ClickHouse/base/common/wide_integer_impl.h

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#pragma once
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/// 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"
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#include <cmath>
#include <cfloat>
#include <cassert>
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#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{};
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res.items[T::_impl::big(0)] = std::numeric_limits<typename wide::integer<Bits, Signed>::signed_base_type>::min();
return res;
}
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return wide::integer<Bits, Signed>(0);
}
static constexpr wide::integer<Bits, Signed> max() noexcept
{
using T = wide::integer<Bits, Signed>;
T res{};
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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();
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for (unsigned i = 1; i < wide::integer<Bits, Signed>::_impl::item_count; ++i)
{
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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;
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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;
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static_assert(Bits % base_bits == 0);
/// Simple iteration in both directions
static constexpr unsigned little(unsigned idx) { return idx; }
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static constexpr unsigned big(unsigned idx) { return item_count - 1 - idx; }
static constexpr unsigned any(unsigned idx) { return idx; }
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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;
}
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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
{
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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
{
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if constexpr (std::is_signed_v<T>)
return static_cast<int64_t>(f);
else
return static_cast<uint64_t>(f);
}
template <typename Integral>
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constexpr static void wide_integer_from_builtin(integer<Bits, Signed> & self, Integral rhs) noexcept
{
static_assert(sizeof(Integral) <= sizeof(base_type));
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self.items[0] = _impl::to_Integral(rhs);
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if constexpr (std::is_signed_v<Integral>)
{
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if (rhs < 0)
{
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for (size_t i = 1; i < item_count; ++i)
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self.items[i] = -1;
return;
}
}
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for (size_t i = 1; i < item_count; ++i)
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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>
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constexpr static void set_multiplier(integer<Bits, Signed> & self, T t) noexcept
{
constexpr uint64_t max_int = std::numeric_limits<uint64_t>::max();
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/// Implementation specific behaviour on overflow (if we don't check here, stack overflow will triggered in bigint_cast).
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if (!std::isfinite(t))
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{
self = 0;
return;
}
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const T alpha = t / static_cast<T>(max_int);
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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;
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self += static_cast<uint64_t>(t - floor(alpha) * static_cast<T>(max_int)); // += b_i
}
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constexpr static void wide_integer_from_builtin(integer<Bits, Signed> & self, double rhs) noexcept
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{
constexpr int64_t max_int = std::numeric_limits<int64_t>::max();
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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.
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// TODO Be compatible with Apple aarch64
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#if not (defined(__APPLE__) && defined(__aarch64__))
static_assert(LDBL_MANT_DIG >= 64,
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"On your system long double has less than 64 precision bits, "
"which may result in UB when initializing double from int64_t");
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#endif
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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
{
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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)
{
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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()
{
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return sizeof(T) <= byte_count;
}
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constexpr static integer<Bits, Signed> shift_left(const integer<Bits, Signed> & rhs, unsigned n) noexcept
{
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integer<Bits, Signed> lhs;
unsigned items_shift = n / base_bits;
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if (unsigned bit_shift = n % base_bits)
{
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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)
{
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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;
}
}
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else
{
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for (unsigned i = 0; i < item_count - items_shift; ++i)
lhs.items[big(i)] = rhs.items[big(items_shift + i)];
}
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for (unsigned i = 0; i < items_shift; ++i)
lhs.items[little(i)] = 0;
return lhs;
}
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constexpr static integer<Bits, Signed> shift_right(const integer<Bits, Signed> & rhs, unsigned n) noexcept
{
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integer<Bits, Signed> lhs;
unsigned items_shift = n / base_bits;
unsigned bit_shift = n % base_bits;
if (bit_shift)
{
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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)
{
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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;
}
}
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else
{
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for (unsigned i = 0; i < item_count - items_shift; ++i)
lhs.items[little(i)] = rhs.items[little(items_shift + i)];
}
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if (is_negative(rhs))
{
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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();
}
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else
{
for (unsigned i = 0; i < items_shift; ++i)
lhs.items[big(i)] = 0;
}
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return lhs;
}
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private:
template <typename T>
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constexpr static base_type get_item(const T & x, unsigned idx)
{
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if constexpr (IsWideInteger<T>::value)
{
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if (idx < T::_impl::item_count)
return x.items[idx];
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return 0;
}
else
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{
if constexpr (sizeof(T) <= sizeof(base_type))
{
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if (0 == idx)
return x;
}
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else if (idx * sizeof(base_type) < sizeof(T))
return x >> (idx * base_bits); // & std::numeric_limits<base_type>::max()
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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)
{
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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)
{
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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)
{
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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)
{
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if (overflows[i - 1])
{
base_type & res_item = res.items[little(i)];
++res_item;
if (res_item == 0)
overflows[i] = true;
}
}
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return res;
}
template <typename T>
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constexpr static integer<Bits, Signed>
multiply(const integer<Bits, Signed> & lhs, const T & rhs)
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{
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if constexpr (Bits == 256 && sizeof(base_type) == 8)
{
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/// @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)];
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res.items[little(1)] = r12;
res.items[little(2)] = r12 >> 64;
return res;
}
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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;
}
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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)
{
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base_type rhs_item = get_item(rhs, i);
unsigned pos = i * base_bits;
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while (rhs_item)
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{
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#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;
}
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#endif
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if (rhs_item & 1)
res = plus(res, shift_left(lhs, pos));
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rhs_item >>= 1;
++pos;
}
}
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return res;
}
}
public:
constexpr static integer<Bits, Signed> operator_unary_tilda(const integer<Bits, Signed> & lhs) noexcept
{
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integer<Bits, Signed> res;
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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>())
{
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if (is_negative(rhs))
return minus(lhs, -rhs);
else
return plus(lhs, rhs);
}
else
{
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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>())
{
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if (is_negative(rhs))
return plus(lhs, -rhs);
else
return minus(lhs, rhs);
}
else
{
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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>())
{
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integer<Bits, Signed> res;
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if constexpr (std::is_signed_v<Signed>)
{
res = multiply((is_negative(lhs) ? make_positive(lhs) : lhs),
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(is_negative(rhs) ? make_positive(rhs) : rhs));
}
else
{
res = multiply(lhs, (is_negative(rhs) ? make_positive(rhs) : rhs));
}
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if (std::is_same_v<Signed, signed> && is_negative(lhs) != is_negative(rhs))
res = operator_unary_minus(res);
return res;
}
else
{
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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>())
{
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if (std::numeric_limits<T>::is_signed && (is_negative(lhs) != is_negative(rhs)))
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return is_negative(rhs);
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for (unsigned i = 0; i < item_count; ++i)
{
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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
{
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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>())
{
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if (std::numeric_limits<T>::is_signed && (is_negative(lhs) != is_negative(rhs)))
return is_negative(lhs);
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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
{
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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>())
{
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for (unsigned i = 0; i < item_count; ++i)
{
base_type rhs_item = get_item(rhs, any(i));
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if (lhs.items[any(i)] != rhs_item)
return false;
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}
return true;
}
else
{
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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>())
{
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integer<Bits, Signed> res;
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for (unsigned i = 0; i < item_count; ++i)
res.items[little(i)] = lhs.items[little(i)] | get_item(rhs, i);
return res;
}
else
{
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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>())
{
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integer<Bits, Signed> res;
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for (unsigned i = 0; i < item_count; ++i)
res.items[little(i)] = lhs.items[little(i)] & get_item(rhs, i);
return res;
}
else
{
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static_assert(IsWideInteger<T>::value);
return std::common_type_t<integer<Bits, Signed>, T>::_impl::operator_amp(T(lhs), rhs);
}
}
template <typename T>
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constexpr static bool is_zero(const T & x)
{
bool is_zero = true;
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for (auto item : x.items)
{
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if (item != 0)
{
is_zero = false;
break;
}
}
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return is_zero;
}
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/// 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)
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{
static_assert(std::is_unsigned_v<Signed>);
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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;
}
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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);
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quotient = operator_pipe(quotient, x);
}
x = shift_right(x, 1);
denominator = shift_right(denominator, 1);
}
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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));
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if (std::is_same_v<Signed, signed> && is_negative(rhs) != is_negative(lhs))
quotient = operator_unary_minus(quotient);
return quotient;
}
else
{
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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
{
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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;
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for (unsigned i = 0; i < item_count; ++i)
res.items[any(i)] ^= t.items[any(i)];
return res;
}
else
{
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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
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: items{}
{
if constexpr (IsWideInteger<T>::value)
_impl::wide_integer_from_wide_integer(*this, rhs);
else
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_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
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: items{}
{
if (il.size() == 1)
{
if constexpr (IsWideInteger<T>::value)
_impl::wide_integer_from_wide_integer(*this, *il.begin());
else
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_impl::wide_integer_from_builtin(*this, *il.begin());
}
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else if (il.size() == 0)
{
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_impl::wide_integer_from_builtin(*this, 0);
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}
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
{
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_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
{
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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
{
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if (static_cast<size_t>(n) >= Bits)
{
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if (_impl::is_negative(*this))
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*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
{
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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{};
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for (unsigned i = 0; i < _impl::item_count && i < (sizeof(T) + sizeof(base_type) - 1) / sizeof(base_type); ++i)
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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;
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for (unsigned i = 0; i < _impl::item_count; ++i)
{
long double t = res;
res *= std::numeric_limits<base_type>::max();
res += t;
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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
{
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if (static_cast<size_t>(n) >= Bits)
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return integer<Bits, Signed>(0);
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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
{
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if (static_cast<size_t>(n) >= Bits)
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return integer<Bits, Signed>(0);
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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);
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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;
}
};
}