
static const bool value =
(is_signed_number<t2>::value || !is_signed_number<t1>::value)
&& (max_precision<t1>::value <= max_precision<t2>::value);
};
//
// Traits class to determine whether operations on a cpp_int may throw:
//
template <class T>
struct is_non_throwing_cpp_int : public mpl::false_{};
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType>
struct is_non_throwing_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, unchecked, void> > : public mpl::true_ {};
//
// Traits class, determines whether the cpp_int is fixed precision or not:
//
template <class T>
struct is_fixed_precision;
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct is_fixed_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
: public mpl::bool_<max_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value != UINT_MAX> {};
namespace detail{
inline void verify_new_size(unsigned new_size, unsigned min_size, const mpl::int_<checked>&)
{
if(new_size < min_size)
BOOST_THROW_EXCEPTION(std::overflow_error("Unable to allocate sufficient storage for the value of the result: value overflows the maximum allowable magnitude."));
}
inline void verify_new_size(unsigned /*new_size*/, unsigned /*min_size*/, const mpl::int_<unchecked>&){}
template <class U>
inline void verify_limb_mask(bool b, U limb, U mask, const mpl::int_<checked>&)
{
// When we mask out "limb" with "mask", do we loose bits? If so it's an overflow error:
if(b && (limb & ~mask))
BOOST_THROW_EXCEPTION(std::overflow_error("Overflow in cpp_int arithmetic: there is insufficient precision in the target type to hold all of the bits of the result."));
}
template <class U>
inline void verify_limb_mask(bool /*b*/, U /*limb*/, U /*mask*/, const mpl::int_<unchecked>&){}
}
//
// Now define the various data layouts that are possible as partial specializations of the base class,
// starting with the default arbitrary precision signed integer type:
//
template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
struct cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false> : private Allocator::template rebind<limb_type>::other
{
typedef typename Allocator::template rebind<limb_type>::other allocator_type;
typedef typename allocator_type::pointer limb_pointer;
typedef typename allocator_type::const_pointer const_limb_pointer;
typedef mpl::int_<Checked> checked_type;
//
// Interface invariants:
//
BOOST_STATIC_ASSERT(!is_void<Allocator>::value);
private:
struct limb_data
{
unsigned capacity;
limb_pointer data;
};
public:
BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast<limb_type>(0u));
BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = static_cast<limb_type>(1u) << (limb_bits - 1));
BOOST_STATIC_CONSTANT(unsigned, internal_limb_count =
MinBits
? (MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0))
: (sizeof(limb_data) / sizeof(limb_type)));
BOOST_STATIC_CONSTANT(bool, variable = true);
private:
union data_type
{
limb_data ld;
limb_type la[internal_limb_count];
limb_type first;
double_limb_type double_first;
BOOST_CONSTEXPR data_type() : first(0) {}
BOOST_CONSTEXPR data_type(limb_type i) : first(i) {}
BOOST_CONSTEXPR data_type(signed_limb_type i) : first(i < 0 ? static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i) {}
#ifdef BOOST_LITTLE_ENDIAN
BOOST_CONSTEXPR data_type(double_limb_type i) : double_first(i) {}
BOOST_CONSTEXPR data_type(signed_double_limb_type i) : double_first(i < 0 ? static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i) {}
#endif
};
data_type m_data;
unsigned m_limbs;
bool m_sign, m_internal;
public:
//
// Direct construction:
//
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
: m_data(i), m_limbs(1), m_sign(false), m_internal(true) { }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT
: m_data(i), m_limbs(1), m_sign(i < 0), m_internal(true) { }
#if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
: m_data(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false), m_internal(true) { }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT
: m_data(i), m_limbs(i < 0 ? (static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) > static_cast<double_limb_type>(max_limb_value) ? 2 : 1) : (i > max_limb_value ? 2 : 1)),
m_sign(i < 0), m_internal(true) { }
#endif
//
// Helper functions for getting at our internal data, and manipulating storage:
//
BOOST_MP_FORCEINLINE allocator_type& allocator() BOOST_NOEXCEPT { return *this; }
BOOST_MP_FORCEINLINE const allocator_type& allocator()const BOOST_NOEXCEPT { return *this; }
BOOST_MP_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; }
BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; }
BOOST_MP_FORCEINLINE const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_internal ? m_data.la : m_data.ld.data; }
BOOST_MP_FORCEINLINE unsigned capacity()const BOOST_NOEXCEPT { return m_internal ? internal_limb_count : m_data.ld.capacity; }
BOOST_MP_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; }
void sign(bool b) BOOST_NOEXCEPT
{
m_sign = b;
// Check for zero value:
if(m_sign && (m_limbs == 1))
{
if(limbs()[0] == 0)
m_sign = false;
}
}
void resize(unsigned new_size, unsigned min_size)
{
static const unsigned max_limbs = MaxBits / (CHAR_BIT * sizeof(limb_type)) + ((MaxBits % (CHAR_BIT * sizeof(limb_type))) ? 1 : 0);
// We never resize beyond MaxSize:
if(new_size > max_limbs)
new_size = max_limbs;
detail::verify_new_size(new_size, min_size, checked_type());
// See if we have enough capacity already:
unsigned cap = capacity();
if(new_size > cap)
{
// Allocate a new buffer and copy everything over:
cap = (std::min)((std::max)(cap * 4, new_size), max_limbs);
limb_pointer pl = allocator().allocate(cap);
std::memcpy(pl, limbs(), size() * sizeof(limbs()[0]));
if(!m_internal)
allocator().deallocate(limbs(), capacity());
else
m_internal = false;
m_limbs = new_size;
m_data.ld.capacity = cap;
m_data.ld.data = pl;
}
else
{
m_limbs = new_size;
}
}
BOOST_MP_FORCEINLINE void normalize() BOOST_NOEXCEPT
{
limb_pointer p = limbs();
while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(), m_limbs(1), m_sign(false), m_internal(true) {}
BOOST_MP_FORCEINLINE cpp_int_base(const cpp_int_base& o) : allocator_type(o), m_limbs(0), m_internal(true)
{
resize(o.size(), o.size());
std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
m_sign = o.m_sign;
}
#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
cpp_int_base(cpp_int_base&& o)
: allocator_type(static_cast<allocator_type&&>(o)), m_limbs(o.m_limbs), m_sign(o.m_sign), m_internal(o.m_internal)
{
if(m_internal)
{
std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
}
else
{
m_data.ld = o.m_data.ld;
o.m_limbs = 0;
o.m_internal = true;
}
}
cpp_int_base& operator = (cpp_int_base&& o) BOOST_NOEXCEPT
{
if(!m_internal)
allocator().deallocate(m_data.ld.data, m_data.ld.capacity);
*static_cast<allocator_type*>(this) = static_cast<allocator_type&&>(o);
m_limbs = o.m_limbs;
m_sign = o.m_sign;
m_internal = o.m_internal;
if(m_internal)
{
std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
}
else
{
m_data.ld = o.m_data.ld;
o.m_limbs = 0;
o.m_internal = true;
}
return *this;
}
#endif
BOOST_MP_FORCEINLINE ~cpp_int_base() BOOST_NOEXCEPT
{
if(!m_internal)
allocator().deallocate(limbs(), capacity());
}
void assign(const cpp_int_base& o)
{
if(this != &o)
{
static_cast<allocator_type&>(*this) = static_cast<const allocator_type&>(o);
m_limbs = 0;
resize(o.size(), o.size());
std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
m_sign = o.m_sign;
}
}
BOOST_MP_FORCEINLINE void negate() BOOST_NOEXCEPT
{
m_sign = !m_sign;
// Check for zero value:
if(m_sign && (m_limbs == 1))
{
if(limbs()[0] == 0)
m_sign = false;
}
}
BOOST_MP_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
{
return m_sign;
}
BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
{
std::swap(m_data, o.m_data);
std::swap(m_sign, o.m_sign);
std::swap(m_internal, o.m_internal);
std::swap(m_limbs, o.m_limbs);
}
protected:
template <class A>
void check_in_range(const A&) BOOST_NOEXCEPT {}
};
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
const unsigned cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::limb_bits;
template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
const limb_type cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::max_limb_value;
template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
const limb_type cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::sign_bit_mask;
template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
const unsigned cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::internal_limb_count;
template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
const bool cpp_int_base<MinBits, MaxBits, signed_magnitude, Checked, Allocator, false>::variable;
#endif
template <unsigned MinBits, unsigned MaxBits, cpp_int_check_type Checked, class Allocator>
struct cpp_int_base<MinBits, MaxBits, unsigned_magnitude, Checked, Allocator, false> : private Allocator::template rebind<limb_type>::other
{
//
// There is currently no support for unsigned arbitrary precision arithmetic, largely
// because it's not clear what subtraction should do:
//
BOOST_STATIC_ASSERT_MSG(((sizeof(Allocator) == 0) && !is_void<Allocator>::value), "There is curently no support for unsigned arbitrary precision integers.");
};
//
// Fixed precision (i.e. no allocator), signed-magnitude type with limb-usage count:
//
template <unsigned MinBits, cpp_int_check_type Checked>
struct cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>
{
typedef limb_type* limb_pointer;
typedef const limb_type* const_limb_pointer;
typedef mpl::int_<Checked> checked_type;
//
// Interface invariants:
//
BOOST_STATIC_ASSERT_MSG(MinBits > sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
public:
BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast<limb_type>(0u));
BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = static_cast<limb_type>(1u) << (limb_bits - 1));
BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0));
BOOST_STATIC_CONSTANT(bool, variable = false);
BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (MinBits % limb_bits) ? (limb_type(1) << (MinBits % limb_bits)) -1 : (~limb_type(0)));
BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs");
private:
union data_type{
limb_type m_data[internal_limb_count];
limb_type m_first_limb;
double_limb_type m_double_first_limb;
BOOST_CONSTEXPR data_type() : m_first_limb(0) {}
BOOST_CONSTEXPR data_type(limb_type i) : m_first_limb(i) {}
BOOST_CONSTEXPR data_type(double_limb_type i) : m_double_first_limb(i) {}
#if defined(BOOST_MP_USER_DEFINED_LITERALS)
template <limb_type...VALUES>
BOOST_CONSTEXPR data_type(literals::detail::value_pack<VALUES...>) : m_data{ VALUES... } {}
#endif
} m_wrapper;
boost::uint16_t m_limbs;
bool m_sign;
public:
//
// Direct construction:
//
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
: m_wrapper(i), m_limbs(1), m_sign(false) {}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_limb_type i)BOOST_NOEXCEPT
: m_wrapper(limb_type(i < 0 ? static_cast<limb_type>(-static_cast<signed_double_limb_type>(i)) : i)), m_limbs(1), m_sign(i < 0) {}
#if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
: m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1), m_sign(false) {}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(signed_double_limb_type i)BOOST_NOEXCEPT
: m_wrapper(double_limb_type(i < 0 ? static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i)),
m_limbs(i < 0 ? (static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1)),
m_sign(i < 0) {}
#endif
#if defined(BOOST_MP_USER_DEFINED_LITERALS)
template <limb_type...VALUES>
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<VALUES...> i)
: m_wrapper(i), m_limbs(sizeof...(VALUES)), m_sign(false) {}
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<> i)
: m_wrapper(i), m_limbs(1), m_sign(false) {}
BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& a, const literals::detail::negate_tag&)
: m_wrapper(a.m_wrapper), m_limbs(a.m_limbs), m_sign((a.m_limbs == 1) && (*a.limbs() == 0) ? false : !a.m_sign) {}
#endif
//
// Helper functions for getting at our internal data, and manipulating storage:
//
BOOST_MP_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; }
BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return m_sign; }
BOOST_MP_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT
{
m_sign = b;
// Check for zero value:
if(m_sign && (m_limbs == 1))
{
if(limbs()[0] == 0)
m_sign = false;
}
}
BOOST_MP_FORCEINLINE void resize(unsigned new_size, unsigned min_size) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
m_limbs = static_cast<boost::uint16_t>((std::min)(new_size, internal_limb_count));
detail::verify_new_size(m_limbs, min_size, checked_type());
}
BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
limb_pointer p = limbs();
detail::verify_limb_mask(m_limbs == internal_limb_count, p[internal_limb_count-1], upper_limb_mask, checked_type());
p[internal_limb_count-1] &= upper_limb_mask;
while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
if((m_limbs == 1) && (!*p)) m_sign = false; // zero is always unsigned
}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base()BOOST_NOEXCEPT : m_wrapper(limb_type(0u)), m_limbs(1), m_sign(false) {}
// Not defaulted, it breaks constexpr support in the Intel compiler for some reason:
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o)BOOST_NOEXCEPT
: m_wrapper(o.m_wrapper), m_limbs(o.m_limbs), m_sign(o.m_sign) {}
// Defaulted functions:
//~cpp_int_base() BOOST_NOEXCEPT {}
void assign(const cpp_int_base& o) BOOST_NOEXCEPT
{
if(this != &o)
{
m_limbs = o.m_limbs;
std::memcpy(limbs(), o.limbs(), o.size() * sizeof(o.limbs()[0]));
m_sign = o.m_sign;
}
}
BOOST_MP_FORCEINLINE void negate() BOOST_NOEXCEPT
{
m_sign = !m_sign;
// Check for zero value:
if(m_sign && (m_limbs == 1))
{
if(limbs()[0] == 0)
m_sign = false;
}
}
BOOST_MP_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
{
return m_sign;
}
BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
{
for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i)
std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]);
std::swap(m_sign, o.m_sign);
std::swap(m_limbs, o.m_limbs);
}
protected:
template <class A>
void check_in_range(const A&) BOOST_NOEXCEPT {}
};
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
template <unsigned MinBits, cpp_int_check_type Checked>
const unsigned cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::limb_bits;
template <unsigned MinBits, cpp_int_check_type Checked>
const limb_type cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::max_limb_value;
template <unsigned MinBits, cpp_int_check_type Checked>
const limb_type cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::sign_bit_mask;
template <unsigned MinBits, cpp_int_check_type Checked>
const unsigned cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::internal_limb_count;
template <unsigned MinBits, cpp_int_check_type Checked>
const bool cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, false>::variable;
#endif
//
// Fixed precision (i.e. no allocator), unsigned type with limb-usage count:
//
template <unsigned MinBits, cpp_int_check_type Checked>
struct cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>
{
typedef limb_type* limb_pointer;
typedef const limb_type* const_limb_pointer;
typedef mpl::int_<Checked> checked_type;
//
// Interface invariants:
//
BOOST_STATIC_ASSERT_MSG(MinBits > sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
public:
BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(limb_type) * CHAR_BIT);
BOOST_STATIC_CONSTANT(limb_type, max_limb_value = ~static_cast<limb_type>(0u));
BOOST_STATIC_CONSTANT(limb_type, sign_bit_mask = static_cast<limb_type>(1u) << (limb_bits - 1));
BOOST_STATIC_CONSTANT(unsigned, internal_limb_count = MinBits / limb_bits + ((MinBits % limb_bits) ? 1 : 0));
BOOST_STATIC_CONSTANT(bool, variable = false);
BOOST_STATIC_CONSTANT(limb_type, upper_limb_mask = (MinBits % limb_bits) ? (limb_type(1) << (MinBits % limb_bits)) -1 : (~limb_type(0)));
BOOST_STATIC_ASSERT_MSG(internal_limb_count >= 2, "A fixed precision integer type must have at least 2 limbs");
private:
union data_type{
limb_type m_data[internal_limb_count];
limb_type m_first_limb;
double_limb_type m_double_first_limb;
BOOST_CONSTEXPR data_type() : m_first_limb(0) {}
BOOST_CONSTEXPR data_type(limb_type i) : m_first_limb(i) {}
BOOST_CONSTEXPR data_type(double_limb_type i) : m_double_first_limb(i) {}
#if defined(BOOST_MP_USER_DEFINED_LITERALS)
template <limb_type...VALUES>
BOOST_CONSTEXPR data_type(literals::detail::value_pack<VALUES...>) : m_data{ VALUES... } {}
#endif
} m_wrapper;
limb_type m_limbs;
public:
//
// Direct construction:
//
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(limb_type i)BOOST_NOEXCEPT
: m_wrapper(i), m_limbs(1) {}
BOOST_MP_FORCEINLINE cpp_int_base(signed_limb_type i)BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
: m_wrapper(limb_type(i < 0 ? static_cast<limb_type>(-static_cast<signed_double_limb_type>(i)) : i)), m_limbs(1) { if(i < 0) negate(); }
#if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(double_limb_type i)BOOST_NOEXCEPT
: m_wrapper(i), m_limbs(i > max_limb_value ? 2 : 1) {}
BOOST_MP_FORCEINLINE cpp_int_base(signed_double_limb_type i)BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
: m_wrapper(double_limb_type(i < 0 ? static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) : i)),
m_limbs(i < 0 ? (static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i)) > max_limb_value ? 2 : 1) : (i > max_limb_value ? 2 : 1))
{
if (i < 0) negate();
}
#endif
#if defined(BOOST_MP_USER_DEFINED_LITERALS)
template <limb_type...VALUES>
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<VALUES...> i)
: m_wrapper(i), m_limbs(sizeof...(VALUES)) {}
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<>)
: m_wrapper(static_cast<limb_type>(0u)), m_limbs(1) {}
#endif
//
// Helper functions for getting at our internal data, and manipulating storage:
//
BOOST_MP_FORCEINLINE unsigned size()const BOOST_NOEXCEPT { return m_limbs; }
BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return m_wrapper.m_data; }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return m_wrapper.m_data; }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; }
BOOST_MP_FORCEINLINE void sign(bool b) BOOST_MP_NOEXCEPT_IF((Checked == unchecked)) { if(b) negate(); }
BOOST_MP_FORCEINLINE void resize(unsigned new_size, unsigned min_size) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
m_limbs = (std::min)(new_size, internal_limb_count);
detail::verify_new_size(m_limbs, min_size, checked_type());
}
BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
limb_pointer p = limbs();
detail::verify_limb_mask(m_limbs == internal_limb_count, p[internal_limb_count-1], upper_limb_mask, checked_type());
p[internal_limb_count-1] &= upper_limb_mask;
while((m_limbs-1) && !p[m_limbs - 1])--m_limbs;
}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT
: m_wrapper(limb_type(0u)), m_limbs(1) {}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT
: m_wrapper(o.m_wrapper), m_limbs(o.m_limbs) {}
// Defaulted functions:
//~cpp_int_base() BOOST_NOEXCEPT {}
BOOST_MP_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT
{
if(this != &o)
{
m_limbs = o.m_limbs;
std::memcpy(limbs(), o.limbs(), o.size() * sizeof(limbs()[0]));
}
}
private:
void check_negate(const mpl::int_<checked>&)
{
BOOST_THROW_EXCEPTION(std::range_error("Attempt to negate an unsigned number."));
}
void check_negate(const mpl::int_<unchecked>&){}
public:
void negate() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
// Not so much a negate as a complement - this gets called when subtraction
// would result in a "negative" number:
unsigned i;
if((m_limbs == 1) && (m_wrapper.m_data[0] == 0))
return; // negating zero is always zero, and always OK.
check_negate(checked_type());
for(i = m_limbs; i < internal_limb_count; ++i)
m_wrapper.m_data[i] = 0;
m_limbs = internal_limb_count;
for(i = 0; i < internal_limb_count; ++i)
m_wrapper.m_data[i] = ~m_wrapper.m_data[i];
normalize();
eval_increment(static_cast<cpp_int_backend<MinBits, MinBits, unsigned_magnitude, Checked, void>& >(*this));
}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT
{
return false;
}
BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
{
for(unsigned i = 0; i < (std::max)(size(), o.size()); ++i)
std::swap(m_wrapper.m_data[i], o.m_wrapper.m_data[i]);
std::swap(m_limbs, o.m_limbs);
}
protected:
template <class A>
void check_in_range(const A&) BOOST_NOEXCEPT {}
};
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
template <unsigned MinBits, cpp_int_check_type Checked>
const unsigned cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::limb_bits;
template <unsigned MinBits, cpp_int_check_type Checked>
const limb_type cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::max_limb_value;
template <unsigned MinBits, cpp_int_check_type Checked>
const limb_type cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::sign_bit_mask;
template <unsigned MinBits, cpp_int_check_type Checked>
const unsigned cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::internal_limb_count;
template <unsigned MinBits, cpp_int_check_type Checked>
const bool cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, false>::variable;
#endif
//
// Traits classes to figure out a native type with N bits, these vary from boost::uint_t<N> only
// because some platforms have native integer types longer than boost::long_long_type, "really boost::long_long_type" anyone??
//
template <unsigned N, bool s>
struct trivial_limb_type_imp
{
typedef double_limb_type type;
};
template <unsigned N>
struct trivial_limb_type_imp<N, true>
{
typedef typename boost::uint_t<N>::least type;
};
template <unsigned N>
struct trivial_limb_type : public trivial_limb_type_imp<N, N <= sizeof(boost::long_long_type) * CHAR_BIT> {};
//
// Backend for fixed precision signed-magnitude type which will fit entirely inside a "double_limb_type":
//
template <unsigned MinBits, cpp_int_check_type Checked>
struct cpp_int_base<MinBits, MinBits, signed_magnitude, Checked, void, true>
{
typedef typename trivial_limb_type<MinBits>::type local_limb_type;
typedef local_limb_type* limb_pointer;
typedef const local_limb_type* const_limb_pointer;
typedef mpl::int_<Checked> checked_type;
protected:
BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT);
BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = (MinBits < limb_bits) ? local_limb_type((local_limb_type(~local_limb_type(0))) >> (limb_bits - MinBits)) : local_limb_type(~local_limb_type(0)));
private:
local_limb_type m_data;
bool m_sign;
//
// Interface invariants:
//
BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
protected:
template <class T>
typename boost::disable_if_c<!boost::is_integral<T>::value || (std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::digits <= (int)MinBits))>::type
check_in_range(T val, const mpl::int_<checked>&)
{
typedef typename common_type<typename make_unsigned<T>::type, local_limb_type>::type common_type;
if(static_cast<common_type>(boost::multiprecision::detail::unsigned_abs(val)) > static_cast<common_type>(limb_mask))
BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
}
template <class T>
typename boost::disable_if_c<boost::is_integral<T>::value || (std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::digits <= (int)MinBits))>::type
check_in_range(T val, const mpl::int_<checked>&)
{
using std::abs;
typedef typename common_type<T, local_limb_type>::type common_type;
if (static_cast<common_type>(abs(val)) > static_cast<common_type>(limb_mask))
BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
}
template <class T, int C>
void check_in_range(T, const mpl::int_<C>&) BOOST_NOEXCEPT {}
template <class T>
void check_in_range(T val) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<T>(), checked_type())))
{
check_in_range(val, checked_type());
}
public:
//
// Direct construction:
//
template <class SI>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == unchecked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<SI>())))
: m_data(i < 0 ? static_cast<local_limb_type>(static_cast<typename make_unsigned<SI>::type>(boost::multiprecision::detail::unsigned_abs(i)) & limb_mask) : static_cast<local_limb_type>(i & limb_mask)), m_sign(i < 0) {}
template <class SI>
BOOST_MP_FORCEINLINE cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<SI>())))
: m_data(i < 0 ? (static_cast<local_limb_type>(static_cast<typename make_unsigned<SI>::type>(boost::multiprecision::detail::unsigned_abs(i)) & limb_mask)) : static_cast<local_limb_type>(i & limb_mask)), m_sign(i < 0)
{ check_in_range(i); }
template <class UI>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == unchecked)>::type const* = 0) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(i) & limb_mask), m_sign(false) {}
template <class UI>
BOOST_MP_FORCEINLINE cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == checked)>::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<UI>())))
: m_data(static_cast<local_limb_type>(i) & limb_mask), m_sign(false) { check_in_range(i); }
template <class F>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(F i, typename boost::enable_if_c<is_floating_point<F>::value && (Checked == unchecked)>::type const* = 0) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(std::fabs(i)) & limb_mask), m_sign(i < 0) {}
template <class F>
BOOST_MP_FORCEINLINE cpp_int_base(F i, typename boost::enable_if_c<is_floating_point<F>::value && (Checked == checked)>::type const* = 0)
: m_data(static_cast<local_limb_type>(std::fabs(i)) & limb_mask), m_sign(i < 0) { check_in_range(i); }
#if defined(BOOST_MP_USER_DEFINED_LITERALS)
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<>) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(0u)), m_sign(false) {}
template <limb_type a>
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a>)BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(a)), m_sign(false) {}
template <limb_type a, limb_type b>
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a, b>)BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(a) | (static_cast<local_limb_type>(b) << bits_per_limb)), m_sign(false) {}
BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& a, const literals::detail::negate_tag&)BOOST_NOEXCEPT
: m_data(a.m_data), m_sign(a.m_data ? !a.m_sign : false) {}
#endif
//
// Helper functions for getting at our internal data, and manipulating storage:
//
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; }
BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; }
BOOST_MP_FORCEINLINE bool sign()const BOOST_NOEXCEPT { return m_sign; }
BOOST_MP_FORCEINLINE void sign(bool b) BOOST_NOEXCEPT
{
m_sign = b;
// Check for zero value:
if(m_sign && !m_data)
{
m_sign = false;
}
}
BOOST_MP_FORCEINLINE void resize(unsigned new_size, unsigned min_size)
{
detail::verify_new_size(2, min_size, checked_type());
}
BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
if(!m_data)
m_sign = false; // zero is always unsigned
detail::verify_limb_mask(true, m_data, limb_mask, checked_type());
m_data &= limb_mask;
}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(0), m_sign(false) {}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT
: m_data(o.m_data), m_sign(o.m_sign) {}
//~cpp_int_base() BOOST_NOEXCEPT {}
BOOST_MP_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT
{
m_data = o.m_data;
m_sign = o.m_sign;
}
BOOST_MP_FORCEINLINE void negate() BOOST_NOEXCEPT
{
m_sign = !m_sign;
// Check for zero value:
if(m_data == 0)
{
m_sign = false;
}
}
BOOST_MP_FORCEINLINE bool isneg()const BOOST_NOEXCEPT
{
return m_sign;
}
BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
{
std::swap(m_sign, o.m_sign);
std::swap(m_data, o.m_data);
}
};
//
// Backend for unsigned fixed precision (i.e. no allocator) type which will fit entirely inside a "double_limb_type":
//
template <unsigned MinBits, cpp_int_check_type Checked>
struct cpp_int_base<MinBits, MinBits, unsigned_magnitude, Checked, void, true>
{
typedef typename trivial_limb_type<MinBits>::type local_limb_type;
typedef local_limb_type* limb_pointer;
typedef const local_limb_type* const_limb_pointer;
private:
BOOST_STATIC_CONSTANT(unsigned, limb_bits = sizeof(local_limb_type) * CHAR_BIT);
BOOST_STATIC_CONSTANT(local_limb_type, limb_mask = limb_bits != MinBits ?
static_cast<local_limb_type>(static_cast<local_limb_type>(~local_limb_type(0)) >> (limb_bits - MinBits))
: static_cast<local_limb_type>(~local_limb_type(0)));
local_limb_type m_data;
typedef mpl::int_<Checked> checked_type;
//
// Interface invariants:
//
BOOST_STATIC_ASSERT_MSG(MinBits <= sizeof(double_limb_type) * CHAR_BIT, "Template parameter MinBits is inconsistent with the parameter trivial - did you mistakingly try to override the trivial parameter?");
protected:
template <class T>
typename boost::disable_if_c<std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::digits <= (int)MinBits)>::type
check_in_range(T val, const mpl::int_<checked>&, const boost::false_type&)
{
typedef typename common_type<T, local_limb_type>::type common_type;
if(static_cast<common_type>(val) > limb_mask)
BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
}
template <class T>
void check_in_range(T val, const mpl::int_<checked>&, const boost::true_type&)
{
typedef typename common_type<T, local_limb_type>::type common_type;
if(static_cast<common_type>(val) > limb_mask)
BOOST_THROW_EXCEPTION(std::range_error("The argument to a cpp_int constructor exceeded the largest value it can represent."));
if(val < 0)
BOOST_THROW_EXCEPTION(std::range_error("The argument to an unsigned cpp_int constructor was negative."));
}
template <class T, int C, bool B>
BOOST_MP_FORCEINLINE void check_in_range(T, const mpl::int_<C>&, const boost::integral_constant<bool, B>&) BOOST_NOEXCEPT {}
template <class T>
BOOST_MP_FORCEINLINE void check_in_range(T val) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<T>(), checked_type(), is_signed<T>())))
{
check_in_range(val, checked_type(), is_signed<T>());
}
public:
//
// Direct construction:
//
#ifdef __MSVC_RUNTIME_CHECKS
template <class SI>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT
: m_data(i < 0 ? (1 + ~static_cast<local_limb_type>(-i & limb_mask)) & limb_mask : static_cast<local_limb_type>(i & limb_mask)) {}
template <class SI>
BOOST_MP_FORCEINLINE cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<SI>())))
: m_data(i < 0 ? 1 + ~static_cast<local_limb_type>(-i & limb_mask) : static_cast<local_limb_type>(i & limb_mask)) { check_in_range(i); }
template <class UI>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(i & limb_mask)) {}
template <class UI>
BOOST_MP_FORCEINLINE cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<UI>())))
: m_data(static_cast<local_limb_type>(i & limb_mask)) { check_in_range(i); }
#else
template <class SI>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT
: m_data(i < 0 ? (1 + ~static_cast<local_limb_type>(-i)) & limb_mask : static_cast<local_limb_type>(i) & limb_mask) {}
template <class SI>
BOOST_MP_FORCEINLINE cpp_int_base(SI i, typename boost::enable_if_c<is_signed<SI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<SI>())))
: m_data(i < 0 ? 1 + ~static_cast<local_limb_type>(-i) : static_cast<local_limb_type>(i)) { check_in_range(i); }
template <class UI>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == unchecked) >::type const* = 0) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(i) & limb_mask) {}
template <class UI>
BOOST_MP_FORCEINLINE cpp_int_base(UI i, typename boost::enable_if_c<is_unsigned<UI>::value && (Checked == checked) >::type const* = 0) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_base>().check_in_range(std::declval<UI>())))
: m_data(static_cast<local_limb_type>(i)) { check_in_range(i); }
#endif
template <class F>
BOOST_MP_FORCEINLINE cpp_int_base(F i, typename boost::enable_if<is_floating_point<F> >::type const* = 0) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
: m_data(static_cast<local_limb_type>(std::fabs(i)) & limb_mask)
{
check_in_range(i);
if(i < 0)
negate();
}
#if defined(BOOST_MP_USER_DEFINED_LITERALS)
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<>) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(0u)) {}
template <limb_type a>
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a>) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(a)) {}
template <limb_type a, limb_type b>
BOOST_CONSTEXPR cpp_int_base(literals::detail::value_pack<a, b>) BOOST_NOEXCEPT
: m_data(static_cast<local_limb_type>(a) | (static_cast<local_limb_type>(b) << bits_per_limb)) {}
#endif
//
// Helper functions for getting at our internal data, and manipulating storage:
//
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR unsigned size()const BOOST_NOEXCEPT { return 1; }
BOOST_MP_FORCEINLINE limb_pointer limbs() BOOST_NOEXCEPT { return &m_data; }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR const_limb_pointer limbs()const BOOST_NOEXCEPT { return &m_data; }
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool sign()const BOOST_NOEXCEPT { return false; }
BOOST_MP_FORCEINLINE void sign(bool b) BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
if(b)
negate();
}
BOOST_MP_FORCEINLINE void resize(unsigned, unsigned min_size)
{
detail::verify_new_size(2, min_size, checked_type());
}
BOOST_MP_FORCEINLINE void normalize() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
detail::verify_limb_mask(true, m_data, limb_mask, checked_type());
m_data &= limb_mask;
}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base() BOOST_NOEXCEPT : m_data(0) {}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_base(const cpp_int_base& o) BOOST_NOEXCEPT
: m_data(o.m_data) {}
//~cpp_int_base() BOOST_NOEXCEPT {}
BOOST_MP_FORCEINLINE void assign(const cpp_int_base& o) BOOST_NOEXCEPT
{
m_data = o.m_data;
}
BOOST_MP_FORCEINLINE void negate() BOOST_MP_NOEXCEPT_IF((Checked == unchecked))
{
if(Checked == checked)
{
BOOST_THROW_EXCEPTION(std::range_error("Attempt to negate an unsigned type."));
}
m_data = ~m_data;
++m_data;
}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR bool isneg()const BOOST_NOEXCEPT
{
return false;
}
BOOST_MP_FORCEINLINE void do_swap(cpp_int_base& o) BOOST_NOEXCEPT
{
std::swap(m_data, o.m_data);
}
};
//
// Traits class, lets us know whether type T can be directly converted to the base type,
// used to enable/disable constructors etc:
//
template <class Arg, class Base>
struct is_allowed_cpp_int_base_conversion : public mpl::if_c<
is_same<Arg, limb_type>::value || is_same<Arg, signed_limb_type>::value
#if defined(BOOST_LITTLE_ENDIAN) && !defined(BOOST_MP_TEST_NO_LE)
|| is_same<Arg, double_limb_type>::value || is_same<Arg, signed_double_limb_type>::value
#endif
#if defined(BOOST_MP_USER_DEFINED_LITERALS)
|| literals::detail::is_value_pack<Arg>::value
#endif
|| (is_trivial_cpp_int<Base>::value && is_arithmetic<Arg>::value),
mpl::true_,
mpl::false_
>::type
{};
//
// Now the actual backend, normalising parameters passed to the base class:
//
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct cpp_int_backend
: public cpp_int_base<
min_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
max_precision<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
SignType,
Checked,
Allocator,
is_trivial_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value>
{
typedef cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> self_type;
typedef cpp_int_base<
min_precision<self_type>::value,
max_precision<self_type>::value,
SignType,
Checked,
Allocator,
is_trivial_cpp_int<self_type>::value> base_type;
typedef mpl::bool_<is_trivial_cpp_int<self_type>::value> trivial_tag;
public:
typedef typename mpl::if_<
trivial_tag,
mpl::list<
signed char, short, int, long,
boost::long_long_type, signed_double_limb_type>,
mpl::list<signed_limb_type, signed_double_limb_type>
>::type signed_types;
typedef typename mpl::if_<
trivial_tag,
mpl::list<unsigned char, unsigned short, unsigned,
unsigned long, boost::ulong_long_type, double_limb_type>,
mpl::list<limb_type, double_limb_type>
>::type unsigned_types;
typedef typename mpl::if_<
trivial_tag,
mpl::list<float, double, long double>,
mpl::list<long double>
>::type float_types;
typedef mpl::int_<Checked> checked_type;
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend() BOOST_NOEXCEPT{}
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& o) BOOST_MP_NOEXCEPT_IF(boost::is_void<Allocator>::value) : base_type(o) {}
#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(cpp_int_backend&& o) BOOST_NOEXCEPT
: base_type(static_cast<base_type&&>(o)) {}
#endif
//
// Direct construction from arithmetic type:
//
template <class Arg>
BOOST_MP_FORCEINLINE BOOST_CONSTEXPR cpp_int_backend(Arg i, typename boost::enable_if_c<is_allowed_cpp_int_base_conversion<Arg, base_type>::value >::type const* = 0)BOOST_MP_NOEXCEPT_IF(noexcept(base_type(std::declval<Arg>())))
: base_type(i) {}
private:
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::true_ const&, mpl::true_ const &)
{
// Assigning trivial type to trivial type:
this->check_in_range(*other.limbs());
*this->limbs() = static_cast<typename self_type::local_limb_type>(*other.limbs());
this->sign(other.sign());
this->normalize();
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::true_ const&, mpl::false_ const &)
{
// non-trivial to trivial narrowing conversion:
double_limb_type v = *other.limbs();
if(other.size() > 1)
{
v |= static_cast<double_limb_type>(other.limbs()[1]) << bits_per_limb;
if((Checked == checked) && (other.size() > 2))
{
BOOST_THROW_EXCEPTION(std::range_error("Assignment of a cpp_int that is out of range for the target type."));
}
}
*this = v;
this->sign(other.sign());
this->normalize();
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::false_ const&, mpl::true_ const &)
{
// trivial to non-trivial, treat the trivial argument as if it were an unsigned arithmetic type, then set the sign afterwards:
*this = static_cast<
typename boost::multiprecision::detail::canonical<
typename cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>::local_limb_type,
cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>
>::type
>(*other.limbs());
this->sign(other.sign());
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
void do_assign(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other, mpl::false_ const&, mpl::false_ const &)
{
// regular non-trivial to non-trivial assign:
this->resize(other.size(), other.size());
std::memcpy(this->limbs(), other.limbs(), (std::min)(other.size(), this->size()) * sizeof(this->limbs()[0]));
this->sign(other.sign());
this->normalize();
}
public:
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
cpp_int_backend(
const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other,
typename boost::enable_if_c<is_implicit_cpp_int_conversion<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>, self_type>::value>::type* = 0)
: base_type()
{
do_assign(
other,
mpl::bool_<is_trivial_cpp_int<self_type>::value>(),
mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>());
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
explicit cpp_int_backend(
const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other,
typename boost::disable_if_c<is_implicit_cpp_int_conversion<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>, self_type>::value>::type* = 0)
: base_type()
{
do_assign(
other,
mpl::bool_<is_trivial_cpp_int<self_type>::value>(),
mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>());
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
cpp_int_backend& operator=(
const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& other)
{
do_assign(
other,
mpl::bool_<is_trivial_cpp_int<self_type>::value>(),
mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value>());
return *this;
}
#ifdef BOOST_MP_USER_DEFINED_LITERALS
BOOST_CONSTEXPR cpp_int_backend(const cpp_int_backend& a, const literals::detail::negate_tag& tag)
: base_type(static_cast<const base_type&>(a), tag){}
#endif
BOOST_MP_FORCEINLINE cpp_int_backend& operator = (const cpp_int_backend& o) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().assign(std::declval<const cpp_int_backend&>())))
{
this->assign(o);
return *this;
}
#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
BOOST_MP_FORCEINLINE cpp_int_backend& operator = (cpp_int_backend&& o) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<base_type&>() = std::declval<base_type>()))
{
*static_cast<base_type*>(this) = static_cast<base_type&&>(o);
return *this;
}
#endif
private:
template <class A>
typename boost::enable_if<is_unsigned<A> >::type do_assign_arithmetic(A val, const mpl::true_&)
BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().check_in_range(std::declval<A>())))
{
this->check_in_range(val);
*this->limbs() = static_cast<typename self_type::local_limb_type>(val);
this->normalize();
}
template <class A>
typename boost::disable_if_c<is_unsigned<A>::value || !is_integral<A>::value >::type do_assign_arithmetic(A val, const mpl::true_&)
BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().check_in_range(std::declval<A>())) && noexcept(std::declval<cpp_int_backend>().sign(true)))
{
this->check_in_range(val);
*this->limbs() = (val < 0) ? static_cast<typename self_type::local_limb_type>(boost::multiprecision::detail::unsigned_abs(val)) : static_cast<typename self_type::local_limb_type>(val);
this->sign(val < 0);
this->normalize();
}
template <class A>
typename boost::enable_if_c< !is_integral<A>::value>::type do_assign_arithmetic(A val, const mpl::true_&)
{
this->check_in_range(val);
*this->limbs() = (val < 0) ? static_cast<typename self_type::local_limb_type>(boost::multiprecision::detail::abs(val)) : static_cast<typename self_type::local_limb_type>(val);
this->sign(val < 0);
this->normalize();
}
BOOST_MP_FORCEINLINE void do_assign_arithmetic(limb_type i, const mpl::false_&) BOOST_NOEXCEPT
{
this->resize(1, 1);
*this->limbs() = i;
this->sign(false);
}
BOOST_MP_FORCEINLINE void do_assign_arithmetic(signed_limb_type i, const mpl::false_&) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().sign(true)))
{
this->resize(1, 1);
*this->limbs() = static_cast<limb_type>(boost::multiprecision::detail::unsigned_abs(i));
this->sign(i < 0);
}
void do_assign_arithmetic(double_limb_type i, const mpl::false_&) BOOST_NOEXCEPT
{
BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type));
BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2);
typename base_type::limb_pointer p = this->limbs();
#ifdef __MSVC_RUNTIME_CHECKS
*p = static_cast<limb_type>(i & ~static_cast<limb_type>(0));
#else
*p = static_cast<limb_type>(i);
#endif
p[1] = static_cast<limb_type>(i >> base_type::limb_bits);
this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
this->sign(false);
}
void do_assign_arithmetic(signed_double_limb_type i, const mpl::false_&) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().sign(true)))
{
BOOST_STATIC_ASSERT(sizeof(i) == 2 * sizeof(limb_type));
BOOST_STATIC_ASSERT(base_type::internal_limb_count >= 2);
bool s = false;
double_limb_type ui;
if(i < 0)
s = true;
ui = static_cast<double_limb_type>(boost::multiprecision::detail::unsigned_abs(i));
typename base_type::limb_pointer p = this->limbs();
#ifdef __MSVC_RUNTIME_CHECKS
*p = static_cast<limb_type>(ui & ~static_cast<limb_type>(0));
#else
*p = static_cast<limb_type>(ui);
#endif
p[1] = static_cast<limb_type>(ui >> base_type::limb_bits);
this->resize(p[1] ? 2 : 1, p[1] ? 2 : 1);
this->sign(s);
}
void do_assign_arithmetic(long double a, const mpl::false_&)
{
using default_ops::eval_add;
using default_ops::eval_subtract;
using std::frexp;
using std::ldexp;
using std::floor;
if(a < 0)
{
do_assign_arithmetic(-a, mpl::false_());
this->sign(true);
return;
}
if (a == 0) {
*this = static_cast<limb_type>(0u);
}
if (a == 1) {
*this = static_cast<limb_type>(1u);
}
BOOST_ASSERT(!(boost::math::isinf)(a));
BOOST_ASSERT(!(boost::math::isnan)(a));
int e;
long double f, term;
*this = static_cast<limb_type>(0u);
f = frexp(a, &e);
static const limb_type shift = std::numeric_limits<limb_type>::digits;
while(f)
{
// extract int sized bits from f:
f = ldexp(f, shift);
term = floor(f);
e -= shift;
eval_left_shift(*this, shift);
if(term > 0)
eval_add(*this, static_cast<limb_type>(term));
else
eval_subtract(*this, static_cast<limb_type>(-term));
f -= term;
}
if(e > 0)
eval_left_shift(*this, e);
else if(e < 0)
eval_right_shift(*this, -e);
}
public:
template <class Arithmetic>
BOOST_MP_FORCEINLINE typename boost::enable_if_c<!boost::multiprecision::detail::is_byte_container<Arithmetic>::value, cpp_int_backend&>::type operator = (Arithmetic val) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<cpp_int_backend>().do_assign_arithmetic(std::declval<Arithmetic>(), trivial_tag())))
{
do_assign_arithmetic(val, trivial_tag());
return *this;
}
private:
void do_assign_string(const char* s, const mpl::true_&)
{
std::size_t n = s ? std::strlen(s) : 0;
*this = 0;
unsigned radix = 10;
bool isneg = false;
if(n && (*s == '-'))
{
--n;
++s;
isneg = true;
}
if(n && (*s == '0'))
{
if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
{
radix = 16;
s +=2;
n -= 2;
}
else
{
radix = 8;
n -= 1;
}
}
if(n)
{
unsigned val;
while(*s)
{
if(*s >= '0' && *s <= '9')
val = *s - '0';
else if(*s >= 'a' && *s <= 'f')
val = 10 + *s - 'a';
else if(*s >= 'A' && *s <= 'F')
val = 10 + *s - 'A';
else
val = radix + 1;
if(val >= radix)
{
BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
}
*this->limbs() = detail::checked_multiply(*this->limbs(), static_cast<typename base_type::local_limb_type>(radix), checked_type());
*this->limbs() = detail::checked_add(*this->limbs(), static_cast<typename base_type::local_limb_type>(val), checked_type());
++s;
}
}
if(isneg)
this->negate();
}
void do_assign_string(const char* s, const mpl::false_&)
{
using default_ops::eval_multiply;
using default_ops::eval_add;
std::size_t n = s ? std::strlen(s) : 0;
*this = static_cast<limb_type>(0u);
unsigned radix = 10;
bool isneg = false;
if(n && (*s == '-'))
{
--n;
++s;
isneg = true;
}
if(n && (*s == '0'))
{
if((n > 1) && ((s[1] == 'x') || (s[1] == 'X')))
{
radix = 16;
s +=2;
n -= 2;
}
else
{
radix = 8;
n -= 1;
}
}
//
// Exception guarantee: create the result in stack variable "result"
// then do a swap at the end. In the event of a throw, *this will
// be left unchanged.
//
cpp_int_backend result;
if(n)
{
if(radix == 16)
{
while(*s == '0') ++s;
std::size_t bitcount = 4 * std::strlen(s);
limb_type val;
std::size_t limb, shift;
if(bitcount > 4)
bitcount -= 4;
else
bitcount = 0;
std::size_t newsize = bitcount / (sizeof(limb_type) * CHAR_BIT) + 1;
result.resize(static_cast<unsigned>(newsize), static_cast<unsigned>(newsize)); // will throw if this is a checked integer that cannot be resized
std::memset(result.limbs(), 0, result.size() * sizeof(limb_type));
while(*s)
{
if(*s >= '0' && *s <= '9')
val = *s - '0';
else if(*s >= 'a' && *s <= 'f')
val = 10 + *s - 'a';
else if(*s >= 'A' && *s <= 'F')
val = 10 + *s - 'A';
else
{
BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
}
limb = bitcount / (sizeof(limb_type) * CHAR_BIT);
shift = bitcount % (sizeof(limb_type) * CHAR_BIT);
val <<= shift;
if(result.size() > limb)
{
result.limbs()[limb] |= val;
}
++s;
bitcount -= 4;
}
result.normalize();
}
else if(radix == 8)
{
while(*s == '0') ++s;
std::size_t bitcount = 3 * std::strlen(s);
limb_type val;
std::size_t limb, shift;
if(bitcount > 3)
bitcount -= 3;
else
bitcount = 0;
std::size_t newsize = bitcount / (sizeof(limb_type) * CHAR_BIT) + 1;
result.resize(static_cast<unsigned>(newsize), static_cast<unsigned>(newsize)); // will throw if this is a checked integer that cannot be resized
std::memset(result.limbs(), 0, result.size() * sizeof(limb_type));
while(*s)
{
if(*s >= '0' && *s <= '7')
val = *s - '0';
else
{
BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected content found while parsing character string."));
}
limb = bitcount / (sizeof(limb_type) * CHAR_BIT);
shift = bitcount % (sizeof(limb_type) * CHAR_BIT);
if(result.size() > limb)
{
result.limbs()[limb] |= (val << shift);
if(shift > sizeof(limb_type) * CHAR_BIT - 3)
{
// Deal with the bits in val that overflow into the next limb:
val >>= (sizeof(limb_type) * CHAR_BIT - shift);
if(val)
{
// If this is the most-significant-limb, we may need to allocate an extra one for the overflow:
if(limb + 1 == newsize)
result.resize(static_cast<unsigned>(newsize + 1), static_cast<unsigned>(newsize + 1));
if(result.size() > limb + 1)
{
result.limbs()[limb + 1] |= val;
}
}
}
}
++s;
bitcount -= 3;
}
result.normalize();
}
else
{
// Base 10, we extract blocks of size 10^9 at a time, that way
// the number of multiplications is kept to a minimum:
limb_type block_mult = max_block_10;
while(*s)
{
limb_type block = 0;
for(unsigned i = 0; i < digits_per_block_10; ++i)
{
limb_type val;
if(*s >= '0' && *s <= '9')
val = *s - '0';
else
BOOST_THROW_EXCEPTION(std::runtime_error("Unexpected character encountered in input."));
block *= 10;
block += val;
if(!*++s)
{
block_mult = block_multiplier(i);
break;
}
}
eval_multiply(result, block_mult);
eval_add(result, block);
}
}
}
if(isneg)
result.negate();
result.swap(*this);
}
public:
cpp_int_backend& operator = (const char* s)
{
do_assign_string(s, trivial_tag());
return *this;
}
BOOST_MP_FORCEINLINE void swap(cpp_int_backend& o) BOOST_NOEXCEPT
{
this->do_swap(o);
}
private:
std::string do_get_trivial_string(std::ios_base::fmtflags f, const mpl::false_&)const
{
typedef typename mpl::if_c<sizeof(typename base_type::local_limb_type) == 1, unsigned, typename base_type::local_limb_type>::type io_type;
if(this->sign() && (((f & std::ios_base::hex) == std::ios_base::hex) || ((f & std::ios_base::oct) == std::ios_base::oct)))
BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
std::stringstream ss;
ss.flags(f & ~std::ios_base::showpos);
ss << static_cast<io_type>(*this->limbs());
std::string result;
if(this->sign())
result += '-';
else if(f & std::ios_base::showpos)
result += '+';
result += ss.str();
return result;
}
std::string do_get_trivial_string(std::ios_base::fmtflags f, const mpl::true_&)const
{
// Even though we have only one limb, we can't do IO on it :-(
int base = 10;
if((f & std::ios_base::oct) == std::ios_base::oct)
base = 8;
else if((f & std::ios_base::hex) == std::ios_base::hex)
base = 16;
std::string result;
unsigned Bits = sizeof(typename base_type::local_limb_type) * CHAR_BIT;
if(base == 8 || base == 16)
{
if(this->sign())
BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
limb_type shift = base == 8 ? 3 : 4;
limb_type mask = static_cast<limb_type>((1u << shift) - 1);
typename base_type::local_limb_type v = *this->limbs();
result.assign(Bits / shift + (Bits % shift ? 1 : 0), '0');
std::string::difference_type pos = result.size() - 1;
for(unsigned i = 0; i < Bits / shift; ++i)
{
char c = '0' + static_cast<char>(v & mask);
if(c > '9')
c += 'A' - '9' - 1;
result[pos--] = c;
v >>= shift;
}
if(Bits % shift)
{
mask = static_cast<limb_type>((1u << (Bits % shift)) - 1);
char c = '0' + static_cast<char>(v & mask);
if(c > '9')
c += 'A' - '9';
result[pos] = c;
}
//
// Get rid of leading zeros:
//
std::string::size_type n = result.find_first_not_of('0');
if(!result.empty() && (n == std::string::npos))
n = result.size() - 1;
result.erase(0, n);
if(f & std::ios_base::showbase)
{
const char* pp = base == 8 ? "0" : "0x";
result.insert(static_cast<std::string::size_type>(0), pp);
}
}
else
{
result.assign(Bits / 3 + 1, '0');
std::string::difference_type pos = result.size() - 1;
typename base_type::local_limb_type v(*this->limbs());
bool neg = false;
if(this->sign())
{
neg = true;
}
while(v)
{
result[pos] = (v % 10) + '0';
--pos;
v /= 10;
}
std::string::size_type n = result.find_first_not_of('0');
result.erase(0, n);
if(result.empty())
result = "0";
if(neg)
result.insert(static_cast<std::string::size_type>(0), 1, '-');
else if(f & std::ios_base::showpos)
result.insert(static_cast<std::string::size_type>(0), 1, '+');
}
return result;
}
std::string do_get_string(std::ios_base::fmtflags f, const mpl::true_&)const
{
#ifdef BOOST_MP_NO_DOUBLE_LIMB_TYPE_IO
return do_get_trivial_string(f, mpl::bool_<is_same<typename base_type::local_limb_type, double_limb_type>::value>());
#else
return do_get_trivial_string(f, mpl::bool_<false>());
#endif
}
std::string do_get_string(std::ios_base::fmtflags f, const mpl::false_&)const
{
using default_ops::eval_get_sign;
int base = 10;
if((f & std::ios_base::oct) == std::ios_base::oct)
base = 8;
else if((f & std::ios_base::hex) == std::ios_base::hex)
base = 16;
std::string result;
unsigned Bits = this->size() * base_type::limb_bits;
if(base == 8 || base == 16)
{
if(this->sign())
BOOST_THROW_EXCEPTION(std::runtime_error("Base 8 or 16 printing of negative numbers is not supported."));
limb_type shift = base == 8 ? 3 : 4;
limb_type mask = static_cast<limb_type>((1u << shift) - 1);
cpp_int_backend t(*this);
result.assign(Bits / shift + ((Bits % shift) ? 1 : 0), '0');
std::string::difference_type pos = result.size() - 1;
for(unsigned i = 0; i < Bits / shift; ++i)
{
char c = '0' + static_cast<char>(t.limbs()[0] & mask);
if(c > '9')
c += 'A' - '9' - 1;
result[pos--] = c;
eval_right_shift(t, shift);
}
if(Bits % shift)
{
mask = static_cast<limb_type>((1u << (Bits % shift)) - 1);
char c = '0' + static_cast<char>(t.limbs()[0] & mask);
if(c > '9')
c += 'A' - '9';
result[pos] = c;
}
//
// Get rid of leading zeros:
//
std::string::size_type n = result.find_first_not_of('0');
if(!result.empty() && (n == std::string::npos))
n = result.size() - 1;
result.erase(0, n);
if(f & std::ios_base::showbase)
{
const char* pp = base == 8 ? "0" : "0x";
result.insert(static_cast<std::string::size_type>(0), pp);
}
}
else
{
result.assign(Bits / 3 + 1, '0');
std::string::difference_type pos = result.size() - 1;
cpp_int_backend t(*this);
cpp_int_backend r;
bool neg = false;
if(t.sign())
{
t.negate();
neg = true;
}
if(this->size() == 1)
{
result = boost::lexical_cast<std::string>(t.limbs()[0]);
}
else
{
cpp_int_backend block10;
block10 = max_block_10;
while(eval_get_sign(t) != 0)
{
cpp_int_backend t2;
divide_unsigned_helper(&t2, t, block10, r);
t = t2;
limb_type v = r.limbs()[0];
for(unsigned i = 0; i < digits_per_block_10; ++i)
{
char c = '0' + v % 10;
v /= 10;
result[pos] = c;
if(pos-- == 0)
break;
}
}
}
std::string::size_type n = result.find_first_not_of('0');
result.erase(0, n);
if(result.empty())
result = "0";
if(neg)
result.insert(static_cast<std::string::size_type>(0), 1, '-');
else if(f & std::ios_base::showpos)
result.insert(static_cast<std::string::size_type>(0), 1, '+');
}
return result;
}
public:
std::string str(std::streamsize /*digits*/, std::ios_base::fmtflags f)const
{
return do_get_string(f, trivial_tag());
}
private:
template <class Container>
void construct_from_container(const Container& c, const mpl::false_&)
{
//
// We assume that c is a sequence of (unsigned) bytes with the most significant byte first:
//
unsigned newsize = static_cast<unsigned>(c.size() / sizeof(limb_type));
if(c.size() % sizeof(limb_type))
{
++newsize;
}
if(newsize)
{
this->resize(newsize, newsize); // May throw
std::memset(this->limbs(), 0, this->size());
typename Container::const_iterator i(c.begin()), j(c.end());
unsigned byte_location = static_cast<unsigned>(c.size() - 1);
while(i != j)
{
unsigned limb = byte_location / sizeof(limb_type);
unsigned shift = (byte_location % sizeof(limb_type)) * CHAR_BIT;
if(this->size() > limb)
this->limbs()[limb] |= static_cast<limb_type>(static_cast<unsigned char>(*i)) << shift;
++i;
--byte_location;
}
}
}
template <class Container>
void construct_from_container(const Container& c, const mpl::true_&)
{
//
// We assume that c is a sequence of (unsigned) bytes with the most significant byte first:
//
typedef typename base_type::local_limb_type local_limb_type;
*this->limbs() = 0;
if(c.size())
{
typename Container::const_iterator i(c.begin()), j(c.end());
unsigned byte_location = static_cast<unsigned>(c.size() - 1);
while(i != j)
{
unsigned limb = byte_location / sizeof(local_limb_type);
unsigned shift = (byte_location % sizeof(local_limb_type)) * CHAR_BIT;
if(limb == 0)
this->limbs()[0] |= static_cast<limb_type>(static_cast<unsigned char>(*i)) << shift;
++i;
--byte_location;
}
}
}
public:
template <class Container>
cpp_int_backend(const Container& c, typename boost::enable_if_c<boost::multiprecision::detail::is_byte_container<Container>::value>::type const* = 0)
{
//
// We assume that c is a sequence of (unsigned) bytes with the most significant byte first:
//
construct_from_container(c, trivial_tag());
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::false_&, const mpl::false_&)const BOOST_NOEXCEPT
{
if(this->sign() != o.sign())
return this->sign() ? -1 : 1;
// Only do the compare if the same sign:
int result = compare_unsigned(o);
if(this->sign())
result = -result;
return result;
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::true_&, const mpl::false_&)const
{
cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> t(*this);
return t.compare(o);
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::false_&, const mpl::true_&)const
{
cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> t(o);
return compare(t);
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
int compare_imp(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o, const mpl::true_&, const mpl::true_&)const BOOST_NOEXCEPT
{
if(this->sign())
{
if(o.sign())
{
return *this->limbs() < *o.limbs() ? 1 : (*this->limbs() > *o.limbs() ? -1 : 0);
}
else
return -1;
}
else
{
if(o.sign())
return 1;
return *this->limbs() < *o.limbs() ? -1 : (*this->limbs() > *o.limbs() ? 1 : 0);
}
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
int compare(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o)const BOOST_NOEXCEPT
{
typedef mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value> t1;
typedef mpl::bool_<is_trivial_cpp_int<cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> >::value> t2;
return compare_imp(o, t1(), t2());
}
template <unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
int compare_unsigned(const cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2>& o)const BOOST_NOEXCEPT
{
if(this->size() != o.size())
{
return this->size() > o.size() ? 1 : -1;
}
typename base_type::const_limb_pointer pa = this->limbs();
typename base_type::const_limb_pointer pb = o.limbs();
for(int i = this->size() - 1; i >= 0; --i)
{
if(pa[i] != pb[i])
return pa[i] > pb[i] ? 1 : -1;
}
return 0;
}
template <class Arithmetic>
BOOST_MP_FORCEINLINE typename boost::enable_if<is_arithmetic<Arithmetic>, int>::type compare(Arithmetic i)const
{
// braindead version:
cpp_int_backend t;
t = i;
return compare(t);
}
};
} // namespace backends
namespace default_ops{
template <class Backend>
struct double_precision_type;
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct double_precision_type<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >
{
typedef typename mpl::if_c<
backends::is_fixed_precision<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
backends::cpp_int_backend<
(is_void<Allocator>::value ?
2 * backends::max_precision<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value
: MinBits),
2 * backends::max_precision<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> >::value,
SignType,
Checked,
Allocator>,
backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>
>::type type;
};
}
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked>
struct expression_template_default<backends::cpp_int_backend<MinBits, MaxBits, SignType, Checked, void> >
{
static const expression_template_option value = et_off;
};
using boost::multiprecision::backends::cpp_int_backend;
template <unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator>
struct number_category<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator> > : public mpl::int_<number_kind_integer>{};
typedef number<cpp_int_backend<> > cpp_int;
typedef rational_adaptor<cpp_int_backend<> > cpp_rational_backend;
typedef number<cpp_rational_backend> cpp_rational;
// Fixed precision unsigned types:
typedef number<cpp_int_backend<128, 128, unsigned_magnitude, unchecked, void> > uint128_t;
typedef number<cpp_int_backend<256, 256, unsigned_magnitude, unchecked, void> > uint256_t;
typedef number<cpp_int_backend<512, 512, unsigned_magnitude, unchecked, void> > uint512_t;
typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, unchecked, void> > uint1024_t;
// Fixed precision signed types:
typedef number<cpp_int_backend<128, 128, signed_magnitude, unchecked, void> > int128_t;
typedef number<cpp_int_backend<256, 256, signed_magnitude, unchecked, void> > int256_t;
typedef number<cpp_int_backend<512, 512, signed_magnitude, unchecked, void> > int512_t;
typedef number<cpp_int_backend<1024, 1024, signed_magnitude, unchecked, void> > int1024_t;
// Over again, but with checking enabled this time:
typedef number<cpp_int_backend<0, 0, signed_magnitude, checked> > checked_cpp_int;
typedef rational_adaptor<cpp_int_backend<0, 0, signed_magnitude, checked> > checked_cpp_rational_backend;
typedef number<checked_cpp_rational_backend> checked_cpp_rational;
// Fixed precision unsigned types:
typedef number<cpp_int_backend<128, 128, unsigned_magnitude, checked, void> > checked_uint128_t;
typedef number<cpp_int_backend<256, 256, unsigned_magnitude, checked, void> > checked_uint256_t;
typedef number<cpp_int_backend<512, 512, unsigned_magnitude, checked, void> > checked_uint512_t;
typedef number<cpp_int_backend<1024, 1024, unsigned_magnitude, checked, void> > checked_uint1024_t;
// Fixed precision signed types:
typedef number<cpp_int_backend<128, 128, signed_magnitude, checked, void> > checked_int128_t;
typedef number<cpp_int_backend<256, 256, signed_magnitude, checked, void> > checked_int256_t;
typedef number<cpp_int_backend<512, 512, signed_magnitude, checked, void> > checked_int512_t;
typedef number<cpp_int_backend<1024, 1024, signed_magnitude, checked, void> > checked_int1024_t;
#ifdef BOOST_NO_SFINAE_EXPR
namespace detail{
template<unsigned MinBits, unsigned MaxBits, cpp_integer_type SignType, cpp_int_check_type Checked, class Allocator, unsigned MinBits2, unsigned MaxBits2, cpp_integer_type SignType2, cpp_int_check_type Checked2, class Allocator2>
struct is_explicitly_convertible<cpp_int_backend<MinBits, MaxBits, SignType, Checked, Allocator>, cpp_int_backend<MinBits2, MaxBits2, SignType2, Checked2, Allocator2> > : public mpl::true_ {};
}
#endif
#ifdef _MSC_VER
#pragma warning(pop)
#endif
}} // namespaces
//
// Last of all we include the implementations of all the eval_* non member functions:
//
#include <boost/multiprecision/cpp_int/comparison.hpp>
#include <boost/multiprecision/cpp_int/add.hpp>
#include <boost/multiprecision/cpp_int/multiply.hpp>
#include <boost/multiprecision/cpp_int/divide.hpp>
#include <boost/multiprecision/cpp_int/bitwise.hpp>
#include <boost/multiprecision/cpp_int/misc.hpp>
#include <boost/multiprecision/cpp_int/limits.hpp>
#ifdef BOOST_MP_USER_DEFINED_LITERALS
#include <boost/multiprecision/cpp_int/literals.hpp>
#endif
#include <boost/multiprecision/cpp_int/serialize.hpp>
#include <boost/multiprecision/cpp_int/import_export.hpp>
#endif
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