ClickHouse/base/common/wide_integer_impl.h
2020-10-10 21:37:02 +03:00

1340 lines
42 KiB
C++

#pragma once
/// Original is here https://github.com/cerevra/int
/// Distributed under the Boost Software License, Version 1.0.
/// (See at http://www.boost.org/LICENSE_1_0.txt)
#include "throwError.h"
namespace wide
{
template <typename T>
struct IsWideInteger
{
static const constexpr bool value = false;
};
template <size_t Bits, typename Signed>
struct IsWideInteger<wide::integer<Bits, Signed>>
{
static const constexpr bool value = true;
};
template <typename T>
static constexpr bool ArithmeticConcept() noexcept
{
return std::is_arithmetic_v<T> || IsWideInteger<T>::value;
}
template <typename T>
static constexpr bool IntegralConcept() noexcept
{
return std::is_integral_v<T> || IsWideInteger<T>::value;
}
}
namespace std
{
// numeric limits
template <size_t Bits, typename Signed>
class numeric_limits<wide::integer<Bits, Signed>>
{
public:
static constexpr bool is_specialized = true;
static constexpr bool is_signed = is_same<Signed, signed>::value;
static constexpr bool is_integer = true;
static constexpr bool is_exact = true;
static constexpr bool has_infinity = false;
static constexpr bool has_quiet_NaN = false;
static constexpr bool has_signaling_NaN = true;
static constexpr std::float_denorm_style has_denorm = std::denorm_absent;
static constexpr bool has_denorm_loss = false;
static constexpr std::float_round_style round_style = std::round_toward_zero;
static constexpr bool is_iec559 = false;
static constexpr bool is_bounded = true;
static constexpr bool is_modulo = true;
static constexpr int digits = Bits - (is_same<Signed, signed>::value ? 1 : 0);
static constexpr int digits10 = digits * 0.30103 /*std::log10(2)*/;
static constexpr int max_digits10 = 0;
static constexpr int radix = 2;
static constexpr int min_exponent = 0;
static constexpr int min_exponent10 = 0;
static constexpr int max_exponent = 0;
static constexpr int max_exponent10 = 0;
static constexpr bool traps = true;
static constexpr bool tinyness_before = false;
static constexpr wide::integer<Bits, Signed> min() noexcept
{
if (is_same<Signed, signed>::value)
{
using T = wide::integer<Bits, signed>;
T res{};
res.items[T::_impl::big(0)] = std::numeric_limits<typename wide::integer<Bits, Signed>::signed_base_type>::min();
return res;
}
return 0;
}
static constexpr wide::integer<Bits, Signed> max() noexcept
{
using T = wide::integer<Bits, Signed>;
T res{};
res.items[T::_impl::big(0)] = is_same<Signed, signed>::value
? std::numeric_limits<typename wide::integer<Bits, Signed>::signed_base_type>::max()
: std::numeric_limits<typename wide::integer<Bits, Signed>::base_type>::max();
for (unsigned i = 1; i < wide::integer<Bits, Signed>::_impl::item_count; ++i)
{
res.items[T::_impl::big(i)] = std::numeric_limits<typename wide::integer<Bits, Signed>::base_type>::max();
}
return res;
}
static constexpr wide::integer<Bits, Signed> lowest() noexcept { return min(); }
static constexpr wide::integer<Bits, Signed> epsilon() noexcept { return 0; }
static constexpr wide::integer<Bits, Signed> round_error() noexcept { return 0; }
static constexpr wide::integer<Bits, Signed> infinity() noexcept { return 0; }
static constexpr wide::integer<Bits, Signed> quiet_NaN() noexcept { return 0; }
static constexpr wide::integer<Bits, Signed> signaling_NaN() noexcept { return 0; }
static constexpr wide::integer<Bits, Signed> denorm_min() noexcept { return 0; }
};
// type traits
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
struct common_type<wide::integer<Bits, Signed>, wide::integer<Bits2, Signed2>>
{
using type = std::conditional_t < Bits == Bits2,
wide::integer<
Bits,
std::conditional_t<(std::is_same_v<Signed, Signed2> && std::is_same_v<Signed2, signed>), signed, unsigned>>,
std::conditional_t<Bits2<Bits, wide::integer<Bits, Signed>, wide::integer<Bits2, Signed2>>>;
};
template <size_t Bits, typename Signed, typename Arithmetic>
struct common_type<wide::integer<Bits, Signed>, Arithmetic>
{
static_assert(wide::ArithmeticConcept<Arithmetic>());
using type = std::conditional_t<
std::is_floating_point_v<Arithmetic>,
Arithmetic,
std::conditional_t<
sizeof(Arithmetic) < Bits * sizeof(long),
wide::integer<Bits, Signed>,
std::conditional_t<
Bits * sizeof(long) < sizeof(Arithmetic),
Arithmetic,
std::conditional_t<
Bits * sizeof(long) == sizeof(Arithmetic) && (std::is_same_v<Signed, signed> || std::is_signed_v<Arithmetic>),
Arithmetic,
wide::integer<Bits, Signed>>>>>;
};
template <typename Arithmetic, size_t Bits, typename Signed>
struct common_type<Arithmetic, wide::integer<Bits, Signed>> : common_type<wide::integer<Bits, Signed>, Arithmetic>
{
};
}
namespace wide
{
template <size_t Bits, typename Signed>
struct integer<Bits, Signed>::_impl
{
static constexpr size_t _Bits = Bits;
static constexpr const unsigned byte_count = Bits / 8;
static constexpr const unsigned item_count = byte_count / sizeof(base_type);
static constexpr const unsigned base_bits = sizeof(base_type) * 8;
static_assert(Bits % base_bits == 0);
/// Simple iteration in both directions
static constexpr unsigned little(unsigned idx) { return idx; }
static constexpr unsigned big(unsigned idx) { return item_count - 1 - idx; }
static constexpr unsigned any(unsigned idx) { return idx; }
template <class T>
constexpr static bool is_negative(const T & n) noexcept
{
if constexpr (std::is_signed_v<T>)
return n < 0;
else
return false;
}
template <size_t B, class T>
constexpr static bool is_negative(const integer<B, T> & n) noexcept
{
if constexpr (std::is_same_v<T, signed>)
return static_cast<signed_base_type>(n.items[big(0)]) < 0;
else
return false;
}
template <typename T>
constexpr static auto make_positive(const T & n) noexcept
{
if constexpr (std::is_signed_v<T>)
return n < 0 ? -n : n;
else
return n;
}
template <size_t B, class S>
constexpr static integer<B, S> make_positive(const integer<B, S> & n) noexcept
{
return is_negative(n) ? operator_unary_minus(n) : n;
}
template <typename T>
constexpr static auto to_Integral(T f) noexcept
{
if constexpr (std::is_same_v<T, __int128>)
return f;
else if constexpr (std::is_signed_v<T>)
return static_cast<int64_t>(f);
else
return static_cast<uint64_t>(f);
}
template <typename Integral>
constexpr static void wide_integer_from_bultin(integer<Bits, Signed> & self, Integral rhs) noexcept
{
self.items[0] = _impl::to_Integral(rhs);
if constexpr (std::is_same_v<Integral, __int128>)
self.items[1] = rhs >> base_bits;
constexpr const unsigned start = (sizeof(Integral) == 16) ? 2 : 1;
if constexpr (std::is_signed_v<Integral>)
{
if (rhs < 0)
{
for (unsigned i = start; i < item_count; ++i)
self.items[i] = -1;
return;
}
}
for (unsigned i = start; i < item_count; ++i)
self.items[i] = 0;
}
constexpr static void wide_integer_from_bultin(integer<Bits, Signed> & self, double rhs) noexcept
{
if ((rhs > 0 && rhs < std::numeric_limits<uint64_t>::max()) || (rhs < 0 && rhs > std::numeric_limits<int64_t>::min()))
{
self = to_Integral(rhs);
return;
}
long double r = rhs;
if (r < 0)
r = -r;
size_t count = r / std::numeric_limits<uint64_t>::max();
self = count;
self *= std::numeric_limits<uint64_t>::max();
long double to_diff = count;
to_diff *= std::numeric_limits<uint64_t>::max();
self += to_Integral(r - to_diff);
if (rhs < 0)
self = -self;
}
template <size_t Bits2, typename Signed2>
constexpr static void
wide_integer_from_wide_integer(integer<Bits, Signed> & self, const integer<Bits2, Signed2> & rhs) noexcept
{
constexpr const unsigned min_bits = (Bits < Bits2) ? Bits : Bits2;
constexpr const unsigned to_copy = min_bits / base_bits;
for (unsigned i = 0; i < to_copy; ++i)
self.items[i] = rhs.items[i];
if constexpr (Bits > Bits2)
{
if constexpr (std::is_signed_v<Signed2>)
{
if (rhs < 0)
{
for (unsigned i = to_copy; i < item_count; ++i)
self.items[i] = -1;
return;
}
}
for (unsigned i = to_copy; i < item_count; ++i)
self.items[i] = 0;
}
}
template <typename T>
constexpr static bool should_keep_size()
{
return sizeof(T) <= byte_count;
}
constexpr static integer<Bits, Signed> shift_left(const integer<Bits, Signed> & rhs, unsigned n) noexcept
{
integer<Bits, Signed> lhs;
unsigned items_shift = n / base_bits;
if (unsigned bit_shift = n % base_bits)
{
unsigned overflow_shift = base_bits - bit_shift;
lhs.items[big(0)] = rhs.items[big(items_shift)] << bit_shift;
for (unsigned i = 1; i < item_count - items_shift; ++i)
{
lhs.items[big(i - 1)] |= rhs.items[big(items_shift + i)] >> overflow_shift;
lhs.items[big(i)] = rhs.items[big(items_shift + i)] << bit_shift;
}
}
else
{
for (unsigned i = 0; i < item_count - items_shift; ++i)
lhs.items[big(i)] = rhs.items[big(items_shift + i)];
}
for (unsigned i = 0; i < items_shift; ++i)
lhs.items[little(i)] = 0;
return lhs;
}
constexpr static integer<Bits, Signed> shift_right(const integer<Bits, Signed> & rhs, unsigned n) noexcept
{
integer<Bits, Signed> lhs;
unsigned items_shift = n / base_bits;
unsigned bit_shift = n % base_bits;
if (bit_shift)
{
unsigned overflow_shift = base_bits - bit_shift;
lhs.items[little(0)] = rhs.items[little(items_shift)] >> bit_shift;
for (unsigned i = 1; i < item_count - items_shift; ++i)
{
lhs.items[little(i - 1)] |= rhs.items[little(items_shift + i)] << overflow_shift;
lhs.items[little(i)] = rhs.items[little(items_shift + i)] >> bit_shift;
}
}
else
{
for (unsigned i = 0; i < item_count - items_shift; ++i)
lhs.items[little(i)] = rhs.items[little(items_shift + i)];
}
if (is_negative(rhs))
{
if (bit_shift)
lhs.items[big(items_shift)] |= std::numeric_limits<base_type>::max() << (base_bits - bit_shift);
for (unsigned i = item_count - items_shift; i < items_shift; ++i)
lhs.items[little(i)] = std::numeric_limits<base_type>::max();
}
else
{
for (unsigned i = item_count - items_shift; i < items_shift; ++i)
lhs.items[little(i)] = 0;
}
return lhs;
}
private:
template <typename T>
constexpr static base_type get_item(const T & x, unsigned number)
{
if constexpr (IsWideInteger<T>::value)
{
if (number < T::_impl::item_count)
return x.items[number];
return 0;
}
else
{
if constexpr (sizeof(T) <= sizeof(base_type))
{
if (!number)
return x;
}
else if (number * sizeof(base_type) < sizeof(T))
return x >> (number * base_bits); // & std::numeric_limits<base_type>::max()
return 0;
}
}
template <typename T>
constexpr static integer<Bits, Signed>
minus(const integer<Bits, Signed> & lhs, T rhs)
{
constexpr const unsigned rhs_items = (sizeof(T) > sizeof(base_type)) ? (sizeof(T) / sizeof(base_type)) : 1;
constexpr const unsigned op_items = (item_count < rhs_items) ? item_count : rhs_items;
integer<Bits, Signed> res(lhs);
bool underflows[item_count] = {};
for (unsigned i = 0; i < op_items; ++i)
{
base_type rhs_item = get_item(rhs, i);
base_type & res_item = res.items[little(i)];
underflows[i] = res_item < rhs_item;
res_item -= rhs_item;
}
for (unsigned i = 1; i < item_count; ++i)
{
if (underflows[i-1])
{
base_type & res_item = res.items[little(i)];
if (res_item == 0)
underflows[i] = true;
--res_item;
}
}
return res;
}
template <typename T>
constexpr static integer<Bits, Signed>
plus(const integer<Bits, Signed> & lhs, T rhs)
{
constexpr const unsigned rhs_items = (sizeof(T) > sizeof(base_type)) ? (sizeof(T) / sizeof(base_type)) : 1;
constexpr const unsigned op_items = (item_count < rhs_items) ? item_count : rhs_items;
integer<Bits, Signed> res(lhs);
bool overflows[item_count] = {};
for (unsigned i = 0; i < op_items; ++i)
{
base_type rhs_item = get_item(rhs, i);
base_type & res_item = res.items[little(i)];
res_item += rhs_item;
overflows[i] = res_item < rhs_item;
}
for (unsigned i = 1; i < item_count; ++i)
{
if (overflows[i-1])
{
base_type & res_item = res.items[little(i)];
++res_item;
if (res_item == 0)
overflows[i] = true;
}
}
return res;
}
template <typename T>
constexpr static integer<Bits, Signed>
multiply(const integer<Bits, Signed> & lhs, const T & rhs)
{
if constexpr (Bits == 256 && sizeof(base_type) == 8)
{
/// @sa https://github.com/abseil/abseil-cpp/blob/master/absl/numeric/int128.h
using HalfType = unsigned __int128;
HalfType a01 = (HalfType(lhs.items[little(1)]) << 64) + lhs.items[little(0)];
HalfType a23 = (HalfType(lhs.items[little(3)]) << 64) + lhs.items[little(2)];
HalfType a0 = lhs.items[little(0)];
HalfType a1 = lhs.items[little(1)];
HalfType b01 = rhs;
uint64_t b0 = b01;
uint64_t b1 = 0;
HalfType b23 = 0;
if constexpr (sizeof(T) > 8)
b1 = b01 >> 64;
if constexpr (sizeof(T) > 16)
b23 = (HalfType(rhs.items[little(3)]) << 64) + rhs.items[little(2)];
HalfType r23 = a23 * b01 + a01 * b23 + a1 * b1;
HalfType r01 = a0 * b0;
HalfType r12 = (r01 >> 64) + (r23 << 64);
HalfType r12_x = a1 * b0;
integer<Bits, Signed> res;
res.items[little(0)] = r01;
res.items[little(3)] = r23 >> 64;
if constexpr (sizeof(T) > 8)
{
HalfType r12_y = a0 * b1;
r12_x += r12_y;
if (r12_x < r12_y)
++res.items[little(3)];
}
r12 += r12_x;
if (r12 < r12_x)
++res.items[little(3)];
res.items[little(1)] = r12;
res.items[little(2)] = r12 >> 64;
return res;
}
else
{
integer<Bits, Signed> res{};
#if 1
integer<Bits, Signed> lhs2 = plus(lhs, shift_left(lhs, 1));
integer<Bits, Signed> lhs3 = plus(lhs2, shift_left(lhs, 2));
#endif
for (unsigned i = 0; i < item_count; ++i)
{
base_type rhs_item = get_item(rhs, i);
unsigned pos = i * base_bits;
while (rhs_item)
{
#if 1 /// optimization
if ((rhs_item & 0x7) == 0x7)
{
res = plus(res, shift_left(lhs3, pos));
rhs_item >>= 3;
pos += 3;
continue;
}
if ((rhs_item & 0x3) == 0x3)
{
res = plus(res, shift_left(lhs2, pos));
rhs_item >>= 2;
pos += 2;
continue;
}
#endif
if (rhs_item & 1)
res = plus(res, shift_left(lhs, pos));
rhs_item >>= 1;
++pos;
}
}
return res;
}
}
public:
constexpr static integer<Bits, Signed> operator_unary_tilda(const integer<Bits, Signed> & lhs) noexcept
{
integer<Bits, Signed> res;
for (unsigned i = 0; i < item_count; ++i)
res.items[any(i)] = ~lhs.items[any(i)];
return res;
}
constexpr static integer<Bits, Signed>
operator_unary_minus(const integer<Bits, Signed> & lhs) noexcept(std::is_same_v<Signed, unsigned>)
{
return plus(operator_unary_tilda(lhs), 1);
}
template <typename T>
constexpr static auto operator_plus(const integer<Bits, Signed> & lhs, const T & rhs) noexcept(std::is_same_v<Signed, unsigned>)
{
if constexpr (should_keep_size<T>())
{
if (is_negative(rhs))
return minus(lhs, -rhs);
else
return plus(lhs, rhs);
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, integer<T::_impl::_Bits, Signed>>::_impl::operator_plus(
integer<T::_impl::_Bits, Signed>(lhs), rhs);
}
}
template <typename T>
constexpr static auto operator_minus(const integer<Bits, Signed> & lhs, const T & rhs) noexcept(std::is_same_v<Signed, unsigned>)
{
if constexpr (should_keep_size<T>())
{
if (is_negative(rhs))
return plus(lhs, -rhs);
else
return minus(lhs, rhs);
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, integer<T::_impl::_Bits, Signed>>::_impl::operator_minus(
integer<T::_impl::_Bits, Signed>(lhs), rhs);
}
}
template <typename T>
constexpr static auto operator_star(const integer<Bits, Signed> & lhs, const T & rhs)
{
if constexpr (should_keep_size<T>())
{
integer<Bits, Signed> res;
if constexpr (std::is_signed_v<Signed>)
{
res = multiply((is_negative(lhs) ? make_positive(lhs) : lhs),
(is_negative(rhs) ? make_positive(rhs) : rhs));
}
else
{
res = multiply(lhs, (is_negative(rhs) ? make_positive(rhs) : rhs));
}
if (std::is_same_v<Signed, signed> && is_negative(lhs) != is_negative(rhs))
res = operator_unary_minus(res);
return res;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, T>::_impl::operator_star(T(lhs), rhs);
}
}
template <typename T>
constexpr static bool operator_more(const integer<Bits, Signed> & lhs, const T & rhs) noexcept
{
if constexpr (should_keep_size<T>())
{
if (std::numeric_limits<T>::is_signed && (is_negative(lhs) != is_negative(rhs)))
return is_negative(rhs);
for (unsigned i = 0; i < item_count; ++i)
{
base_type rhs_item = get_item(rhs, big(i));
if (lhs.items[big(i)] != rhs_item)
return lhs.items[big(i)] > rhs_item;
}
return false;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, T>::_impl::operator_more(T(lhs), rhs);
}
}
template <typename T>
constexpr static bool operator_less(const integer<Bits, Signed> & lhs, const T & rhs) noexcept
{
if constexpr (should_keep_size<T>())
{
if (std::numeric_limits<T>::is_signed && (is_negative(lhs) != is_negative(rhs)))
return is_negative(lhs);
for (unsigned i = 0; i < item_count; ++i)
{
base_type rhs_item = get_item(rhs, big(i));
if (lhs.items[big(i)] != rhs_item)
return lhs.items[big(i)] < rhs_item;
}
return false;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, T>::_impl::operator_less(T(lhs), rhs);
}
}
template <typename T>
constexpr static bool operator_eq(const integer<Bits, Signed> & lhs, const T & rhs) noexcept
{
if constexpr (should_keep_size<T>())
{
for (unsigned i = 0; i < item_count; ++i)
{
base_type rhs_item = get_item(rhs, any(i));
if (lhs.items[any(i)] != rhs_item)
return false;
}
return true;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, T>::_impl::operator_eq(T(lhs), rhs);
}
}
template <typename T>
constexpr static auto operator_pipe(const integer<Bits, Signed> & lhs, const T & rhs) noexcept
{
if constexpr (should_keep_size<T>())
{
integer<Bits, Signed> res;
for (unsigned i = 0; i < item_count; ++i)
res.items[little(i)] = lhs.items[little(i)] | get_item(rhs, i);
return res;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, T>::_impl::operator_pipe(T(lhs), rhs);
}
}
template <typename T>
constexpr static auto operator_amp(const integer<Bits, Signed> & lhs, const T & rhs) noexcept
{
if constexpr (should_keep_size<T>())
{
integer<Bits, Signed> res;
for (unsigned i = 0; i < item_count; ++i)
res.items[little(i)] = lhs.items[little(i)] & get_item(rhs, i);
return res;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, T>::_impl::operator_amp(T(lhs), rhs);
}
}
private:
template <typename T>
constexpr static bool is_zero(const T & x)
{
bool is_zero = true;
for (auto item : x.items)
{
if (item != 0)
{
is_zero = false;
break;
}
}
return is_zero;
}
/// returns quotient as result and remainder in numerator.
template <typename T>
constexpr static T divide(T & numerator, T && denominator)
{
if (is_zero(denominator))
throwError("divide by zero");
T & n = numerator;
T & d = denominator;
T x = 1;
T quotient = 0;
while (!operator_more(d, n) && operator_eq(operator_amp(shift_right(d, base_bits * item_count - 1), 1), 0))
{
x = shift_left(x, 1);
d = shift_left(d, 1);
}
while (!operator_eq(x, 0))
{
if (!operator_more(d, n))
{
n = operator_minus(n, d);
quotient = operator_pipe(quotient, x);
}
x = shift_right(x, 1);
d = shift_right(d, 1);
}
return quotient;
}
public:
template <typename T>
constexpr static auto operator_slash(const integer<Bits, Signed> & lhs, const T & rhs)
{
if constexpr (should_keep_size<T>())
{
integer<Bits, Signed> numerator = make_positive(lhs);
integer<Bits, Signed> quotient = divide(numerator, make_positive(integer<Bits, Signed>(rhs)));
if (std::is_same_v<Signed, signed> && is_negative(rhs) != is_negative(lhs))
quotient = operator_unary_minus(quotient);
return quotient;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, integer<T::_impl::_Bits, Signed>>::operator_slash(T(lhs), rhs);
}
}
template <typename T>
constexpr static auto operator_percent(const integer<Bits, Signed> & lhs, const T & rhs)
{
if constexpr (should_keep_size<T>())
{
integer<Bits, Signed> remainder = make_positive(lhs);
divide(remainder, make_positive(integer<Bits, Signed>(rhs)));
if (std::is_same_v<Signed, signed> && is_negative(lhs))
remainder = operator_unary_minus(remainder);
return remainder;
}
else
{
static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, integer<T::_impl::_Bits, Signed>>::operator_percent(T(lhs), rhs);
}
}
// ^
template <typename T>
constexpr static auto operator_circumflex(const integer<Bits, Signed> & lhs, const T & rhs) noexcept
{
if constexpr (should_keep_size<T>())
{
integer<Bits, Signed> t(rhs);
integer<Bits, Signed> res = lhs;
for (unsigned i = 0; i < item_count; ++i)
res.items[any(i)] ^= t.items[any(i)];
return res;
}
else
{
static_assert(IsWideInteger<T>::value);
return T::operator_circumflex(T(lhs), rhs);
}
}
constexpr static integer<Bits, Signed> from_str(const char * c)
{
integer<Bits, Signed> res = 0;
bool is_neg = std::is_same_v<Signed, signed> && *c == '-';
if (is_neg)
++c;
if (*c == '0' && (*(c + 1) == 'x' || *(c + 1) == 'X'))
{ // hex
++c;
++c;
while (*c)
{
if (*c >= '0' && *c <= '9')
{
res = multiply(res, 16U);
res = plus(res, *c - '0');
++c;
}
else if (*c >= 'a' && *c <= 'f')
{
res = multiply(res, 16U);
res = plus(res, *c - 'a' + 10U);
++c;
}
else if (*c >= 'A' && *c <= 'F')
{ // tolower must be used, but it is not constexpr
res = multiply(res, 16U);
res = plus(res, *c - 'A' + 10U);
++c;
}
else
throwError("invalid char from");
}
}
else
{ // dec
while (*c)
{
if (*c < '0' || *c > '9')
throwError("invalid char from");
res = multiply(res, 10U);
res = plus(res, *c - '0');
++c;
}
}
if (is_neg)
res = operator_unary_minus(res);
return res;
}
};
// Members
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed>::integer(T rhs) noexcept
: items{}
{
if constexpr (IsWideInteger<T>::value)
_impl::wide_integer_from_wide_integer(*this, rhs);
else
_impl::wide_integer_from_bultin(*this, rhs);
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed>::integer(std::initializer_list<T> il) noexcept
: items{}
{
if (il.size() == 1)
{
if constexpr (IsWideInteger<T>::value)
_impl::wide_integer_from_wide_integer(*this, *il.begin());
else
_impl::wide_integer_from_bultin(*this, *il.begin());
}
else
_impl::wide_integer_from_bultin(*this, 0);
}
template <size_t Bits, typename Signed>
template <size_t Bits2, typename Signed2>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator=(const integer<Bits2, Signed2> & rhs) noexcept
{
_impl::wide_integer_from_wide_integer(*this, rhs);
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator=(T rhs) noexcept
{
_impl::wide_integer_from_bultin(*this, rhs);
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator*=(const T & rhs)
{
*this = *this * rhs;
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator/=(const T & rhs)
{
*this = *this / rhs;
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator+=(const T & rhs) noexcept(std::is_same_v<Signed, unsigned>)
{
*this = *this + rhs;
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator-=(const T & rhs) noexcept(std::is_same_v<Signed, unsigned>)
{
*this = *this - rhs;
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator%=(const T & rhs)
{
*this = *this % rhs;
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator&=(const T & rhs) noexcept
{
*this = *this & rhs;
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator|=(const T & rhs) noexcept
{
*this = *this | rhs;
return *this;
}
template <size_t Bits, typename Signed>
template <typename T>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator^=(const T & rhs) noexcept
{
*this = *this ^ rhs;
return *this;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator<<=(int n) noexcept
{
if (static_cast<size_t>(n) >= Bits)
*this = 0;
else if (n > 0)
*this = _impl::shift_left(*this, n);
return *this;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator>>=(int n) noexcept
{
if (static_cast<size_t>(n) >= Bits)
{
if (is_negative(*this))
*this = -1;
else
*this = 0;
}
else if (n > 0)
*this = _impl::shift_right(*this, n);
return *this;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator++() noexcept(std::is_same_v<Signed, unsigned>)
{
*this = _impl::operator_plus(*this, 1);
return *this;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> integer<Bits, Signed>::operator++(int) noexcept(std::is_same_v<Signed, unsigned>)
{
auto tmp = *this;
*this = _impl::operator_plus(*this, 1);
return tmp;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> & integer<Bits, Signed>::operator--() noexcept(std::is_same_v<Signed, unsigned>)
{
*this = _impl::operator_minus(*this, 1);
return *this;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> integer<Bits, Signed>::operator--(int) noexcept(std::is_same_v<Signed, unsigned>)
{
auto tmp = *this;
*this = _impl::operator_minus(*this, 1);
return tmp;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed>::operator bool() const noexcept
{
return !_impl::operator_eq(*this, 0);
}
template <size_t Bits, typename Signed>
template <class T, class>
constexpr integer<Bits, Signed>::operator T() const noexcept
{
if constexpr (std::is_same_v<T, __int128>)
{
static_assert(Bits >= 128);
return (__int128(items[1]) << 64) | items[0];
}
else
{
static_assert(std::numeric_limits<T>::is_integer);
return items[0];
}
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed>::operator long double() const noexcept
{
if (_impl::operator_eq(*this, 0))
return 0;
integer<Bits, Signed> tmp = *this;
if (_impl::is_negative(*this))
tmp = -tmp;
long double res = 0;
for (unsigned i = 0; i < _impl::item_count; ++i)
{
long double t = res;
res *= std::numeric_limits<base_type>::max();
res += t;
res += tmp.items[_impl::big(i)];
}
if (_impl::is_negative(*this))
res = -res;
return res;
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed>::operator double() const noexcept
{
return static_cast<long double>(*this);
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed>::operator float() const noexcept
{
return static_cast<long double>(*this);
}
// Unary operators
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> operator~(const integer<Bits, Signed> & lhs) noexcept
{
return integer<Bits, Signed>::_impl::operator_unary_tilda(lhs);
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> operator-(const integer<Bits, Signed> & lhs) noexcept(std::is_same_v<Signed, unsigned>)
{
return integer<Bits, Signed>::_impl::operator_unary_minus(lhs);
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> operator+(const integer<Bits, Signed> & lhs) noexcept(std::is_same_v<Signed, unsigned>)
{
return lhs;
}
#define CT(x) \
std::common_type_t<std::decay_t<decltype(rhs)>, std::decay_t<decltype(lhs)>> { x }
// Binary operators
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator*(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_star(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
std::common_type_t<Arithmetic, Arithmetic2> constexpr operator*(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) * CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator/(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_slash(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
std::common_type_t<Arithmetic, Arithmetic2> constexpr operator/(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) / CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator+(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_plus(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
std::common_type_t<Arithmetic, Arithmetic2> constexpr operator+(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) + CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator-(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_minus(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
std::common_type_t<Arithmetic, Arithmetic2> constexpr operator-(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) - CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator%(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_percent(lhs, rhs);
}
template <typename Integral, typename Integral2, class>
std::common_type_t<Integral, Integral2> constexpr operator%(const Integral & lhs, const Integral2 & rhs)
{
return CT(lhs) % CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator&(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_amp(lhs, rhs);
}
template <typename Integral, typename Integral2, class>
std::common_type_t<Integral, Integral2> constexpr operator&(const Integral & lhs, const Integral2 & rhs)
{
return CT(lhs) & CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator|(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_pipe(lhs, rhs);
}
template <typename Integral, typename Integral2, class>
std::common_type_t<Integral, Integral2> constexpr operator|(const Integral & lhs, const Integral2 & rhs)
{
return CT(lhs) | CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>> constexpr
operator^(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_circumflex(lhs, rhs);
}
template <typename Integral, typename Integral2, class>
std::common_type_t<Integral, Integral2> constexpr operator^(const Integral & lhs, const Integral2 & rhs)
{
return CT(lhs) ^ CT(rhs);
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> operator<<(const integer<Bits, Signed> & lhs, int n) noexcept
{
if (static_cast<size_t>(n) >= Bits)
return 0;
if (n <= 0)
return lhs;
return integer<Bits, Signed>::_impl::shift_left(lhs, n);
}
template <size_t Bits, typename Signed>
constexpr integer<Bits, Signed> operator>>(const integer<Bits, Signed> & lhs, int n) noexcept
{
if (static_cast<size_t>(n) >= Bits)
return 0;
if (n <= 0)
return lhs;
return integer<Bits, Signed>::_impl::shift_right(lhs, n);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
constexpr bool operator<(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_less(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
constexpr bool operator<(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) < CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
constexpr bool operator>(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_more(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
constexpr bool operator>(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) > CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
constexpr bool operator<=(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_less(lhs, rhs)
|| std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_eq(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
constexpr bool operator<=(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) <= CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
constexpr bool operator>=(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_more(lhs, rhs)
|| std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_eq(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
constexpr bool operator>=(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) >= CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
constexpr bool operator==(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_eq(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
constexpr bool operator==(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) == CT(rhs);
}
template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
constexpr bool operator!=(const integer<Bits, Signed> & lhs, const integer<Bits2, Signed2> & rhs)
{
return !std::common_type_t<integer<Bits, Signed>, integer<Bits2, Signed2>>::_impl::operator_eq(lhs, rhs);
}
template <typename Arithmetic, typename Arithmetic2, class>
constexpr bool operator!=(const Arithmetic & lhs, const Arithmetic2 & rhs)
{
return CT(lhs) != CT(rhs);
}
#undef CT
}
namespace std
{
template <size_t Bits, typename Signed>
struct hash<wide::integer<Bits, Signed>>
{
std::size_t operator()(const wide::integer<Bits, Signed> & lhs) const
{
static_assert(Bits % (sizeof(size_t) * 8) == 0);
const auto * ptr = reinterpret_cast<const size_t *>(lhs.items);
unsigned count = Bits / (sizeof(size_t) * 8);
size_t res = 0;
for (unsigned i = 0; i < count; ++i)
res ^= ptr[i];
return res;
}
};
}