mirror of
https://github.com/ClickHouse/ClickHouse.git
synced 2024-11-25 09:02:00 +00:00
1425 lines
46 KiB
C++
1425 lines
46 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"
|
|
|
|
#include <cmath>
|
|
#include <cfloat>
|
|
#include <cassert>
|
|
#include <limits>
|
|
|
|
|
|
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 wide::integer<Bits, Signed>(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[integer<B, T>::_impl::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) ? integer<B, S>(operator_unary_minus(n)) : n;
|
|
}
|
|
|
|
template <typename T>
|
|
__attribute__((no_sanitize("undefined"))) constexpr static auto to_Integral(T f) noexcept
|
|
{
|
|
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_builtin(integer<Bits, Signed> & self, Integral rhs) noexcept
|
|
{
|
|
static_assert(sizeof(Integral) <= sizeof(base_type));
|
|
|
|
self.items[0] = _impl::to_Integral(rhs);
|
|
|
|
if constexpr (std::is_signed_v<Integral>)
|
|
{
|
|
if (rhs < 0)
|
|
{
|
|
for (size_t i = 1; i < item_count; ++i)
|
|
self.items[i] = -1;
|
|
return;
|
|
}
|
|
}
|
|
|
|
for (size_t i = 1; i < item_count; ++i)
|
|
self.items[i] = 0;
|
|
}
|
|
|
|
/**
|
|
* N.B. t is constructed from double, so max(t) = max(double) ~ 2^310
|
|
* the recursive call happens when t / 2^64 > 2^64, so there won't be more than 5 of them.
|
|
*
|
|
* t = a1 * max_int + b1, a1 > max_int, b1 < max_int
|
|
* a1 = a2 * max_int + b2, a2 > max_int, b2 < max_int
|
|
* a_(n - 1) = a_n * max_int + b2, a_n <= max_int <- base case.
|
|
*/
|
|
template <class T>
|
|
constexpr static void set_multiplier(integer<Bits, Signed> & self, T t) noexcept
|
|
{
|
|
constexpr uint64_t max_int = std::numeric_limits<uint64_t>::max();
|
|
|
|
/// Implementation specific behaviour on overflow (if we don't check here, stack overflow will triggered in bigint_cast).
|
|
if (!std::isfinite(t))
|
|
{
|
|
self = 0;
|
|
return;
|
|
}
|
|
|
|
const T alpha = t / static_cast<T>(max_int);
|
|
|
|
if (alpha <= static_cast<T>(max_int))
|
|
self = static_cast<uint64_t>(alpha);
|
|
else // max(double) / 2^64 will surely contain less than 52 precision bits, so speed up computations.
|
|
set_multiplier<double>(self, alpha);
|
|
|
|
self *= max_int;
|
|
self += static_cast<uint64_t>(t - floor(alpha) * static_cast<T>(max_int)); // += b_i
|
|
}
|
|
|
|
constexpr static void wide_integer_from_builtin(integer<Bits, Signed> & self, double rhs) noexcept
|
|
{
|
|
constexpr int64_t max_int = std::numeric_limits<int64_t>::max();
|
|
constexpr int64_t min_int = std::numeric_limits<int64_t>::lowest();
|
|
|
|
/// There are values in int64 that have more than 53 significant bits (in terms of double
|
|
/// representation). Such values, being promoted to double, are rounded up or down. If they are rounded up,
|
|
/// the result may not fit in 64 bits.
|
|
/// The example of such a number is 9.22337e+18.
|
|
/// As to_Integral does a static_cast to int64_t, it may result in UB.
|
|
/// The necessary check here is that long double has enough significant (mantissa) bits to store the
|
|
/// int64_t max value precisely.
|
|
|
|
// TODO Be compatible with Apple aarch64
|
|
#if not (defined(__APPLE__) && defined(__aarch64__))
|
|
static_assert(LDBL_MANT_DIG >= 64,
|
|
"On your system long double has less than 64 precision bits, "
|
|
"which may result in UB when initializing double from int64_t");
|
|
#endif
|
|
|
|
if (rhs > static_cast<long double>(min_int) && rhs < static_cast<long double>(max_int))
|
|
{
|
|
self = static_cast<int64_t>(rhs);
|
|
return;
|
|
}
|
|
|
|
const long double rhs_long_double = (static_cast<long double>(rhs) < 0)
|
|
? -static_cast<long double>(rhs)
|
|
: rhs;
|
|
|
|
set_multiplier(self, rhs_long_double);
|
|
|
|
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 = 0; i < items_shift; ++i)
|
|
lhs.items[big(i)] = std::numeric_limits<base_type>::max();
|
|
}
|
|
else
|
|
{
|
|
for (unsigned i = 0; i < items_shift; ++i)
|
|
lhs.items[big(i)] = 0;
|
|
}
|
|
|
|
return lhs;
|
|
}
|
|
|
|
private:
|
|
template <typename T>
|
|
constexpr static base_type get_item(const T & x, unsigned idx)
|
|
{
|
|
if constexpr (IsWideInteger<T>::value)
|
|
{
|
|
if (idx < T::_impl::item_count)
|
|
return x.items[idx];
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
if constexpr (sizeof(T) <= sizeof(base_type))
|
|
{
|
|
if (0 == idx)
|
|
return x;
|
|
}
|
|
else if (idx * sizeof(base_type) < sizeof(T))
|
|
return x >> (idx * 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 if constexpr (Bits == 128 && sizeof(base_type) == 8)
|
|
{
|
|
using CompilerUInt128 = unsigned __int128;
|
|
CompilerUInt128 a = (CompilerUInt128(lhs.items[1]) << 64) + lhs.items[0];
|
|
CompilerUInt128 b = (CompilerUInt128(rhs.items[1]) << 64) + rhs.items[0];
|
|
CompilerUInt128 c = a * b;
|
|
integer<Bits, Signed> res;
|
|
res.items[0] = c;
|
|
res.items[1] = c >> 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_greater(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_greater(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);
|
|
}
|
|
}
|
|
|
|
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 <size_t Bits2>
|
|
constexpr static integer<Bits2, unsigned> divide(integer<Bits2, unsigned> & numerator, integer<Bits2, unsigned> denominator)
|
|
{
|
|
static_assert(std::is_unsigned_v<Signed>);
|
|
|
|
if constexpr (Bits == 128 && sizeof(base_type) == 8)
|
|
{
|
|
using CompilerUInt128 = unsigned __int128;
|
|
|
|
CompilerUInt128 a = (CompilerUInt128(numerator.items[1]) << 64) + numerator.items[0];
|
|
CompilerUInt128 b = (CompilerUInt128(denominator.items[1]) << 64) + denominator.items[0];
|
|
CompilerUInt128 c = a / b;
|
|
|
|
integer<Bits, Signed> res;
|
|
res.items[0] = c;
|
|
res.items[1] = c >> 64;
|
|
|
|
CompilerUInt128 remainder = a - b * c;
|
|
numerator.items[0] = remainder;
|
|
numerator.items[1] = remainder >> 64;
|
|
|
|
return res;
|
|
}
|
|
|
|
if (is_zero(denominator))
|
|
throwError("Division by zero");
|
|
|
|
integer<Bits2, unsigned> x = 1;
|
|
integer<Bits2, unsigned> quotient = 0;
|
|
|
|
while (!operator_greater(denominator, numerator) && is_zero(operator_amp(shift_right(denominator, Bits2 - 1), 1)))
|
|
{
|
|
x = shift_left(x, 1);
|
|
denominator = shift_left(denominator, 1);
|
|
}
|
|
|
|
while (!is_zero(x))
|
|
{
|
|
if (!operator_greater(denominator, numerator))
|
|
{
|
|
numerator = operator_minus(numerator, denominator);
|
|
quotient = operator_pipe(quotient, x);
|
|
}
|
|
|
|
x = shift_right(x, 1);
|
|
denominator = shift_right(denominator, 1);
|
|
}
|
|
|
|
return quotient;
|
|
}
|
|
|
|
template <typename T>
|
|
constexpr static auto operator_slash(const integer<Bits, Signed> & lhs, const T & rhs)
|
|
{
|
|
if constexpr (should_keep_size<T>())
|
|
{
|
|
integer<Bits, unsigned> numerator = make_positive(lhs);
|
|
integer<Bits, unsigned> denominator = make_positive(integer<Bits, Signed>(rhs));
|
|
integer<Bits, unsigned> quotient = integer<Bits, unsigned>::_impl::divide(numerator, std::move(denominator));
|
|
|
|
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, unsigned> remainder = make_positive(lhs);
|
|
integer<Bits, unsigned> denominator = make_positive(integer<Bits, Signed>(rhs));
|
|
integer<Bits, unsigned>::_impl::divide(remainder, std::move(denominator));
|
|
|
|
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_builtin(*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_builtin(*this, *il.begin());
|
|
}
|
|
else if (il.size() == 0)
|
|
{
|
|
_impl::wide_integer_from_builtin(*this, 0);
|
|
}
|
|
else
|
|
{
|
|
auto it = il.begin();
|
|
for (size_t i = 0; i < _impl::item_count; ++i)
|
|
if (it < il.end())
|
|
items[i] = *it;
|
|
}
|
|
}
|
|
|
|
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_builtin(*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 (_impl::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
|
|
{
|
|
static_assert(std::numeric_limits<T>::is_integer);
|
|
|
|
/// NOTE: memcpy will suffice, but unfortunately, this function is constexpr.
|
|
|
|
using UnsignedT = std::make_unsigned_t<T>;
|
|
|
|
UnsignedT res{};
|
|
for (unsigned i = 0; i < _impl::item_count && i < (sizeof(T) + sizeof(base_type) - 1) / sizeof(base_type); ++i)
|
|
res += UnsignedT(items[i]) << (sizeof(base_type) * 8 * i);
|
|
|
|
return res;
|
|
}
|
|
|
|
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 integer<Bits, Signed>(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 integer<Bits, Signed>(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_greater(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_greater(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;
|
|
}
|
|
};
|
|
|
|
}
|