text: //
  // Copyright 2017 The Abseil Authors.
  //
  // Licensed under the Apache License, Version 2.0 (the "License");
  // you may not use this file except in compliance with the License.
  // You may obtain a copy of the License at
  //
  //      http://www.apache.org/licenses/LICENSE-2.0
  //
  // Unless required by applicable law or agreed to in writing, software
  // distributed under the License is distributed on an "AS IS" BASIS,
  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  // See the License for the specific language governing permissions and
  // limitations under the License.
  //
  // -----------------------------------------------------------------------------
  // File: int128.h
  // -----------------------------------------------------------------------------
  //
  // This header file defines 128-bit integer types. Currently, this file defines
  // `uint128`, an unsigned 128-bit integer; a signed 128-bit integer is
  // forthcoming.
  
  #ifndef ABSL_NUMERIC_INT128_H_
  #define ABSL_NUMERIC_INT128_H_
  
  #include <cassert>
  #include <cmath>
  #include <cstdint>
  #include <cstring>
  #include <iosfwd>
  #include <limits>
  
  #include "absl/base/config.h"
  #include "absl/base/macros.h"
  #include "absl/base/port.h"
  
  namespace absl {
  
  // uint128
  //
  // An unsigned 128-bit integer type. The API is meant to mimic an intrinsic type
  // as closely as is practical, including exhibiting undefined behavior in
  // analogous cases (e.g. division by zero). This type is intended to be a
  // drop-in replacement once C++ supports an intrinsic `uint128_t` type; when
  // that occurs, existing uses of `uint128` will continue to work using that new
  // type.
  //
  // Note: code written with this type will continue to compile once `uint128_t`
  // is introduced, provided the replacement helper functions
  // `Uint128(Low|High)64()` and `MakeUint128()` are made.
  //
  // A `uint128` supports the following:
  //
  //   * Implicit construction from integral types
  //   * Explicit conversion to integral types
  //
  // Additionally, if your compiler supports `__int128`, `uint128` is
  // interoperable with that type. (Abseil checks for this compatibility through
  // the `ABSL_HAVE_INTRINSIC_INT128` macro.)
  //
  // However, a `uint128` differs from intrinsic integral types in the following
  // ways:
  //
  //   * Errors on implicit conversions that does not preserve value (such as
  //     loss of precision when converting to float values).
  //   * Requires explicit construction from and conversion to floating point
  //     types.
  //   * Conversion to integral types requires an explicit static_cast() to
  //     mimic use of the `-Wnarrowing` compiler flag.
  //
  // Example:
  //
  //     float y = kuint128max; // Error. uint128 cannot be implicitly converted
  //                            // to float.
  //
  //     uint128 v;
  //     uint64_t i = v                          // Error
  //     uint64_t i = static_cast<uint64_t>(v)   // OK
  //
  class alignas(16) uint128 {
   public:
    uint128() = default;
  
    // Constructors from arithmetic types
    constexpr uint128(int v);                 // NOLINT(runtime/explicit)
    constexpr uint128(unsigned int v);        // NOLINT(runtime/explicit)
    constexpr uint128(long v);                // NOLINT(runtime/int)
    constexpr uint128(unsigned long v);       // NOLINT(runtime/int)
    constexpr uint128(long long v);           // NOLINT(runtime/int)
    constexpr uint128(unsigned long long v);  // NOLINT(runtime/int)
  #ifdef ABSL_HAVE_INTRINSIC_INT128
    constexpr uint128(__int128 v);           // NOLINT(runtime/explicit)
    constexpr uint128(unsigned __int128 v);  // NOLINT(runtime/explicit)
  #endif  // ABSL_HAVE_INTRINSIC_INT128
    explicit uint128(float v);        // NOLINT(runtime/explicit)
    explicit uint128(double v);       // NOLINT(runtime/explicit)
    explicit uint128(long double v);  // NOLINT(runtime/explicit)
  
    // Assignment operators from arithmetic types
    uint128& operator=(int v);
    uint128& operator=(unsigned int v);
    uint128& operator=(long v);                // NOLINT(runtime/int)
    uint128& operator=(unsigned long v);       // NOLINT(runtime/int)
    uint128& operator=(long long v);           // NOLINT(runtime/int)
    uint128& operator=(unsigned long long v);  // NOLINT(runtime/int)
  #ifdef ABSL_HAVE_INTRINSIC_INT128
    uint128& operator=(__int128 v);
    uint128& operator=(unsigned __int128 v);
  #endif  // ABSL_HAVE_INTRINSIC_INT128
  
    // Conversion operators to other arithmetic types
    constexpr explicit operator bool() const;
    constexpr explicit operator char() const;
    constexpr explicit operator signed char() const;
    constexpr explicit operator unsigned char() const;
    constexpr explicit operator char16_t() const;
    constexpr explicit operator char32_t() const;
    constexpr explicit operator wchar_t() const;
    constexpr explicit operator short() const;  // NOLINT(runtime/int)
    // NOLINTNEXTLINE(runtime/int)
    constexpr explicit operator unsigned short() const;
    constexpr explicit operator int() const;
    constexpr explicit operator unsigned int() const;
    constexpr explicit operator long() const;  // NOLINT(runtime/int)
    // NOLINTNEXTLINE(runtime/int)
    constexpr explicit operator unsigned long() const;
    // NOLINTNEXTLINE(runtime/int)
    constexpr explicit operator long long() const;
    // NOLINTNEXTLINE(runtime/int)
    constexpr explicit operator unsigned long long() const;
  #ifdef ABSL_HAVE_INTRINSIC_INT128
    constexpr explicit operator __int128() const;
    constexpr explicit operator unsigned __int128() const;
  #endif  // ABSL_HAVE_INTRINSIC_INT128
    explicit operator float() const;
    explicit operator double() const;
    explicit operator long double() const;
  
    // Trivial copy constructor, assignment operator and destructor.
  
    // Arithmetic operators.
    uint128& operator+=(const uint128& other);
    uint128& operator-=(const uint128& other);
    uint128& operator*=(const uint128& other);
    // Long division/modulo for uint128.
    uint128& operator/=(const uint128& other);
    uint128& operator%=(const uint128& other);
    uint128 operator++(int);
    uint128 operator--(int);
    uint128& operator<<=(int);
    uint128& operator>>=(int);
    uint128& operator&=(const uint128& other);
    uint128& operator|=(const uint128& other);
    uint128& operator^=(const uint128& other);
    uint128& operator++();
    uint128& operator--();
  
    // Uint128Low64()
    //
    // Returns the lower 64-bit value of a `uint128` value.
    friend uint64_t Uint128Low64(const uint128& v);
  
    // Uint128High64()
    //
    // Returns the higher 64-bit value of a `uint128` value.
    friend uint64_t Uint128High64(const uint128& v);
  
    // MakeUInt128()
    //
    // Constructs a `uint128` numeric value from two 64-bit unsigned integers.
    // Note that this factory function is the only way to construct a `uint128`
    // from integer values greater than 2^64.
    //
    // Example:
    //
    //   absl::uint128 big = absl::MakeUint128(1, 0);
    friend constexpr uint128 MakeUint128(uint64_t top, uint64_t bottom);
  
   private:
    constexpr uint128(uint64_t top, uint64_t bottom);
  
    // TODO(strel) Update implementation to use __int128 once all users of
    // uint128 are fixed to not depend on alignof(uint128) == 8. Also add
    // alignas(16) to class definition to keep alignment consistent across
    // platforms.
  #if defined(ABSL_IS_LITTLE_ENDIAN)
    uint64_t lo_;
    uint64_t hi_;
  #elif defined(ABSL_IS_BIG_ENDIAN)
    uint64_t hi_;
    uint64_t lo_;
  #else  // byte order
  #error "Unsupported byte order: must be little-endian or big-endian."
  #endif  // byte order
  };
  
  extern const uint128 kuint128max;
  
  // allow uint128 to be logged
  extern std::ostream& operator<<(std::ostream& o, const uint128& b);
  
  // TODO(strel) add operator>>(std::istream&, uint128&)
  
  // Methods to access low and high pieces of 128-bit value.
  uint64_t Uint128Low64(const uint128& v);
  uint64_t Uint128High64(const uint128& v);
  
  // TODO(absl-team): Implement signed 128-bit type
  
  // --------------------------------------------------------------------------
  //                      Implementation details follow
  // --------------------------------------------------------------------------
  
  inline constexpr uint128 MakeUint128(uint64_t top, uint64_t bottom) {
    return uint128(top, bottom);
  }
  
  // Assignment from integer types.
  
  inline uint128& uint128::operator=(int v) {
    return *this = uint128(v);
  }
  
  inline uint128& uint128::operator=(unsigned int v) {
    return *this = uint128(v);
  }
  
  inline uint128& uint128::operator=(long v) {  // NOLINT(runtime/int)
    return *this = uint128(v);
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline uint128& uint128::operator=(unsigned long v) {
    return *this = uint128(v);
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline uint128& uint128::operator=(long long v) {
    return *this = uint128(v);
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline uint128& uint128::operator=(unsigned long long v) {
    return *this = uint128(v);
  }
  
  #ifdef ABSL_HAVE_INTRINSIC_INT128
  inline uint128& uint128::operator=(__int128 v) {
    return *this = uint128(v);
  }
  
  inline uint128& uint128::operator=(unsigned __int128 v) {
    return *this = uint128(v);
  }
  #endif  // ABSL_HAVE_INTRINSIC_INT128
  
  // Shift and arithmetic operators.
  
  inline uint128 operator<<(const uint128& lhs, int amount) {
    return uint128(lhs) <<= amount;
  }
  
  inline uint128 operator>>(const uint128& lhs, int amount) {
    return uint128(lhs) >>= amount;
  }
  
  inline uint128 operator+(const uint128& lhs, const uint128& rhs) {
    return uint128(lhs) += rhs;
  }
  
  inline uint128 operator-(const uint128& lhs, const uint128& rhs) {
    return uint128(lhs) -= rhs;
  }
  
  inline uint128 operator*(const uint128& lhs, const uint128& rhs) {
    return uint128(lhs) *= rhs;
  }
  
  inline uint128 operator/(const uint128& lhs, const uint128& rhs) {
    return uint128(lhs) /= rhs;
  }
  
  inline uint128 operator%(const uint128& lhs, const uint128& rhs) {
    return uint128(lhs) %= rhs;
  }
  
  inline uint64_t Uint128Low64(const uint128& v) { return v.lo_; }
  
  inline uint64_t Uint128High64(const uint128& v) { return v.hi_; }
  
  // Constructors from integer types.
  
  #if defined(ABSL_IS_LITTLE_ENDIAN)
  
  inline constexpr uint128::uint128(uint64_t top, uint64_t bottom)
      : lo_(bottom), hi_(top) {}
  
  inline constexpr uint128::uint128(int v)
      : lo_(v), hi_(v < 0 ? std::numeric_limits<uint64_t>::max() : 0) {}
  inline constexpr uint128::uint128(long v)  // NOLINT(runtime/int)
      : lo_(v), hi_(v < 0 ? std::numeric_limits<uint64_t>::max() : 0) {}
  inline constexpr uint128::uint128(long long v)  // NOLINT(runtime/int)
      : lo_(v), hi_(v < 0 ? std::numeric_limits<uint64_t>::max() : 0) {}
  
  inline constexpr uint128::uint128(unsigned int v) : lo_(v), hi_(0) {}
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::uint128(unsigned long v) : lo_(v), hi_(0) {}
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::uint128(unsigned long long v)
      : lo_(v), hi_(0) {}
  
  #ifdef ABSL_HAVE_INTRINSIC_INT128
  inline constexpr uint128::uint128(__int128 v)
      : lo_(static_cast<uint64_t>(v & ~uint64_t{0})),
        hi_(static_cast<uint64_t>(static_cast<unsigned __int128>(v) >> 64)) {}
  inline constexpr uint128::uint128(unsigned __int128 v)
      : lo_(static_cast<uint64_t>(v & ~uint64_t{0})),
        hi_(static_cast<uint64_t>(v >> 64)) {}
  #endif  // ABSL_HAVE_INTRINSIC_INT128
  
  #elif defined(ABSL_IS_BIG_ENDIAN)
  
  inline constexpr uint128::uint128(uint64_t top, uint64_t bottom)
      : hi_(top), lo_(bottom) {}
  
  inline constexpr uint128::uint128(int v)
      : hi_(v < 0 ? std::numeric_limits<uint64_t>::max() : 0), lo_(v) {}
  inline constexpr uint128::uint128(long v)  // NOLINT(runtime/int)
      : hi_(v < 0 ? std::numeric_limits<uint64_t>::max() : 0), lo_(v) {}
  inline constexpr uint128::uint128(long long v)  // NOLINT(runtime/int)
      : hi_(v < 0 ? std::numeric_limits<uint64_t>::max() : 0), lo_(v) {}
  
  inline constexpr uint128::uint128(unsigned int v) : hi_(0), lo_(v) {}
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::uint128(unsigned long v) : hi_(0), lo_(v) {}
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::uint128(unsigned long long v)
      : hi_(0), lo_(v) {}
  
  #ifdef ABSL_HAVE_INTRINSIC_INT128
  inline constexpr uint128::uint128(__int128 v)
      : hi_(static_cast<uint64_t>(static_cast<unsigned __int128>(v) >> 64)),
        lo_(static_cast<uint64_t>(v & ~uint64_t{0})) {}
  inline constexpr uint128::uint128(unsigned __int128 v)
      : hi_(static_cast<uint64_t>(v >> 64)),
        lo_(static_cast<uint64_t>(v & ~uint64_t{0})) {}
  #endif  // ABSL_HAVE_INTRINSIC_INT128
  
  #else  // byte order
  #error "Unsupported byte order: must be little-endian or big-endian."
  #endif  // byte order
  
  // Conversion operators to integer types.
  
  inline constexpr uint128::operator bool() const {
    return lo_ || hi_;
  }
  
  inline constexpr uint128::operator char() const {
    return static_cast<char>(lo_);
  }
  
  inline constexpr uint128::operator signed char() const {
    return static_cast<signed char>(lo_);
  }
  
  inline constexpr uint128::operator unsigned char() const {
    return static_cast<unsigned char>(lo_);
  }
  
  inline constexpr uint128::operator char16_t() const {
    return static_cast<char16_t>(lo_);
  }
  
  inline constexpr uint128::operator char32_t() const {
    return static_cast<char32_t>(lo_);
  }
  
  inline constexpr uint128::operator wchar_t() const {
    return static_cast<wchar_t>(lo_);
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::operator short() const {
    return static_cast<short>(lo_);  // NOLINT(runtime/int)
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::operator unsigned short() const {
    return static_cast<unsigned short>(lo_);  // NOLINT(runtime/int)
  }
  
  inline constexpr uint128::operator int() const {
    return static_cast<int>(lo_);
  }
  
  inline constexpr uint128::operator unsigned int() const {
    return static_cast<unsigned int>(lo_);
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::operator long() const {
    return static_cast<long>(lo_);  // NOLINT(runtime/int)
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::operator unsigned long() const {
    return static_cast<unsigned long>(lo_);  // NOLINT(runtime/int)
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::operator long long() const {
    return static_cast<long long>(lo_);  // NOLINT(runtime/int)
  }
  
  // NOLINTNEXTLINE(runtime/int)
  inline constexpr uint128::operator unsigned long long() const {
    return static_cast<unsigned long long>(lo_);  // NOLINT(runtime/int)
  }
  
  #ifdef ABSL_HAVE_INTRINSIC_INT128
  inline constexpr uint128::operator __int128() const {
    return (static_cast<__int128>(hi_) << 64) + lo_;
  }
  
  inline constexpr uint128::operator unsigned __int128() const {
    return (static_cast<unsigned __int128>(hi_) << 64) + lo_;
  }
  #endif  // ABSL_HAVE_INTRINSIC_INT128
  
  // Conversion operators to floating point types.
  
  inline uint128::operator float() const {
    return static_cast<float>(lo_) + std::ldexp(static_cast<float>(hi_), 64);
  }
  
  inline uint128::operator double() const {
    return static_cast<double>(lo_) + std::ldexp(static_cast<double>(hi_), 64);
  }
  
  inline uint128::operator long double() const {
    return static_cast<long double>(lo_) +
           std::ldexp(static_cast<long double>(hi_), 64);
  }
  
  // Comparison operators.
  
  inline bool operator==(const uint128& lhs, const uint128& rhs) {
    return (Uint128Low64(lhs) == Uint128Low64(rhs) &&
            Uint128High64(lhs) == Uint128High64(rhs));
  }
  
  inline bool operator!=(const uint128& lhs, const uint128& rhs) {
    return !(lhs == rhs);
  }
  
  inline bool operator<(const uint128& lhs, const uint128& rhs) {
    return (Uint128High64(lhs) == Uint128High64(rhs))
               ? (Uint128Low64(lhs) < Uint128Low64(rhs))
               : (Uint128High64(lhs) < Uint128High64(rhs));
  }
  
  inline bool operator>(const uint128& lhs, const uint128& rhs) {
    return (Uint128High64(lhs) == Uint128High64(rhs))
               ? (Uint128Low64(lhs) > Uint128Low64(rhs))
               : (Uint128High64(lhs) > Uint128High64(rhs));
  }
  
  inline bool operator<=(const uint128& lhs, const uint128& rhs) {
    return (Uint128High64(lhs) == Uint128High64(rhs))
               ? (Uint128Low64(lhs) <= Uint128Low64(rhs))
               : (Uint128High64(lhs) <= Uint128High64(rhs));
  }
  
  inline bool operator>=(const uint128& lhs, const uint128& rhs) {
    return (Uint128High64(lhs) == Uint128High64(rhs))
               ? (Uint128Low64(lhs) >= Uint128Low64(rhs))
               : (Uint128High64(lhs) >= Uint128High64(rhs));
  }
  
  // Unary operators.
  
  inline uint128 operator-(const uint128& val) {
    const uint64_t hi_flip = ~Uint128High64(val);
    const uint64_t lo_flip = ~Uint128Low64(val);
    const uint64_t lo_add = lo_flip + 1;
    if (lo_add < lo_flip) {
      return MakeUint128(hi_flip + 1, lo_add);
    }
    return MakeUint128(hi_flip, lo_add);
  }
  
  inline bool operator!(const uint128& val) {
    return !Uint128High64(val) && !Uint128Low64(val);
  }
  
  // Logical operators.
  
  inline uint128 operator~(const uint128& val) {
    return MakeUint128(~Uint128High64(val), ~Uint128Low64(val));
  }
  
  inline uint128 operator|(const uint128& lhs, const uint128& rhs) {
    return MakeUint128(Uint128High64(lhs) | Uint128High64(rhs),
                             Uint128Low64(lhs) | Uint128Low64(rhs));
  }
  
  inline uint128 operator&(const uint128& lhs, const uint128& rhs) {
    return MakeUint128(Uint128High64(lhs) & Uint128High64(rhs),
                             Uint128Low64(lhs) & Uint128Low64(rhs));
  }
  
  inline uint128 operator^(const uint128& lhs, const uint128& rhs) {
    return MakeUint128(Uint128High64(lhs) ^ Uint128High64(rhs),
                             Uint128Low64(lhs) ^ Uint128Low64(rhs));
  }
  
  inline uint128& uint128::operator|=(const uint128& other) {
    hi_ |= other.hi_;
    lo_ |= other.lo_;
    return *this;
  }
  
  inline uint128& uint128::operator&=(const uint128& other) {
    hi_ &= other.hi_;
    lo_ &= other.lo_;
    return *this;
  }
  
  inline uint128& uint128::operator^=(const uint128& other) {
    hi_ ^= other.hi_;
    lo_ ^= other.lo_;
    return *this;
  }
  
  // Shift and arithmetic assign operators.
  
  inline uint128& uint128::operator<<=(int amount) {
    // Shifts of >= 128 are undefined.
    assert(amount < 128);
  
    // uint64_t shifts of >= 64 are undefined, so we will need some
    // special-casing.
    if (amount < 64) {
      if (amount != 0) {
        hi_ = (hi_ << amount) | (lo_ >> (64 - amount));
        lo_ = lo_ << amount;
      }
    } else {
      hi_ = lo_ << (amount - 64);
      lo_ = 0;
    }
    return *this;
  }
  
  inline uint128& uint128::operator>>=(int amount) {
    // Shifts of >= 128 are undefined.
    assert(amount < 128);
  
    // uint64_t shifts of >= 64 are undefined, so we will need some
    // special-casing.
    if (amount < 64) {
      if (amount != 0) {
        lo_ = (lo_ >> amount) | (hi_ << (64 - amount));
        hi_ = hi_ >> amount;
      }
    } else {
      lo_ = hi_ >> (amount - 64);
      hi_ = 0;
    }
    return *this;
  }
  
  inline uint128& uint128::operator+=(const uint128& other) {
    hi_ += other.hi_;
    uint64_t lolo = lo_ + other.lo_;
    if (lolo < lo_)
      ++hi_;
    lo_ = lolo;
    return *this;
  }
  
  inline uint128& uint128::operator-=(const uint128& other) {
    hi_ -= other.hi_;
    if (other.lo_ > lo_) --hi_;
    lo_ -= other.lo_;
    return *this;
  }
  
  inline uint128& uint128::operator*=(const uint128& other) {
  #if defined(ABSL_HAVE_INTRINSIC_INT128)
    // TODO(strel) Remove once alignment issues are resolved and unsigned __int128
    // can be used for uint128 storage.
    *this = static_cast<unsigned __int128>(*this) *
            static_cast<unsigned __int128>(other);
    return *this;
  #else   // ABSL_HAVE_INTRINSIC128
    uint64_t a96 = hi_ >> 32;
    uint64_t a64 = hi_ & 0xffffffff;
    uint64_t a32 = lo_ >> 32;
    uint64_t a00 = lo_ & 0xffffffff;
    uint64_t b96 = other.hi_ >> 32;
    uint64_t b64 = other.hi_ & 0xffffffff;
    uint64_t b32 = other.lo_ >> 32;
    uint64_t b00 = other.lo_ & 0xffffffff;
    // multiply [a96 .. a00] x [b96 .. b00]
    // terms higher than c96 disappear off the high side
    // terms c96 and c64 are safe to ignore carry bit
    uint64_t c96 = a96 * b00 + a64 * b32 + a32 * b64 + a00 * b96;
    uint64_t c64 = a64 * b00 + a32 * b32 + a00 * b64;
    this->hi_ = (c96 << 32) + c64;
    this->lo_ = 0;
    // add terms after this one at a time to capture carry
    *this += uint128(a32 * b00) << 32;
    *this += uint128(a00 * b32) << 32;
    *this += a00 * b00;
    return *this;
  #endif  // ABSL_HAVE_INTRINSIC128
  }
  
  // Increment/decrement operators.
  
  inline uint128 uint128::operator++(int) {
    uint128 tmp(*this);
    *this += 1;
    return tmp;
  }
  
  inline uint128 uint128::operator--(int) {
    uint128 tmp(*this);
    *this -= 1;
    return tmp;
  }
  
  inline uint128& uint128::operator++() {
    *this += 1;
    return *this;
  }
  
  inline uint128& uint128::operator--() {
    *this -= 1;
    return *this;
  }
  
  }  // namespace absl
  
  #endif  // ABSL_NUMERIC_INT128_H_
  