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 //
 // 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
 //
 //      https://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, `uint128` and `int128`.
 //
 // TODO(absl-team): This module is inconsistent as many inline `uint128` methods
 // are defined in this file, while many inline `int128` methods are defined in
 // the `int128_*_intrinsic.inc` files.
 
 #ifndef ABSL_NUMERIC_INT128_H_
 #define ABSL_NUMERIC_INT128_H_
 
 #include <cassert>
 #include <cmath>
 #include <cstdint>
 #include <cstring>
 #include <iosfwd>
 #include <limits>
 #include <string>
 #include <utility>
 
 #include "absl/base/config.h"
 #include "absl/base/macros.h"
 #include "absl/base/port.h"
 #include "absl/types/compare.h"
 
 #if defined(_MSC_VER)
 // In very old versions of MSVC and when the /Zc:wchar_t flag is off, wchar_t is
 // a typedef for unsigned short.  Otherwise wchar_t is mapped to the __wchar_t
 // builtin type.  We need to make sure not to define operator wchar_t()
 // alongside operator unsigned short() in these instances.
 #define ABSL_INTERNAL_WCHAR_T __wchar_t
 #if defined(_M_X64) && !defined(_M_ARM64EC)
 #include <intrin.h>
 #pragma intrinsic(_umul128)
 #endif  // defined(_M_X64)
 #else   // defined(_MSC_VER)
 #define ABSL_INTERNAL_WCHAR_T wchar_t
 #endif  // defined(_MSC_VER)
 
 namespace absl {
 ABSL_NAMESPACE_BEGIN
 
 class int128;
 
 // 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 well-behaved 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 do 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.
 //   * The alignment requirement of `uint128` may differ from that of an
 //     intrinsic 128-bit integer type depending on platform and build
 //     configuration.
 //
 // Example:
 //
 //     float y = absl::Uint128Max();  // Error. uint128 cannot be implicitly
 //                                    // converted to float.
 //
 //     absl::uint128 v;
 //     uint64_t i = v;                         // Error
 //     uint64_t i = static_cast<uint64_t>(v);  // OK
 //
 class
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
     alignas(unsigned __int128)
 #endif  // ABSL_HAVE_INTRINSIC_INT128
         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
   constexpr uint128(int128 v);             // NOLINT(runtime/explicit)
   explicit uint128(float v);
   explicit uint128(double v);
   explicit uint128(long double v);
 
   // 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
   uint128& operator=(int128 v);
 
   // 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 ABSL_INTERNAL_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+=(uint128 other);
   uint128& operator-=(uint128 other);
   uint128& operator*=(uint128 other);
   // Long division/modulo for uint128.
   uint128& operator/=(uint128 other);
   uint128& operator%=(uint128 other);
   uint128 operator++(int);
   uint128 operator--(int);
   uint128& operator<<=(int);
   uint128& operator>>=(int);
   uint128& operator&=(uint128 other);
   uint128& operator|=(uint128 other);
   uint128& operator^=(uint128 other);
   uint128& operator++();
   uint128& operator--();
 
   // Uint128Low64()
   //
   // Returns the lower 64-bit value of a `uint128` value.
   friend constexpr uint64_t Uint128Low64(uint128 v);
 
   // Uint128High64()
   //
   // Returns the higher 64-bit value of a `uint128` value.
   friend constexpr uint64_t Uint128High64(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 high, uint64_t low);
 
   // Uint128Max()
   //
   // Returns the highest value for a 128-bit unsigned integer.
   friend constexpr uint128 Uint128Max();
 
   // Support for absl::Hash.
   template <typename H>
   friend H AbslHashValue(H h, uint128 v) {
     return H::combine(std::move(h), Uint128High64(v), Uint128Low64(v));
   }
 
   // Support for absl::StrCat() etc.
   template <typename Sink>
   friend void AbslStringify(Sink& sink, uint128 v) {
     sink.Append(v.ToString());
   }
 
  private:
   constexpr uint128(uint64_t high, uint64_t low);
 
   std::string ToString() const;
 
   // 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
 };
 
 // allow uint128 to be logged
 std::ostream& operator<<(std::ostream& os, uint128 v);
 
 // TODO(strel) add operator>>(std::istream&, uint128)
 
 constexpr uint128 Uint128Max() {
   return uint128((std::numeric_limits<uint64_t>::max)(),
                  (std::numeric_limits<uint64_t>::max)());
 }
 
 ABSL_NAMESPACE_END
 }  // namespace absl
 
 // Specialized numeric_limits for uint128.
 namespace std {
 template <>
 class numeric_limits<absl::uint128> {
  public:
   static constexpr bool is_specialized = true;
   static constexpr bool is_signed = false;
   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 = false;
   ABSL_INTERNAL_DISABLE_DEPRECATED_DECLARATION_WARNING
   static constexpr float_denorm_style has_denorm = denorm_absent;
   ABSL_INTERNAL_RESTORE_DEPRECATED_DECLARATION_WARNING
   static constexpr bool has_denorm_loss = false;
   static constexpr float_round_style round_style = 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 = 128;
   static constexpr int digits10 = 38;
   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;
 #ifdef ABSL_HAVE_INTRINSIC_INT128
   static constexpr bool traps = numeric_limits<unsigned __int128>::traps;
 #else   // ABSL_HAVE_INTRINSIC_INT128
   static constexpr bool traps = numeric_limits<uint64_t>::traps;
 #endif  // ABSL_HAVE_INTRINSIC_INT128
   static constexpr bool tinyness_before = false;
 
   static constexpr absl::uint128(min)() { return 0; }
   static constexpr absl::uint128 lowest() { return 0; }
   static constexpr absl::uint128(max)() { return absl::Uint128Max(); }
   static constexpr absl::uint128 epsilon() { return 0; }
   static constexpr absl::uint128 round_error() { return 0; }
   static constexpr absl::uint128 infinity() { return 0; }
   static constexpr absl::uint128 quiet_NaN() { return 0; }
   static constexpr absl::uint128 signaling_NaN() { return 0; }
   static constexpr absl::uint128 denorm_min() { return 0; }
 };
 }  // namespace std
 
 namespace absl {
 ABSL_NAMESPACE_BEGIN
 
 // int128
 //
 // A signed 128-bit integer type. The API is meant to mimic an intrinsic
 // integral type as closely as is practical, including exhibiting undefined
 // behavior in analogous cases (e.g. division by zero).
 //
 // An `int128` supports the following:
 //
 //   * Implicit construction from integral types
 //   * Explicit conversion to integral types
 //
 // However, an `int128` differs from intrinsic integral types in the following
 // ways:
 //
 //   * It is not implicitly convertible to other integral types.
 //   * Requires explicit construction from and conversion to floating point
 //     types.
 
 // Additionally, if your compiler supports `__int128`, `int128` is
 // interoperable with that type. (Abseil checks for this compatibility through
 // the `ABSL_HAVE_INTRINSIC_INT128` macro.)
 //
 // The design goal for `int128` is that it will be compatible with a future
 // `int128_t`, if that type becomes a part of the standard.
 //
 // Example:
 //
 //     float y = absl::int128(17);  // Error. int128 cannot be implicitly
 //                                  // converted to float.
 //
 //     absl::int128 v;
 //     int64_t i = v;                        // Error
 //     int64_t i = static_cast<int64_t>(v);  // OK
 //
 class int128 {
  public:
   int128() = default;
 
   // Constructors from arithmetic types
   constexpr int128(int v);                 // NOLINT(runtime/explicit)
   constexpr int128(unsigned int v);        // NOLINT(runtime/explicit)
   constexpr int128(long v);                // NOLINT(runtime/int)
   constexpr int128(unsigned long v);       // NOLINT(runtime/int)
   constexpr int128(long long v);           // NOLINT(runtime/int)
   constexpr int128(unsigned long long v);  // NOLINT(runtime/int)
 #ifdef ABSL_HAVE_INTRINSIC_INT128
   constexpr int128(__int128 v);  // NOLINT(runtime/explicit)
   constexpr explicit int128(unsigned __int128 v);
 #endif  // ABSL_HAVE_INTRINSIC_INT128
   constexpr explicit int128(uint128 v);
   explicit int128(float v);
   explicit int128(double v);
   explicit int128(long double v);
 
   // Assignment operators from arithmetic types
   int128& operator=(int v);
   int128& operator=(unsigned int v);
   int128& operator=(long v);                // NOLINT(runtime/int)
   int128& operator=(unsigned long v);       // NOLINT(runtime/int)
   int128& operator=(long long v);           // NOLINT(runtime/int)
   int128& operator=(unsigned long long v);  // NOLINT(runtime/int)
 #ifdef ABSL_HAVE_INTRINSIC_INT128
   int128& operator=(__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 ABSL_INTERNAL_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
   int128& operator+=(int128 other);
   int128& operator-=(int128 other);
   int128& operator*=(int128 other);
   int128& operator/=(int128 other);
   int128& operator%=(int128 other);
   int128 operator++(int);  // postfix increment: i++
   int128 operator--(int);  // postfix decrement: i--
   int128& operator++();    // prefix increment:  ++i
   int128& operator--();    // prefix decrement:  --i
   int128& operator&=(int128 other);
   int128& operator|=(int128 other);
   int128& operator^=(int128 other);
   int128& operator<<=(int amount);
   int128& operator>>=(int amount);
 
   // Int128Low64()
   //
   // Returns the lower 64-bit value of a `int128` value.
   friend constexpr uint64_t Int128Low64(int128 v);
 
   // Int128High64()
   //
   // Returns the higher 64-bit value of a `int128` value.
   friend constexpr int64_t Int128High64(int128 v);
 
   // MakeInt128()
   //
   // Constructs a `int128` numeric value from two 64-bit integers. Note that
   // signedness is conveyed in the upper `high` value.
   //
   //   (absl::int128(1) << 64) * high + low
   //
   // Note that this factory function is the only way to construct a `int128`
   // from integer values greater than 2^64 or less than -2^64.
   //
   // Example:
   //
   //   absl::int128 big = absl::MakeInt128(1, 0);
   //   absl::int128 big_n = absl::MakeInt128(-1, 0);
   friend constexpr int128 MakeInt128(int64_t high, uint64_t low);
 
   // Int128Max()
   //
   // Returns the maximum value for a 128-bit signed integer.
   friend constexpr int128 Int128Max();
 
   // Int128Min()
   //
   // Returns the minimum value for a 128-bit signed integer.
   friend constexpr int128 Int128Min();
 
   // Support for absl::Hash.
   template <typename H>
   friend H AbslHashValue(H h, int128 v) {
     return H::combine(std::move(h), Int128High64(v), Int128Low64(v));
   }
 
   // Support for absl::StrCat() etc.
   template <typename Sink>
   friend void AbslStringify(Sink& sink, int128 v) {
     sink.Append(v.ToString());
   }
 
  private:
   constexpr int128(int64_t high, uint64_t low);
 
   std::string ToString() const;
 
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   __int128 v_;
 #else  // ABSL_HAVE_INTRINSIC_INT128
 #if defined(ABSL_IS_LITTLE_ENDIAN)
   uint64_t lo_;
   int64_t hi_;
 #elif defined(ABSL_IS_BIG_ENDIAN)
   int64_t hi_;
   uint64_t lo_;
 #else  // byte order
 #error "Unsupported byte order: must be little-endian or big-endian."
 #endif  // byte order
 #endif  // ABSL_HAVE_INTRINSIC_INT128
 };
 
 std::ostream& operator<<(std::ostream& os, int128 v);
 
 // TODO(absl-team) add operator>>(std::istream&, int128)
 
 constexpr int128 Int128Max() {
   return int128((std::numeric_limits<int64_t>::max)(),
                 (std::numeric_limits<uint64_t>::max)());
 }
 
 constexpr int128 Int128Min() {
   return int128((std::numeric_limits<int64_t>::min)(), 0);
 }
 
 ABSL_NAMESPACE_END
 }  // namespace absl
 
 // Specialized numeric_limits for int128.
 namespace std {
 template <>
 class numeric_limits<absl::int128> {
  public:
   static constexpr bool is_specialized = true;
   static constexpr bool is_signed = true;
   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 = false;
   ABSL_INTERNAL_DISABLE_DEPRECATED_DECLARATION_WARNING
   static constexpr float_denorm_style has_denorm = denorm_absent;
   ABSL_INTERNAL_RESTORE_DEPRECATED_DECLARATION_WARNING
   static constexpr bool has_denorm_loss = false;
   static constexpr float_round_style round_style = round_toward_zero;
   static constexpr bool is_iec559 = false;
   static constexpr bool is_bounded = true;
   static constexpr bool is_modulo = false;
   static constexpr int digits = 127;
   static constexpr int digits10 = 38;
   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;
 #ifdef ABSL_HAVE_INTRINSIC_INT128
   static constexpr bool traps = numeric_limits<__int128>::traps;
 #else   // ABSL_HAVE_INTRINSIC_INT128
   static constexpr bool traps = numeric_limits<uint64_t>::traps;
 #endif  // ABSL_HAVE_INTRINSIC_INT128
   static constexpr bool tinyness_before = false;
 
   static constexpr absl::int128(min)() { return absl::Int128Min(); }
   static constexpr absl::int128 lowest() { return absl::Int128Min(); }
   static constexpr absl::int128(max)() { return absl::Int128Max(); }
   static constexpr absl::int128 epsilon() { return 0; }
   static constexpr absl::int128 round_error() { return 0; }
   static constexpr absl::int128 infinity() { return 0; }
   static constexpr absl::int128 quiet_NaN() { return 0; }
   static constexpr absl::int128 signaling_NaN() { return 0; }
   static constexpr absl::int128 denorm_min() { return 0; }
 };
 }  // namespace std
 
 // --------------------------------------------------------------------------
 //                      Implementation details follow
 // --------------------------------------------------------------------------
 namespace absl {
 ABSL_NAMESPACE_BEGIN
 
 constexpr uint128 MakeUint128(uint64_t high, uint64_t low) {
   return uint128(high, low);
 }
 
 // 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
 
 inline uint128& uint128::operator=(int128 v) { return *this = uint128(v); }
 
 // Arithmetic operators.
 
 constexpr uint128 operator<<(uint128 lhs, int amount);
 constexpr uint128 operator>>(uint128 lhs, int amount);
 constexpr uint128 operator+(uint128 lhs, uint128 rhs);
 constexpr uint128 operator-(uint128 lhs, uint128 rhs);
 uint128 operator*(uint128 lhs, uint128 rhs);
 uint128 operator/(uint128 lhs, uint128 rhs);
 uint128 operator%(uint128 lhs, uint128 rhs);
 
 inline uint128& uint128::operator<<=(int amount) {
   *this = *this << amount;
   return *this;
 }
 
 inline uint128& uint128::operator>>=(int amount) {
   *this = *this >> amount;
   return *this;
 }
 
 inline uint128& uint128::operator+=(uint128 other) {
   *this = *this + other;
   return *this;
 }
 
 inline uint128& uint128::operator-=(uint128 other) {
   *this = *this - other;
   return *this;
 }
 
 inline uint128& uint128::operator*=(uint128 other) {
   *this = *this * other;
   return *this;
 }
 
 inline uint128& uint128::operator/=(uint128 other) {
   *this = *this / other;
   return *this;
 }
 
 inline uint128& uint128::operator%=(uint128 other) {
   *this = *this % other;
   return *this;
 }
 
 constexpr uint64_t Uint128Low64(uint128 v) { return v.lo_; }
 
 constexpr uint64_t Uint128High64(uint128 v) { return v.hi_; }
 
 // Constructors from integer types.
 
 #if defined(ABSL_IS_LITTLE_ENDIAN)
 
 constexpr uint128::uint128(uint64_t high, uint64_t low) : lo_{low}, hi_{high} {}
 
 constexpr uint128::uint128(int v)
     : lo_{static_cast<uint64_t>(v)},
       hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0} {}
 constexpr uint128::uint128(long v)  // NOLINT(runtime/int)
     : lo_{static_cast<uint64_t>(v)},
       hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0} {}
 constexpr uint128::uint128(long long v)  // NOLINT(runtime/int)
     : lo_{static_cast<uint64_t>(v)},
       hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0} {}
 
 constexpr uint128::uint128(unsigned int v) : lo_{v}, hi_{0} {}
 // NOLINTNEXTLINE(runtime/int)
 constexpr uint128::uint128(unsigned long v) : lo_{v}, hi_{0} {}
 // NOLINTNEXTLINE(runtime/int)
 constexpr uint128::uint128(unsigned long long v) : lo_{v}, hi_{0} {}
 
 #ifdef ABSL_HAVE_INTRINSIC_INT128
 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)} {}
 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
 
 constexpr uint128::uint128(int128 v)
     : lo_{Int128Low64(v)}, hi_{static_cast<uint64_t>(Int128High64(v))} {}
 
 #elif defined(ABSL_IS_BIG_ENDIAN)
 
 constexpr uint128::uint128(uint64_t high, uint64_t low) : hi_{high}, lo_{low} {}
 
 constexpr uint128::uint128(int v)
     : hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0},
       lo_{static_cast<uint64_t>(v)} {}
 constexpr uint128::uint128(long v)  // NOLINT(runtime/int)
     : hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0},
       lo_{static_cast<uint64_t>(v)} {}
 constexpr uint128::uint128(long long v)  // NOLINT(runtime/int)
     : hi_{v < 0 ? (std::numeric_limits<uint64_t>::max)() : 0},
       lo_{static_cast<uint64_t>(v)} {}
 
 constexpr uint128::uint128(unsigned int v) : hi_{0}, lo_{v} {}
 // NOLINTNEXTLINE(runtime/int)
 constexpr uint128::uint128(unsigned long v) : hi_{0}, lo_{v} {}
 // NOLINTNEXTLINE(runtime/int)
 constexpr uint128::uint128(unsigned long long v) : hi_{0}, lo_{v} {}
 
 #ifdef ABSL_HAVE_INTRINSIC_INT128
 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})} {}
 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
 
 constexpr uint128::uint128(int128 v)
     : hi_{static_cast<uint64_t>(Int128High64(v))}, lo_{Int128Low64(v)} {}
 
 #else  // byte order
 #error "Unsupported byte order: must be little-endian or big-endian."
 #endif  // byte order
 
 // Conversion operators to integer types.
 
 constexpr uint128::operator bool() const { return lo_ || hi_; }
 
 constexpr uint128::operator char() const { return static_cast<char>(lo_); }
 
 constexpr uint128::operator signed char() const {
   return static_cast<signed char>(lo_);
 }
 
 constexpr uint128::operator unsigned char() const {
   return static_cast<unsigned char>(lo_);
 }
 
 constexpr uint128::operator char16_t() const {
   return static_cast<char16_t>(lo_);
 }
 
 constexpr uint128::operator char32_t() const {
   return static_cast<char32_t>(lo_);
 }
 
 constexpr uint128::operator ABSL_INTERNAL_WCHAR_T() const {
   return static_cast<ABSL_INTERNAL_WCHAR_T>(lo_);
 }
 
 // NOLINTNEXTLINE(runtime/int)
 constexpr uint128::operator short() const { return static_cast<short>(lo_); }
 
 constexpr uint128::operator unsigned short() const {  // NOLINT(runtime/int)
   return static_cast<unsigned short>(lo_);            // NOLINT(runtime/int)
 }
 
 constexpr uint128::operator int() const { return static_cast<int>(lo_); }
 
 constexpr uint128::operator unsigned int() const {
   return static_cast<unsigned int>(lo_);
 }
 
 // NOLINTNEXTLINE(runtime/int)
 constexpr uint128::operator long() const { return static_cast<long>(lo_); }
 
 constexpr uint128::operator unsigned long() const {  // NOLINT(runtime/int)
   return static_cast<unsigned long>(lo_);            // NOLINT(runtime/int)
 }
 
 constexpr uint128::operator long long() const {  // NOLINT(runtime/int)
   return static_cast<long long>(lo_);            // NOLINT(runtime/int)
 }
 
 constexpr uint128::operator unsigned long long() const {  // NOLINT(runtime/int)
   return static_cast<unsigned long long>(lo_);            // NOLINT(runtime/int)
 }
 
 #ifdef ABSL_HAVE_INTRINSIC_INT128
 constexpr uint128::operator __int128() const {
   return (static_cast<__int128>(hi_) << 64) + lo_;
 }
 
 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.
 
 constexpr bool operator==(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return static_cast<unsigned __int128>(lhs) ==
          static_cast<unsigned __int128>(rhs);
 #else
   return (Uint128Low64(lhs) == Uint128Low64(rhs) &&
           Uint128High64(lhs) == Uint128High64(rhs));
 #endif
 }
 
 constexpr bool operator!=(uint128 lhs, uint128 rhs) { return !(lhs == rhs); }
 
 constexpr bool operator<(uint128 lhs, uint128 rhs) {
 #ifdef ABSL_HAVE_INTRINSIC_INT128
   return static_cast<unsigned __int128>(lhs) <
          static_cast<unsigned __int128>(rhs);
 #else
   return (Uint128High64(lhs) == Uint128High64(rhs))
              ? (Uint128Low64(lhs) < Uint128Low64(rhs))
              : (Uint128High64(lhs) < Uint128High64(rhs));
 #endif
 }
 
 constexpr bool operator>(uint128 lhs, uint128 rhs) { return rhs < lhs; }
 
 constexpr bool operator<=(uint128 lhs, uint128 rhs) { return !(rhs < lhs); }
 
 constexpr bool operator>=(uint128 lhs, uint128 rhs) { return !(lhs < rhs); }
 
 #ifdef __cpp_impl_three_way_comparison
 constexpr absl::strong_ordering operator<=>(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   if (auto lhs_128 = static_cast<unsigned __int128>(lhs),
       rhs_128 = static_cast<unsigned __int128>(rhs);
       lhs_128 < rhs_128) {
     return absl::strong_ordering::less;
   } else if (lhs_128 > rhs_128) {
     return absl::strong_ordering::greater;
   } else {
     return absl::strong_ordering::equal;
   }
 #else
   if (uint64_t lhs_high = Uint128High64(lhs), rhs_high = Uint128High64(rhs);
       lhs_high < rhs_high) {
     return absl::strong_ordering::less;
   } else if (lhs_high > rhs_high) {
     return absl::strong_ordering::greater;
   } else if (uint64_t lhs_low = Uint128Low64(lhs), rhs_low = Uint128Low64(rhs);
              lhs_low < rhs_low) {
     return absl::strong_ordering::less;
   } else if (lhs_low > rhs_low) {
     return absl::strong_ordering::greater;
   } else {
     return absl::strong_ordering::equal;
   }
 #endif
 }
 #endif
 
 // Unary operators.
 
 constexpr inline uint128 operator+(uint128 val) { return val; }
 
 constexpr inline int128 operator+(int128 val) { return val; }
 
 constexpr uint128 operator-(uint128 val) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return -static_cast<unsigned __int128>(val);
 #else
   return MakeUint128(
       ~Uint128High64(val) + static_cast<unsigned long>(Uint128Low64(val) == 0),
       ~Uint128Low64(val) + 1);
 #endif
 }
 
 constexpr inline bool operator!(uint128 val) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return !static_cast<unsigned __int128>(val);
 #else
   return !Uint128High64(val) && !Uint128Low64(val);
 #endif
 }
 
 // Logical operators.
 
 constexpr inline uint128 operator~(uint128 val) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return ~static_cast<unsigned __int128>(val);
 #else
   return MakeUint128(~Uint128High64(val), ~Uint128Low64(val));
 #endif
 }
 
 constexpr inline uint128 operator|(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return static_cast<unsigned __int128>(lhs) |
          static_cast<unsigned __int128>(rhs);
 #else
   return MakeUint128(Uint128High64(lhs) | Uint128High64(rhs),
                      Uint128Low64(lhs) | Uint128Low64(rhs));
 #endif
 }
 
 constexpr inline uint128 operator&(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return static_cast<unsigned __int128>(lhs) &
          static_cast<unsigned __int128>(rhs);
 #else
   return MakeUint128(Uint128High64(lhs) & Uint128High64(rhs),
                      Uint128Low64(lhs) & Uint128Low64(rhs));
 #endif
 }
 
 constexpr inline uint128 operator^(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return static_cast<unsigned __int128>(lhs) ^
          static_cast<unsigned __int128>(rhs);
 #else
   return MakeUint128(Uint128High64(lhs) ^ Uint128High64(rhs),
                      Uint128Low64(lhs) ^ Uint128Low64(rhs));
 #endif
 }
 
 inline uint128& uint128::operator|=(uint128 other) {
   *this = *this | other;
   return *this;
 }
 
 inline uint128& uint128::operator&=(uint128 other) {
   *this = *this & other;
   return *this;
 }
 
 inline uint128& uint128::operator^=(uint128 other) {
   *this = *this ^ other;
   return *this;
 }
 
 // Arithmetic operators.
 
 constexpr uint128 operator<<(uint128 lhs, int amount) {
 #ifdef ABSL_HAVE_INTRINSIC_INT128
   return static_cast<unsigned __int128>(lhs) << amount;
 #else
   // uint64_t shifts of >= 64 are undefined, so we will need some
   // special-casing.
   return amount >= 64  ? MakeUint128(Uint128Low64(lhs) << (amount - 64), 0)
          : amount == 0 ? lhs
                        : MakeUint128((Uint128High64(lhs) << amount) |
                                          (Uint128Low64(lhs) >> (64 - amount)),
                                      Uint128Low64(lhs) << amount);
 #endif
 }
 
 constexpr uint128 operator>>(uint128 lhs, int amount) {
 #ifdef ABSL_HAVE_INTRINSIC_INT128
   return static_cast<unsigned __int128>(lhs) >> amount;
 #else
   // uint64_t shifts of >= 64 are undefined, so we will need some
   // special-casing.
   return amount >= 64  ? MakeUint128(0, Uint128High64(lhs) >> (amount - 64))
          : amount == 0 ? lhs
                        : MakeUint128(Uint128High64(lhs) >> amount,
                                      (Uint128Low64(lhs) >> amount) |
                                          (Uint128High64(lhs) << (64 - amount)));
 #endif
 }
 
 #if !defined(ABSL_HAVE_INTRINSIC_INT128)
 namespace int128_internal {
 constexpr uint128 AddResult(uint128 result, uint128 lhs) {
   // check for carry
   return (Uint128Low64(result) < Uint128Low64(lhs))
              ? MakeUint128(Uint128High64(result) + 1, Uint128Low64(result))
              : result;
 }
 }  // namespace int128_internal
 #endif
 
 constexpr uint128 operator+(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return static_cast<unsigned __int128>(lhs) +
          static_cast<unsigned __int128>(rhs);
 #else
   return int128_internal::AddResult(
       MakeUint128(Uint128High64(lhs) + Uint128High64(rhs),
                   Uint128Low64(lhs) + Uint128Low64(rhs)),
       lhs);
 #endif
 }
 
 #if !defined(ABSL_HAVE_INTRINSIC_INT128)
 namespace int128_internal {
 constexpr uint128 SubstructResult(uint128 result, uint128 lhs, uint128 rhs) {
   // check for carry
   return (Uint128Low64(lhs) < Uint128Low64(rhs))
              ? MakeUint128(Uint128High64(result) - 1, Uint128Low64(result))
              : result;
 }
 }  // namespace int128_internal
 #endif
 
 constexpr uint128 operator-(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   return static_cast<unsigned __int128>(lhs) -
          static_cast<unsigned __int128>(rhs);
 #else
   return int128_internal::SubstructResult(
       MakeUint128(Uint128High64(lhs) - Uint128High64(rhs),
                   Uint128Low64(lhs) - Uint128Low64(rhs)),
       lhs, rhs);
 #endif
 }
 
 inline uint128 operator*(uint128 lhs, uint128 rhs) {
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
   // TODO(strel) Remove once alignment issues are resolved and unsigned __int128
   // can be used for uint128 storage.
   return static_cast<unsigned __int128>(lhs) *
          static_cast<unsigned __int128>(rhs);
 #elif defined(_MSC_VER) && defined(_M_X64) && !defined(_M_ARM64EC)
   uint64_t carry;
   uint64_t low = _umul128(Uint128Low64(lhs), Uint128Low64(rhs), &carry);
   return MakeUint128(Uint128Low64(lhs) * Uint128High64(rhs) +
                          Uint128High64(lhs) * Uint128Low64(rhs) + carry,
                      low);
 #else   // ABSL_HAVE_INTRINSIC128
   uint64_t a32 = Uint128Low64(lhs) >> 32;
   uint64_t a00 = Uint128Low64(lhs) & 0xffffffff;
   uint64_t b32 = Uint128Low64(rhs) >> 32;
   uint64_t b00 = Uint128Low64(rhs) & 0xffffffff;
   uint128 result =
       MakeUint128(Uint128High64(lhs) * Uint128Low64(rhs) +
                       Uint128Low64(lhs) * Uint128High64(rhs) + a32 * b32,
                   a00 * b00);
   result += uint128(a32 * b00) << 32;
   result += uint128(a00 * b32) << 32;
   return result;
 #endif  // ABSL_HAVE_INTRINSIC128
 }
 
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
 inline uint128 operator/(uint128 lhs, uint128 rhs) {
   return static_cast<unsigned __int128>(lhs) /
          static_cast<unsigned __int128>(rhs);
 }
 
 inline uint128 operator%(uint128 lhs, uint128 rhs) {
   return static_cast<unsigned __int128>(lhs) %
          static_cast<unsigned __int128>(rhs);
 }
 #endif
 
 // 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;
 }
 
 constexpr int128 MakeInt128(int64_t high, uint64_t low) {
   return int128(high, low);
 }
 
 // Assignment from integer types.
 inline int128& int128::operator=(int v) { return *this = int128(v); }
 
 inline int128& int128::operator=(unsigned int v) { return *this = int128(v); }
 
 inline int128& int128::operator=(long v) {  // NOLINT(runtime/int)
   return *this = int128(v);
 }
 
 // NOLINTNEXTLINE(runtime/int)
 inline int128& int128::operator=(unsigned long v) { return *this = int128(v); }
 
 // NOLINTNEXTLINE(runtime/int)
 inline int128& int128::operator=(long long v) { return *this = int128(v); }
 
 // NOLINTNEXTLINE(runtime/int)
 inline int128& int128::operator=(unsigned long long v) {
   return *this = int128(v);
 }
 
 // Arithmetic operators.
 constexpr int128 operator-(int128 v);
 constexpr int128 operator+(int128 lhs, int128 rhs);
 constexpr int128 operator-(int128 lhs, int128 rhs);
 int128 operator*(int128 lhs, int128 rhs);
 int128 operator/(int128 lhs, int128 rhs);
 int128 operator%(int128 lhs, int128 rhs);
 constexpr int128 operator|(int128 lhs, int128 rhs);
 constexpr int128 operator&(int128 lhs, int128 rhs);
 constexpr int128 operator^(int128 lhs, int128 rhs);
 constexpr int128 operator<<(int128 lhs, int amount);
 constexpr int128 operator>>(int128 lhs, int amount);
 
 inline int128& int128::operator+=(int128 other) {
   *this = *this + other;
   return *this;
 }
 
 inline int128& int128::operator-=(int128 other) {
   *this = *this - other;
   return *this;
 }
 
 inline int128& int128::operator*=(int128 other) {
   *this = *this * other;
   return *this;
 }
 
 inline int128& int128::operator/=(int128 other) {
   *this = *this / other;
   return *this;
 }
 
 inline int128& int128::operator%=(int128 other) {
   *this = *this % other;
   return *this;
 }
 
 inline int128& int128::operator|=(int128 other) {
   *this = *this | other;
   return *this;
 }
 
 inline int128& int128::operator&=(int128 other) {
   *this = *this & other;
   return *this;
 }
 
 inline int128& int128::operator^=(int128 other) {
   *this = *this ^ other;
   return *this;
 }
 
 inline int128& int128::operator<<=(int amount) {
   *this = *this << amount;
   return *this;
 }
 
 inline int128& int128::operator>>=(int amount) {
   *this = *this >> amount;
   return *this;
 }
 
 // Forward declaration for comparison operators.
 constexpr bool operator!=(int128 lhs, int128 rhs);
 
 namespace int128_internal {
 
 // Casts from unsigned to signed while preserving the underlying binary
 // representation.
 constexpr int64_t BitCastToSigned(uint64_t v) {
   // Casting an unsigned integer to a signed integer of the same
   // width is implementation defined behavior if the source value would not fit
   // in the destination type. We step around it with a roundtrip bitwise not
   // operation to make sure this function remains constexpr. Clang, GCC, and
   // MSVC optimize this to a no-op on x86-64.
   return v & (uint64_t{1} << 63) ? ~static_cast<int64_t>(~v)
                                  : static_cast<int64_t>(v);
 }
 
 }  // namespace int128_internal
 
 #if defined(ABSL_HAVE_INTRINSIC_INT128)
 #include "absl/numeric/int128_have_intrinsic.inc"  // IWYU pragma: export
 #else  // ABSL_HAVE_INTRINSIC_INT128
 #include "absl/numeric/int128_no_intrinsic.inc"  // IWYU pragma: export
 #endif  // ABSL_HAVE_INTRINSIC_INT128
 
 ABSL_NAMESPACE_END
 }  // namespace absl
 
 #undef ABSL_INTERNAL_WCHAR_T
 
 #endif  // ABSL_NUMERIC_INT128_H_

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