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https://github.com/ClickHouse/ClickHouse.git
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1273 lines
40 KiB
C++
1273 lines
40 KiB
C++
/// Original is here https://github.com/cerevra/int
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#pragma once
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#include "throwError.h"
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namespace wide
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{
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template <typename T>
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struct IsWideInteger
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{
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static const constexpr bool value = false;
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};
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template <size_t Bits, typename Signed>
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struct IsWideInteger<wide::integer<Bits, Signed>>
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{
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static const constexpr bool value = true;
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};
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template <typename T>
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static constexpr bool ArithmeticConcept() noexcept
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{
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return std::is_arithmetic_v<T> || IsWideInteger<T>::value;
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}
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template <typename T>
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static constexpr bool IntegralConcept() noexcept
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{
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return std::is_integral_v<T> || IsWideInteger<T>::value;
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}
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}
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namespace std
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{
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// numeric limits
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template <size_t Bits, typename Signed>
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class numeric_limits<wide::integer<Bits, Signed>>
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{
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public:
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static constexpr bool is_specialized = true;
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static constexpr bool is_signed = is_same<Signed, signed>::value;
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static constexpr bool is_integer = true;
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static constexpr bool is_exact = true;
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static constexpr bool has_infinity = false;
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static constexpr bool has_quiet_NaN = false;
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static constexpr bool has_signaling_NaN = true;
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static constexpr std::float_denorm_style has_denorm = std::denorm_absent;
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static constexpr bool has_denorm_loss = false;
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static constexpr std::float_round_style round_style = std::round_toward_zero;
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static constexpr bool is_iec559 = false;
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static constexpr bool is_bounded = true;
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static constexpr bool is_modulo = true;
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static constexpr int digits = Bits - (is_same<Signed, signed>::value ? 1 : 0);
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static constexpr int digits10 = digits * 0.30103 /*std::log10(2)*/;
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static constexpr int max_digits10 = 0;
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static constexpr int radix = 2;
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static constexpr int min_exponent = 0;
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static constexpr int min_exponent10 = 0;
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static constexpr int max_exponent = 0;
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static constexpr int max_exponent10 = 0;
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static constexpr bool traps = true;
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static constexpr bool tinyness_before = false;
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static constexpr wide::integer<Bits, Signed> min() noexcept
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{
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if (is_same<Signed, signed>::value)
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{
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using T = wide::integer<Bits, signed>;
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T res{};
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res.items[T::_impl::big(0)] = std::numeric_limits<typename wide::integer<Bits, Signed>::signed_base_type>::min();
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return res;
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}
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return 0;
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}
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static constexpr wide::integer<Bits, Signed> max() noexcept
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{
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using T = wide::integer<Bits, Signed>;
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T res{};
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res.items[T::_impl::big(0)] = is_same<Signed, signed>::value
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? std::numeric_limits<typename wide::integer<Bits, Signed>::signed_base_type>::max()
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: 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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{
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res.items[T::_impl::big(i)] = std::numeric_limits<typename wide::integer<Bits, Signed>::base_type>::max();
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}
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return res;
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}
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static constexpr wide::integer<Bits, Signed> lowest() noexcept { return min(); }
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static constexpr wide::integer<Bits, Signed> epsilon() noexcept { return 0; }
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static constexpr wide::integer<Bits, Signed> round_error() noexcept { return 0; }
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static constexpr wide::integer<Bits, Signed> infinity() noexcept { return 0; }
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static constexpr wide::integer<Bits, Signed> quiet_NaN() noexcept { return 0; }
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static constexpr wide::integer<Bits, Signed> signaling_NaN() noexcept { return 0; }
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static constexpr wide::integer<Bits, Signed> denorm_min() noexcept { return 0; }
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};
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// type traits
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template <size_t Bits, typename Signed, size_t Bits2, typename Signed2>
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struct common_type<wide::integer<Bits, Signed>, wide::integer<Bits2, Signed2>>
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{
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using type = std::conditional_t < Bits == Bits2,
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wide::integer<
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Bits,
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std::conditional_t<(std::is_same_v<Signed, Signed2> && std::is_same_v<Signed2, signed>), signed, unsigned>>,
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std::conditional_t<Bits2<Bits, wide::integer<Bits, Signed>, wide::integer<Bits2, Signed2>>>;
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};
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template <size_t Bits, typename Signed, typename Arithmetic>
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struct common_type<wide::integer<Bits, Signed>, Arithmetic>
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{
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static_assert(wide::ArithmeticConcept<Arithmetic>());
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using type = std::conditional_t<
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std::is_floating_point_v<Arithmetic>,
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Arithmetic,
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std::conditional_t<
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sizeof(Arithmetic) < Bits * sizeof(long),
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wide::integer<Bits, Signed>,
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std::conditional_t<
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Bits * sizeof(long) < sizeof(Arithmetic),
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Arithmetic,
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std::conditional_t<
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Bits * sizeof(long) == sizeof(Arithmetic) && (std::is_same_v<Signed, signed> || std::is_signed_v<Arithmetic>),
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Arithmetic,
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wide::integer<Bits, Signed>>>>>;
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};
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template <typename Arithmetic, size_t Bits, typename Signed>
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struct common_type<Arithmetic, wide::integer<Bits, Signed>> : common_type<wide::integer<Bits, Signed>, Arithmetic>
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{
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};
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}
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namespace wide
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{
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template <size_t Bits, typename Signed>
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struct integer<Bits, Signed>::_impl
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{
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static constexpr size_t _Bits = Bits;
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static constexpr const unsigned byte_count = Bits / 8;
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static constexpr const unsigned item_count = byte_count / sizeof(base_type);
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static constexpr const unsigned base_bits = sizeof(base_type) * 8;
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static_assert(Bits % base_bits == 0);
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/// Simple iteration in both directions
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static constexpr unsigned little(unsigned idx) { return idx; }
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static constexpr unsigned big(unsigned idx) { return item_count - 1 - idx; }
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static constexpr unsigned any(unsigned idx) { return idx; }
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template <class T>
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constexpr static bool is_negative(const T & n) noexcept
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{
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if constexpr (std::is_signed_v<T>)
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return n < 0;
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else
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return false;
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}
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template <size_t B, class T>
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constexpr static bool is_negative(const integer<B, T> & n) noexcept
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{
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if constexpr (std::is_same_v<T, signed>)
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return static_cast<signed_base_type>(n.items[big(0)]) < 0;
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else
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return false;
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}
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template <typename T>
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constexpr static auto make_positive(const T & n) noexcept
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{
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if constexpr (std::is_signed_v<T>)
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return n < 0 ? -n : n;
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else
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return n;
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}
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template <size_t B, class S>
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constexpr static integer<B, S> make_positive(const integer<B, S> & n) noexcept
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{
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return is_negative(n) ? operator_unary_minus(n) : n;
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}
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template <typename T>
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constexpr static auto to_Integral(T f) noexcept
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{
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if constexpr (std::is_same_v<T, __int128>)
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return f;
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else if constexpr (std::is_signed_v<T>)
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return static_cast<int64_t>(f);
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else
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return static_cast<uint64_t>(f);
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}
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template <typename Integral>
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constexpr static void wide_integer_from_bultin(integer<Bits, Signed> & self, Integral rhs) noexcept
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{
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self.items[0] = _impl::to_Integral(rhs);
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if constexpr (std::is_same_v<Integral, __int128>)
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self.items[1] = rhs >> base_bits;
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constexpr const unsigned start = (sizeof(Integral) == 16) ? 2 : 1;
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if constexpr (std::is_signed_v<Integral>)
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{
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if (rhs < 0)
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{
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for (unsigned i = start; i < item_count; ++i)
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self.items[i] = -1;
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return;
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}
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}
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for (unsigned i = start; i < item_count; ++i)
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self.items[i] = 0;
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}
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constexpr static void wide_integer_from_bultin(integer<Bits, Signed> & self, double rhs) noexcept
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{
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if ((rhs > 0 && rhs < std::numeric_limits<uint64_t>::max()) || (rhs < 0 && rhs > std::numeric_limits<int64_t>::min()))
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{
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self = to_Integral(rhs);
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return;
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}
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long double r = rhs;
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if (r < 0)
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r = -r;
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size_t count = r / std::numeric_limits<uint64_t>::max();
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self = count;
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self *= std::numeric_limits<uint64_t>::max();
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long double to_diff = count;
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to_diff *= std::numeric_limits<uint64_t>::max();
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self += to_Integral(r - to_diff);
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if (rhs < 0)
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self = -self;
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}
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template <size_t Bits2, typename Signed2>
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constexpr static void
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wide_integer_from_wide_integer(integer<Bits, Signed> & self, const integer<Bits2, Signed2> & rhs) noexcept
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{
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constexpr const unsigned min_bits = (Bits < Bits2) ? Bits : Bits2;
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constexpr const unsigned to_copy = min_bits / base_bits;
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for (unsigned i = 0; i < to_copy; ++i)
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self.items[i] = rhs.items[i];
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if constexpr (Bits > Bits2)
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{
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if constexpr (std::is_signed_v<Signed2>)
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{
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if (rhs < 0)
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{
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for (unsigned i = to_copy; i < item_count; ++i)
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self.items[i] = -1;
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return;
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}
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}
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for (unsigned i = to_copy; i < item_count; ++i)
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self.items[i] = 0;
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}
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}
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template <typename T>
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constexpr static bool should_keep_size()
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{
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return sizeof(T) <= byte_count;
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}
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constexpr static integer<Bits, Signed> shift_left(const integer<Bits, Signed> & rhs, unsigned n) noexcept
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{
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integer<Bits, Signed> lhs;
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unsigned items_shift = n / base_bits;
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if (unsigned bit_shift = n % base_bits)
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{
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unsigned overflow_shift = base_bits - bit_shift;
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lhs.items[big(0)] = rhs.items[big(items_shift)] << bit_shift;
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for (unsigned i = 1; i < item_count - items_shift; ++i)
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{
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lhs.items[big(i - 1)] |= rhs.items[big(items_shift + i)] >> overflow_shift;
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lhs.items[big(i)] = rhs.items[big(items_shift + i)] << bit_shift;
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}
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}
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else
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{
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for (unsigned i = 0; i < item_count - items_shift; ++i)
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lhs.items[big(i)] = rhs.items[big(items_shift + i)];
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}
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for (unsigned i = 0; i < items_shift; ++i)
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lhs.items[little(i)] = 0;
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return lhs;
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}
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constexpr static integer<Bits, Signed> shift_right(const integer<Bits, Signed> & rhs, unsigned n) noexcept
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{
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integer<Bits, Signed> lhs;
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unsigned items_shift = n / base_bits;
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unsigned bit_shift = n % base_bits;
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if (bit_shift)
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{
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unsigned overflow_shift = base_bits - bit_shift;
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lhs.items[little(0)] = rhs.items[little(items_shift)] >> bit_shift;
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for (unsigned i = 1; i < item_count - items_shift; ++i)
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{
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lhs.items[little(i - 1)] |= rhs.items[little(items_shift + i)] << overflow_shift;
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lhs.items[little(i)] = rhs.items[little(items_shift + i)] >> bit_shift;
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}
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}
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else
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{
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for (unsigned i = 0; i < item_count - items_shift; ++i)
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lhs.items[little(i)] = rhs.items[little(items_shift + i)];
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}
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if (is_negative(rhs))
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{
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if (bit_shift)
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lhs.items[big(items_shift)] |= std::numeric_limits<base_type>::max() << (base_bits - bit_shift);
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for (unsigned i = item_count - items_shift; i < items_shift; ++i)
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lhs.items[little(i)] = std::numeric_limits<base_type>::max();
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}
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else
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{
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for (unsigned i = item_count - items_shift; i < items_shift; ++i)
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lhs.items[little(i)] = 0;
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}
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return lhs;
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}
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private:
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template <typename T>
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constexpr static base_type get_item(const T & x, unsigned number)
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{
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if constexpr (IsWideInteger<T>::value)
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{
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if (number < T::_impl::item_count)
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return x.items[number];
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return 0;
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}
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else
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{
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if (number * sizeof(base_type) < sizeof(T))
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return x >> (number * base_bits); // & std::numeric_limits<base_type>::max()
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return 0;
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}
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}
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template <typename T>
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constexpr static integer<Bits, Signed>
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op_minus(const integer<Bits, Signed> & lhs, T rhs)
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{
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integer<Bits, Signed> res;
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bool is_underflow = false;
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for (unsigned i = 0; i < item_count; ++i)
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{
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base_type lhs_item = lhs.items[little(i)];
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base_type rhs_item = get_item(rhs, i);
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if (is_underflow)
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{
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is_underflow = (lhs_item == 0);
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--lhs_item;
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}
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if (lhs_item < rhs_item)
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is_underflow = true;
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res.items[little(i)] = lhs_item - rhs_item;
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}
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return res;
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}
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template <typename T>
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constexpr static integer<Bits, Signed>
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op_plus(const integer<Bits, Signed> & lhs, T rhs)
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{
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integer<Bits, Signed> res;
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bool is_overflow = false;
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for (unsigned i = 0; i < item_count; ++i)
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{
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base_type lhs_item = lhs.items[little(i)];
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base_type rhs_item = get_item(rhs, i);
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if (is_overflow)
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{
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++lhs_item;
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is_overflow = (lhs_item == 0);
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}
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base_type & res_item = res.items[little(i)];
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res_item = lhs_item + rhs_item;
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if (res_item < rhs_item)
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is_overflow = true;
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}
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return res;
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}
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template <typename T>
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constexpr static auto op_multiply(const integer<Bits, Signed> & lhs, const T & rhs)
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{
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integer<Bits, Signed> res{};
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#if 1
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integer<Bits, Signed> lhs2 = op_plus(lhs, shift_left(lhs, 1));
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integer<Bits, Signed> lhs3 = op_plus(lhs2, shift_left(lhs, 2));
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#endif
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for (unsigned i = 0; i < item_count; ++i)
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{
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base_type rhs_item = get_item(rhs, i);
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unsigned pos = i * base_bits;
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while (rhs_item)
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{
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#if 1 /// optimization
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if ((rhs_item & 0x7) == 0x7)
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{
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res = op_plus(res, shift_left(lhs3, pos));
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rhs_item >>= 3;
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pos += 3;
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continue;
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}
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if ((rhs_item & 0x3) == 0x3)
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{
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res = op_plus(res, shift_left(lhs2, pos));
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rhs_item >>= 2;
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pos += 2;
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continue;
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}
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#endif
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if (rhs_item & 1)
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res = op_plus(res, shift_left(lhs, pos));
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rhs_item >>= 1;
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++pos;
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}
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}
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return res;
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}
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public:
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constexpr static integer<Bits, Signed> operator_unary_tilda(const integer<Bits, Signed> & lhs) noexcept
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{
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integer<Bits, Signed> res;
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for (unsigned i = 0; i < item_count; ++i)
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res.items[any(i)] = ~lhs.items[any(i)];
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return res;
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}
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constexpr static integer<Bits, Signed>
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operator_unary_minus(const integer<Bits, Signed> & lhs) noexcept(std::is_same_v<Signed, unsigned>)
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{
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return op_plus(operator_unary_tilda(lhs), 1);
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}
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template <typename T>
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constexpr static auto operator_plus(const integer<Bits, Signed> & lhs, const T & rhs) noexcept(std::is_same_v<Signed, unsigned>)
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{
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if constexpr (should_keep_size<T>())
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{
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if (is_negative(rhs))
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return op_minus(lhs, -rhs);
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else
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return op_plus(lhs, rhs);
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}
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else
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{
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static_assert(IsWideInteger<T>::value);
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return std::common_type_t<integer<Bits, Signed>, integer<T::_impl::_Bits, Signed>>::_impl::operator_plus(
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integer<T::_impl::_Bits, Signed>(lhs), rhs);
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}
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}
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template <typename T>
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constexpr static auto operator_minus(const integer<Bits, Signed> & lhs, const T & rhs) noexcept(std::is_same_v<Signed, unsigned>)
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{
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if constexpr (should_keep_size<T>())
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{
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if (is_negative(rhs))
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return op_plus(lhs, -rhs);
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else
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return op_minus(lhs, rhs);
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}
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else
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{
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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>())
|
|
{
|
|
integer<Bits, Signed> res;
|
|
|
|
if constexpr (std::is_signed_v<Signed>)
|
|
{
|
|
res = op_multiply((is_negative(lhs) ? make_positive(lhs) : lhs),
|
|
(is_negative(rhs) ? make_positive(rhs) : rhs));
|
|
}
|
|
else
|
|
{
|
|
res = op_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 = op_multiply(res, 16U);
|
|
res = op_plus(res, *c - '0');
|
|
++c;
|
|
}
|
|
else if (*c >= 'a' && *c <= 'f')
|
|
{
|
|
res = op_multiply(res, 16U);
|
|
res = op_plus(res, *c - 'a' + 10U);
|
|
++c;
|
|
}
|
|
else if (*c >= 'A' && *c <= 'F')
|
|
{ // tolower must be used, but it is not constexpr
|
|
res = op_multiply(res, 16U);
|
|
res = op_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 = op_multiply(res, 10U);
|
|
res = op_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;
|
|
}
|
|
};
|
|
|
|
}
|