Initial Commit

6 files changed, 1388 insertions, 0 deletions

diff --git a/absl/numeric/BUILD.bazel b/absl/numeric/BUILD.bazel
new file mode 100644
index 000000000000..2c80db302a0a
--- /dev/null
+++ b/absl/numeric/BUILD.bazel
@@ -0,0 +1,39 @@
+load(
+    "//absl:copts.bzl",
+    "ABSL_DEFAULT_COPTS",
+    "ABSL_TEST_COPTS",
+)
+load(
+    "//absl:test_dependencies.bzl",
+    "GUNIT_MAIN_DEPS_SELECTOR",
+)
+
+package(default_visibility = ["//visibility:public"])
+
+licenses(["unencumbered"])  # Owned by Google
+
+cc_library(
+    name = "int128",
+    srcs = ["int128.cc"],
+    hdrs = ["int128.h"],
+    copts = ABSL_DEFAULT_COPTS,
+    deps = [
+        "//absl/base:config",
+        "//absl/base:core_headers",
+    ],
+)
+
+cc_test(
+    name = "int128_test",
+    size = "small",
+    srcs = [
+        "int128_test.cc",
+    ],
+    copts = ABSL_TEST_COPTS,
+    deps = [
+        ":int128",
+        "//absl/base",
+        "//absl/base:core_headers",
+        "//absl/meta:type_traits",
+    ] + select(GUNIT_MAIN_DEPS_SELECTOR),
+)
diff --git a/absl/numeric/int128.cc b/absl/numeric/int128.cc
new file mode 100644
index 000000000000..184041fe4a22
--- /dev/null
+++ b/absl/numeric/int128.cc
@@ -0,0 +1,200 @@
+// 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.
+
+#include "absl/numeric/int128.h"
+
+#include <cassert>
+#include <cstdlib>
+#include <iomanip>
+#include <iostream>  // NOLINT(readability/streams)
+#include <sstream>
+
+namespace absl {
+
+const uint128 kuint128max = MakeUint128(std::numeric_limits<uint64_t>::max(),
+                                        std::numeric_limits<uint64_t>::max());
+
+namespace {
+
+// Returns the 0-based position of the last set bit (i.e., most significant bit)
+// in the given uint64_t. The argument may not be 0.
+//
+// For example:
+//   Given: 5 (decimal) == 101 (binary)
+//   Returns: 2
+#define STEP(T, n, pos, sh)                   \
+  do {                                        \
+    if ((n) >= (static_cast<T>(1) << (sh))) { \
+      (n) = (n) >> (sh);                      \
+      (pos) |= (sh);                          \
+    }                                         \
+  } while (0)
+static inline int Fls64(uint64_t n) {
+  assert(n != 0);
+  int pos = 0;
+  STEP(uint64_t, n, pos, 0x20);
+  uint32_t n32 = static_cast<uint32_t>(n);
+  STEP(uint32_t, n32, pos, 0x10);
+  STEP(uint32_t, n32, pos, 0x08);
+  STEP(uint32_t, n32, pos, 0x04);
+  return pos + ((uint64_t{0x3333333322221100} >> (n32 << 2)) & 0x3);
+}
+#undef STEP
+
+// Like Fls64() above, but returns the 0-based position of the last set bit
+// (i.e., most significant bit) in the given uint128. The argument may not be 0.
+static inline int Fls128(uint128 n) {
+  if (uint64_t hi = Uint128High64(n)) {
+    return Fls64(hi) + 64;
+  }
+  return Fls64(Uint128Low64(n));
+}
+
+// Long division/modulo for uint128 implemented using the shift-subtract
+// division algorithm adapted from:
+// http://stackoverflow.com/questions/5386377/division-without-using
+void DivModImpl(uint128 dividend, uint128 divisor, uint128* quotient_ret,
+                uint128* remainder_ret) {
+  assert(divisor != 0);
+
+  if (divisor > dividend) {
+    *quotient_ret = 0;
+    *remainder_ret = dividend;
+    return;
+  }
+
+  if (divisor == dividend) {
+    *quotient_ret = 1;
+    *remainder_ret = 0;
+    return;
+  }
+
+  uint128 denominator = divisor;
+  uint128 quotient = 0;
+
+  // Left aligns the MSB of the denominator and the dividend.
+  const int shift = Fls128(dividend) - Fls128(denominator);
+  denominator <<= shift;
+
+  // Uses shift-subtract algorithm to divide dividend by denominator. The
+  // remainder will be left in dividend.
+  for (int i = 0; i <= shift; ++i) {
+    quotient <<= 1;
+    if (dividend >= denominator) {
+      dividend -= denominator;
+      quotient |= 1;
+    }
+    denominator >>= 1;
+  }
+
+  *quotient_ret = quotient;
+  *remainder_ret = dividend;
+}
+
+template <typename T>
+uint128 Initialize128FromFloat(T v) {
+  // Rounding behavior is towards zero, same as for built-in types.
+
+  // Undefined behavior if v is NaN or cannot fit into uint128.
+  assert(!std::isnan(v) && v > -1 && v < std::ldexp(static_cast<T>(1), 128));
+
+  if (v >= std::ldexp(static_cast<T>(1), 64)) {
+    uint64_t hi = static_cast<uint64_t>(std::ldexp(v, -64));
+    uint64_t lo = static_cast<uint64_t>(v - std::ldexp(static_cast<T>(hi), 64));
+    return MakeUint128(hi, lo);
+  }
+
+  return MakeUint128(0, static_cast<uint64_t>(v));
+}
+}  // namespace
+
+uint128::uint128(float v) : uint128(Initialize128FromFloat(v)) {}
+uint128::uint128(double v) : uint128(Initialize128FromFloat(v)) {}
+uint128::uint128(long double v) : uint128(Initialize128FromFloat(v)) {}
+
+uint128& uint128::operator/=(const uint128& divisor) {
+  uint128 quotient = 0;
+  uint128 remainder = 0;
+  DivModImpl(*this, divisor, &quotient, &remainder);
+  *this = quotient;
+  return *this;
+}
+uint128& uint128::operator%=(const uint128& divisor) {
+  uint128 quotient = 0;
+  uint128 remainder = 0;
+  DivModImpl(*this, divisor, &quotient, &remainder);
+  *this = remainder;
+  return *this;
+}
+
+std::ostream& operator<<(std::ostream& o, const uint128& b) {
+  std::ios_base::fmtflags flags = o.flags();
+
+  // Select a divisor which is the largest power of the base < 2^64.
+  uint128 div;
+  int div_base_log;
+  switch (flags & std::ios::basefield) {
+    case std::ios::hex:
+      div = 0x1000000000000000;  // 16^15
+      div_base_log = 15;
+      break;
+    case std::ios::oct:
+      div = 01000000000000000000000;  // 8^21
+      div_base_log = 21;
+      break;
+    default:  // std::ios::dec
+      div = 10000000000000000000u;  // 10^19
+      div_base_log = 19;
+      break;
+  }
+
+  // Now piece together the uint128 representation from three chunks of
+  // the original value, each less than "div" and therefore representable
+  // as a uint64_t.
+  std::ostringstream os;
+  std::ios_base::fmtflags copy_mask =
+      std::ios::basefield | std::ios::showbase | std::ios::uppercase;
+  os.setf(flags & copy_mask, copy_mask);
+  uint128 high = b;
+  uint128 low;
+  DivModImpl(high, div, &high, &low);
+  uint128 mid;
+  DivModImpl(high, div, &high, &mid);
+  if (Uint128Low64(high) != 0) {
+    os << Uint128Low64(high);
+    os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
+    os << Uint128Low64(mid);
+    os << std::setw(div_base_log);
+  } else if (Uint128Low64(mid) != 0) {
+    os << Uint128Low64(mid);
+    os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
+  }
+  os << Uint128Low64(low);
+  std::string rep = os.str();
+
+  // Add the requisite padding.
+  std::streamsize width = o.width(0);
+  if (static_cast<size_t>(width) > rep.size()) {
+    if ((flags & std::ios::adjustfield) == std::ios::left) {
+      rep.append(width - rep.size(), o.fill());
+    } else {
+      rep.insert(0, width - rep.size(), o.fill());
+    }
+  }
+
+  // Stream the final representation in a single "<<" call.
+  return o << rep;
+}
+
+}  // namespace absl
diff --git a/absl/numeric/int128.h b/absl/numeric/int128.h
new file mode 100644
index 000000000000..72be806a4f01
--- /dev/null
+++ b/absl/numeric/int128.h
@@ -0,0 +1,651 @@
+//
+// 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 `unint128_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
+//
+// NOTE: the alignment requirement of `uint128` is due to change, so users
+// should take care to avoid depending on the current 8 byte alignment.
+// TODO(strel) Remove alignment note above once alignof(uint128) becomes 16.
+class 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(b/31950287): 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_
diff --git a/absl/numeric/int128_have_intrinsic.inc b/absl/numeric/int128_have_intrinsic.inc
new file mode 100644
index 000000000000..bb6491e178ab
--- /dev/null
+++ b/absl/numeric/int128_have_intrinsic.inc
@@ -0,0 +1,3 @@
+// This file will contain :int128 implementation details that depend on internal
+// representation when ABSL_HAVE_INTRINSIC_INT128 is defined. This file will be
+// included by int128.h.
\ No newline at end of file
diff --git a/absl/numeric/int128_no_intrinsic.inc b/absl/numeric/int128_no_intrinsic.inc
new file mode 100644
index 000000000000..2dbff2b31565
--- /dev/null
+++ b/absl/numeric/int128_no_intrinsic.inc
@@ -0,0 +1,3 @@
+// This file will contain :int128 implementation details that depend on internal
+// representation when ABSL_HAVE_INTRINSIC_INT128 is *not* defined. This file
+// will be included by int128.h.
diff --git a/absl/numeric/int128_test.cc b/absl/numeric/int128_test.cc
new file mode 100644
index 000000000000..c8aabeb3184a
--- /dev/null
+++ b/absl/numeric/int128_test.cc
@@ -0,0 +1,492 @@
+// 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.
+
+#include "absl/numeric/int128.h"
+
+#include <algorithm>
+#include <limits>
+#include <random>
+#include <sstream>
+#include <type_traits>
+#include <utility>
+#include <vector>
+
+#include "gtest/gtest.h"
+#include "absl/base/internal/cycleclock.h"
+#include "absl/meta/type_traits.h"
+
+#if defined(_MSC_VER) && _MSC_VER == 1900
+// Disable "unary minus operator applied to unsigned type" warnings in Microsoft
+// Visual C++ 14 (2015).
+#pragma warning(disable:4146)
+#endif
+
+namespace {
+
+template <typename T>
+class Uint128IntegerTraitsTest : public ::testing::Test {};
+typedef ::testing::Types<bool, char, signed char, unsigned char, char16_t,
+                         char32_t, wchar_t,
+                         short,           // NOLINT(runtime/int)
+                         unsigned short,  // NOLINT(runtime/int)
+                         int, unsigned int,
+                         long,                // NOLINT(runtime/int)
+                         unsigned long,       // NOLINT(runtime/int)
+                         long long,           // NOLINT(runtime/int)
+                         unsigned long long>  // NOLINT(runtime/int)
+    IntegerTypes;
+
+template <typename T>
+class Uint128FloatTraitsTest : public ::testing::Test {};
+typedef ::testing::Types<float, double, long double> FloatingPointTypes;
+
+TYPED_TEST_CASE(Uint128IntegerTraitsTest, IntegerTypes);
+
+TYPED_TEST(Uint128IntegerTraitsTest, ConstructAssignTest) {
+  static_assert(std::is_constructible<absl::uint128, TypeParam>::value,
+                "absl::uint128 must be constructible from TypeParam");
+  static_assert(std::is_assignable<absl::uint128&, TypeParam>::value,
+                "absl::uint128 must be assignable from TypeParam");
+  static_assert(!std::is_assignable<TypeParam&, absl::uint128>::value,
+                "TypeParam must not be assignable from absl::uint128");
+}
+
+TYPED_TEST_CASE(Uint128FloatTraitsTest, FloatingPointTypes);
+
+TYPED_TEST(Uint128FloatTraitsTest, ConstructAssignTest) {
+  static_assert(std::is_constructible<absl::uint128, TypeParam>::value,
+                "absl::uint128 must be constructible from TypeParam");
+  static_assert(!std::is_assignable<absl::uint128&, TypeParam>::value,
+                "absl::uint128 must not be assignable from TypeParam");
+  static_assert(!std::is_assignable<TypeParam&, absl::uint128>::value,
+                "TypeParam must not be assignable from absl::uint128");
+}
+
+#ifdef ABSL_HAVE_INTRINSIC_INT128
+// These type traits done separately as TYPED_TEST requires typeinfo, and not
+// all platforms have this for __int128 even though they define the type.
+TEST(Uint128, IntrinsicTypeTraitsTest) {
+  static_assert(std::is_constructible<absl::uint128, __int128>::value,
+                "absl::uint128 must be constructible from __int128");
+  static_assert(std::is_assignable<absl::uint128&, __int128>::value,
+                "absl::uint128 must be assignable from __int128");
+  static_assert(!std::is_assignable<__int128&, absl::uint128>::value,
+                "__int128 must not be assignable from absl::uint128");
+
+  static_assert(std::is_constructible<absl::uint128, unsigned __int128>::value,
+                "absl::uint128 must be constructible from unsigned __int128");
+  static_assert(std::is_assignable<absl::uint128&, unsigned __int128>::value,
+                "absl::uint128 must be assignable from unsigned __int128");
+  static_assert(!std::is_assignable<unsigned __int128&, absl::uint128>::value,
+                "unsigned __int128 must not be assignable from absl::uint128");
+}
+#endif  // ABSL_HAVE_INTRINSIC_INT128
+
+TEST(Uint128, AllTests) {
+  absl::uint128 zero = 0;
+  absl::uint128 one = 1;
+  absl::uint128 one_2arg = absl::MakeUint128(0, 1);
+  absl::uint128 two = 2;
+  absl::uint128 three = 3;
+  absl::uint128 big = absl::MakeUint128(2000, 2);
+  absl::uint128 big_minus_one = absl::MakeUint128(2000, 1);
+  absl::uint128 bigger = absl::MakeUint128(2001, 1);
+  absl::uint128 biggest = absl::kuint128max;
+  absl::uint128 high_low = absl::MakeUint128(1, 0);
+  absl::uint128 low_high =
+      absl::MakeUint128(0, std::numeric_limits<uint64_t>::max());
+  EXPECT_LT(one, two);
+  EXPECT_GT(two, one);
+  EXPECT_LT(one, big);
+  EXPECT_LT(one, big);
+  EXPECT_EQ(one, one_2arg);
+  EXPECT_NE(one, two);
+  EXPECT_GT(big, one);
+  EXPECT_GE(big, two);
+  EXPECT_GE(big, big_minus_one);
+  EXPECT_GT(big, big_minus_one);
+  EXPECT_LT(big_minus_one, big);
+  EXPECT_LE(big_minus_one, big);
+  EXPECT_NE(big_minus_one, big);
+  EXPECT_LT(big, biggest);
+  EXPECT_LE(big, biggest);
+  EXPECT_GT(biggest, big);
+  EXPECT_GE(biggest, big);
+  EXPECT_EQ(big, ~~big);
+  EXPECT_EQ(one, one | one);
+  EXPECT_EQ(big, big | big);
+  EXPECT_EQ(one, one | zero);
+  EXPECT_EQ(one, one & one);
+  EXPECT_EQ(big, big & big);
+  EXPECT_EQ(zero, one & zero);
+  EXPECT_EQ(zero, big & ~big);
+  EXPECT_EQ(zero, one ^ one);
+  EXPECT_EQ(zero, big ^ big);
+  EXPECT_EQ(one, one ^ zero);
+
+  // Shift operators.
+  EXPECT_EQ(big, big << 0);
+  EXPECT_EQ(big, big >> 0);
+  EXPECT_GT(big << 1, big);
+  EXPECT_LT(big >> 1, big);
+  EXPECT_EQ(big, (big << 10) >> 10);
+  EXPECT_EQ(big, (big >> 1) << 1);
+  EXPECT_EQ(one, (one << 80) >> 80);
+  EXPECT_EQ(zero, (one >> 80) << 80);
+
+  // Shift assignments.
+  absl::uint128 big_copy = big;
+  EXPECT_EQ(big << 0, big_copy <<= 0);
+  big_copy = big;
+  EXPECT_EQ(big >> 0, big_copy >>= 0);
+  big_copy = big;
+  EXPECT_EQ(big << 1, big_copy <<= 1);
+  big_copy = big;
+  EXPECT_EQ(big >> 1, big_copy >>= 1);
+  big_copy = big;
+  EXPECT_EQ(big << 10, big_copy <<= 10);
+  big_copy = big;
+  EXPECT_EQ(big >> 10, big_copy >>= 10);
+  big_copy = big;
+  EXPECT_EQ(big << 64, big_copy <<= 64);
+  big_copy = big;
+  EXPECT_EQ(big >> 64, big_copy >>= 64);
+  big_copy = big;
+  EXPECT_EQ(big << 73, big_copy <<= 73);
+  big_copy = big;
+  EXPECT_EQ(big >> 73, big_copy >>= 73);
+
+  EXPECT_EQ(Uint128High64(biggest), std::numeric_limits<uint64_t>::max());
+  EXPECT_EQ(Uint128Low64(biggest), std::numeric_limits<uint64_t>::max());
+  EXPECT_EQ(zero + one, one);
+  EXPECT_EQ(one + one, two);
+  EXPECT_EQ(big_minus_one + one, big);
+  EXPECT_EQ(one - one, zero);
+  EXPECT_EQ(one - zero, one);
+  EXPECT_EQ(zero - one, biggest);
+  EXPECT_EQ(big - big, zero);
+  EXPECT_EQ(big - one, big_minus_one);
+  EXPECT_EQ(big + std::numeric_limits<uint64_t>::max(), bigger);
+  EXPECT_EQ(biggest + 1, zero);
+  EXPECT_EQ(zero - 1, biggest);
+  EXPECT_EQ(high_low - one, low_high);
+  EXPECT_EQ(low_high + one, high_low);
+  EXPECT_EQ(Uint128High64((absl::uint128(1) << 64) - 1), 0);
+  EXPECT_EQ(Uint128Low64((absl::uint128(1) << 64) - 1),
+            std::numeric_limits<uint64_t>::max());
+  EXPECT_TRUE(!!one);
+  EXPECT_TRUE(!!high_low);
+  EXPECT_FALSE(!!zero);
+  EXPECT_FALSE(!one);
+  EXPECT_FALSE(!high_low);
+  EXPECT_TRUE(!zero);
+  EXPECT_TRUE(zero == 0);       // NOLINT(readability/check)
+  EXPECT_FALSE(zero != 0);      // NOLINT(readability/check)
+  EXPECT_FALSE(one == 0);       // NOLINT(readability/check)
+  EXPECT_TRUE(one != 0);        // NOLINT(readability/check)
+  EXPECT_FALSE(high_low == 0);  // NOLINT(readability/check)
+  EXPECT_TRUE(high_low != 0);   // NOLINT(readability/check)
+
+  absl::uint128 test = zero;
+  EXPECT_EQ(++test, one);
+  EXPECT_EQ(test, one);
+  EXPECT_EQ(test++, one);
+  EXPECT_EQ(test, two);
+  EXPECT_EQ(test -= 2, zero);
+  EXPECT_EQ(test, zero);
+  EXPECT_EQ(test += 2, two);
+  EXPECT_EQ(test, two);
+  EXPECT_EQ(--test, one);
+  EXPECT_EQ(test, one);
+  EXPECT_EQ(test--, one);
+  EXPECT_EQ(test, zero);
+  EXPECT_EQ(test |= three, three);
+  EXPECT_EQ(test &= one, one);
+  EXPECT_EQ(test ^= three, two);
+  EXPECT_EQ(test >>= 1, one);
+  EXPECT_EQ(test <<= 1, two);
+
+  EXPECT_EQ(big, -(-big));
+  EXPECT_EQ(two, -((-one) - 1));
+  EXPECT_EQ(absl::kuint128max, -one);
+  EXPECT_EQ(zero, -zero);
+}
+
+TEST(Uint128, ConversionTests) {
+  EXPECT_TRUE(absl::MakeUint128(1, 0));
+
+#ifdef ABSL_HAVE_INTRINSIC_INT128
+  unsigned __int128 intrinsic =
+      (static_cast<unsigned __int128>(0x3a5b76c209de76f6) << 64) +
+      0x1f25e1d63a2b46c5;
+  absl::uint128 custom =
+      absl::MakeUint128(0x3a5b76c209de76f6, 0x1f25e1d63a2b46c5);
+
+  EXPECT_EQ(custom, absl::uint128(intrinsic));
+  EXPECT_EQ(custom, absl::uint128(static_cast<__int128>(intrinsic)));
+  EXPECT_EQ(intrinsic, static_cast<unsigned __int128>(custom));
+  EXPECT_EQ(intrinsic, static_cast<__int128>(custom));
+#endif  // ABSL_HAVE_INTRINSIC_INT128
+
+  // verify that an integer greater than 2**64 that can be stored precisely
+  // inside a double is converted to a absl::uint128 without loss of
+  // information.
+  double precise_double = 0x530e * std::pow(2.0, 64.0) + 0xda74000000000000;
+  absl::uint128 from_precise_double(precise_double);
+  absl::uint128 from_precise_ints =
+      absl::MakeUint128(0x530e, 0xda74000000000000);
+  EXPECT_EQ(from_precise_double, from_precise_ints);
+  EXPECT_DOUBLE_EQ(static_cast<double>(from_precise_ints), precise_double);
+
+  double approx_double = 0xffffeeeeddddcccc * std::pow(2.0, 64.0) +
+                         0xbbbbaaaa99998888;
+  absl::uint128 from_approx_double(approx_double);
+  EXPECT_DOUBLE_EQ(static_cast<double>(from_approx_double), approx_double);
+
+  double round_to_zero = 0.7;
+  double round_to_five = 5.8;
+  double round_to_nine = 9.3;
+  EXPECT_EQ(static_cast<absl::uint128>(round_to_zero), 0);
+  EXPECT_EQ(static_cast<absl::uint128>(round_to_five), 5);
+  EXPECT_EQ(static_cast<absl::uint128>(round_to_nine), 9);
+}
+
+TEST(Uint128, OperatorAssignReturnRef) {
+  absl::uint128 v(1);
+  (v += 4) -= 3;
+  EXPECT_EQ(2, v);
+}
+
+TEST(Uint128, Multiply) {
+  absl::uint128 a, b, c;
+
+  // Zero test.
+  a = 0;
+  b = 0;
+  c = a * b;
+  EXPECT_EQ(0, c);
+
+  // Max carries.
+  a = absl::uint128(0) - 1;
+  b = absl::uint128(0) - 1;
+  c = a * b;
+  EXPECT_EQ(1, c);
+
+  // Self-operation with max carries.
+  c = absl::uint128(0) - 1;
+  c *= c;
+  EXPECT_EQ(1, c);
+
+  // 1-bit x 1-bit.
+  for (int i = 0; i < 64; ++i) {
+    for (int j = 0; j < 64; ++j) {
+      a = absl::uint128(1) << i;
+      b = absl::uint128(1) << j;
+      c = a * b;
+      EXPECT_EQ(absl::uint128(1) << (i + j), c);
+    }
+  }
+
+  // Verified with dc.
+  a = absl::MakeUint128(0xffffeeeeddddcccc, 0xbbbbaaaa99998888);
+  b = absl::MakeUint128(0x7777666655554444, 0x3333222211110000);
+  c = a * b;
+  EXPECT_EQ(absl::MakeUint128(0x530EDA741C71D4C3, 0xBF25975319080000), c);
+  EXPECT_EQ(0, c - b * a);
+  EXPECT_EQ(a*a - b*b, (a+b) * (a-b));
+
+  // Verified with dc.
+  a = absl::MakeUint128(0x0123456789abcdef, 0xfedcba9876543210);
+  b = absl::MakeUint128(0x02468ace13579bdf, 0xfdb97531eca86420);
+  c = a * b;
+  EXPECT_EQ(absl::MakeUint128(0x97a87f4f261ba3f2, 0x342d0bbf48948200), c);
+  EXPECT_EQ(0, c - b * a);
+  EXPECT_EQ(a*a - b*b, (a+b) * (a-b));
+}
+
+TEST(Uint128, AliasTests) {
+  absl::uint128 x1 = absl::MakeUint128(1, 2);
+  absl::uint128 x2 = absl::MakeUint128(2, 4);
+  x1 += x1;
+  EXPECT_EQ(x2, x1);
+
+  absl::uint128 x3 = absl::MakeUint128(1, static_cast<uint64_t>(1) << 63);
+  absl::uint128 x4 = absl::MakeUint128(3, 0);
+  x3 += x3;
+  EXPECT_EQ(x4, x3);
+}
+
+TEST(Uint128, DivideAndMod) {
+  using std::swap;
+
+  // a := q * b + r
+  absl::uint128 a, b, q, r;
+
+  // Zero test.
+  a = 0;
+  b = 123;
+  q = a / b;
+  r = a % b;
+  EXPECT_EQ(0, q);
+  EXPECT_EQ(0, r);
+
+  a = absl::MakeUint128(0x530eda741c71d4c3, 0xbf25975319080000);
+  q = absl::MakeUint128(0x4de2cab081, 0x14c34ab4676e4bab);
+  b = absl::uint128(0x1110001);
+  r = absl::uint128(0x3eb455);
+  ASSERT_EQ(a, q * b + r);  // Sanity-check.
+
+  absl::uint128 result_q, result_r;
+  result_q = a / b;
+  result_r = a % b;
+  EXPECT_EQ(q, result_q);
+  EXPECT_EQ(r, result_r);
+
+  // Try the other way around.
+  swap(q, b);
+  result_q = a / b;
+  result_r = a % b;
+  EXPECT_EQ(q, result_q);
+  EXPECT_EQ(r, result_r);
+  // Restore.
+  swap(b, q);
+
+  // Dividend < divisor; result should be q:0 r:<dividend>.
+  swap(a, b);
+  result_q = a / b;
+  result_r = a % b;
+  EXPECT_EQ(0, result_q);
+  EXPECT_EQ(a, result_r);
+  // Try the other way around.
+  swap(a, q);
+  result_q = a / b;
+  result_r = a % b;
+  EXPECT_EQ(0, result_q);
+  EXPECT_EQ(a, result_r);
+  // Restore.
+  swap(q, a);
+  swap(b, a);
+
+  // Try a large remainder.
+  b = a / 2 + 1;
+  absl::uint128 expected_r =
+      absl::MakeUint128(0x29876d3a0e38ea61, 0xdf92cba98c83ffff);
+  // Sanity checks.
+  ASSERT_EQ(a / 2 - 1, expected_r);
+  ASSERT_EQ(a, b + expected_r);
+  result_q = a / b;
+  result_r = a % b;
+  EXPECT_EQ(1, result_q);
+  EXPECT_EQ(expected_r, result_r);
+}
+
+TEST(Uint128, DivideAndModRandomInputs) {
+  const int kNumIters = 1 << 18;
+  std::minstd_rand random(testing::UnitTest::GetInstance()->random_seed());
+  std::uniform_int_distribution<uint64_t> uniform_uint64;
+  for (int i = 0; i < kNumIters; ++i) {
+    const absl::uint128 a =
+        absl::MakeUint128(uniform_uint64(random), uniform_uint64(random));
+    const absl::uint128 b =
+        absl::MakeUint128(uniform_uint64(random), uniform_uint64(random));
+    if (b == 0) {
+      continue;  // Avoid a div-by-zero.
+    }
+    const absl::uint128 q = a / b;
+    const absl::uint128 r = a % b;
+    ASSERT_EQ(a, b * q + r);
+  }
+}
+
+TEST(Uint128, ConstexprTest) {
+  constexpr absl::uint128 zero = absl::uint128();
+  constexpr absl::uint128 one = 1;
+  constexpr absl::uint128 minus_two = -2;
+  EXPECT_EQ(zero, absl::uint128(0));
+  EXPECT_EQ(one, absl::uint128(1));
+  EXPECT_EQ(minus_two, absl::MakeUint128(-1, -2));
+}
+
+TEST(Uint128, Traits) {
+  EXPECT_TRUE(absl::is_trivially_copy_constructible<absl::uint128>::value);
+  EXPECT_TRUE(absl::is_trivially_copy_assignable<absl::uint128>::value);
+  EXPECT_TRUE(std::is_trivially_destructible<absl::uint128>::value);
+}
+
+TEST(Uint128, OStream) {
+  struct {
+    absl::uint128 val;
+    std::ios_base::fmtflags flags;
+    std::streamsize width;
+    char fill;
+    const char* rep;
+  } cases[] = {
+      // zero with different bases
+      {absl::uint128(0), std::ios::dec, 0, '_', "0"},
+      {absl::uint128(0), std::ios::oct, 0, '_', "0"},
+      {absl::uint128(0), std::ios::hex, 0, '_', "0"},
+      // crossover between lo_ and hi_
+      {absl::MakeUint128(0, -1), std::ios::dec, 0, '_', "18446744073709551615"},
+      {absl::MakeUint128(0, -1), std::ios::oct, 0, '_',
+       "1777777777777777777777"},
+      {absl::MakeUint128(0, -1), std::ios::hex, 0, '_', "ffffffffffffffff"},
+      {absl::MakeUint128(1, 0), std::ios::dec, 0, '_', "18446744073709551616"},
+      {absl::MakeUint128(1, 0), std::ios::oct, 0, '_',
+       "2000000000000000000000"},
+      {absl::MakeUint128(1, 0), std::ios::hex, 0, '_', "10000000000000000"},
+      // just the top bit
+      {absl::MakeUint128(0x8000000000000000, 0), std::ios::dec, 0, '_',
+       "170141183460469231731687303715884105728"},
+      {absl::MakeUint128(0x8000000000000000, 0), std::ios::oct, 0, '_',
+       "2000000000000000000000000000000000000000000"},
+      {absl::MakeUint128(0x8000000000000000, 0), std::ios::hex, 0, '_',
+       "80000000000000000000000000000000"},
+      // maximum absl::uint128 value
+      {absl::MakeUint128(-1, -1), std::ios::dec, 0, '_',
+       "340282366920938463463374607431768211455"},
+      {absl::MakeUint128(-1, -1), std::ios::oct, 0, '_',
+       "3777777777777777777777777777777777777777777"},
+      {absl::MakeUint128(-1, -1), std::ios::hex, 0, '_',
+       "ffffffffffffffffffffffffffffffff"},
+      // uppercase
+      {absl::MakeUint128(-1, -1), std::ios::hex | std::ios::uppercase, 0, '_',
+       "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"},
+      // showbase
+      {absl::uint128(1), std::ios::dec | std::ios::showbase, 0, '_', "1"},
+      {absl::uint128(1), std::ios::oct | std::ios::showbase, 0, '_', "01"},
+      {absl::uint128(1), std::ios::hex | std::ios::showbase, 0, '_', "0x1"},
+      // showbase does nothing on zero
+      {absl::uint128(0), std::ios::dec | std::ios::showbase, 0, '_', "0"},
+      {absl::uint128(0), std::ios::oct | std::ios::showbase, 0, '_', "0"},
+      {absl::uint128(0), std::ios::hex | std::ios::showbase, 0, '_', "0"},
+      // showpos does nothing on unsigned types
+      {absl::uint128(1), std::ios::dec | std::ios::showpos, 0, '_', "1"},
+      // padding
+      {absl::uint128(9), std::ios::dec, 6, '_', "_____9"},
+      {absl::uint128(12345), std::ios::dec, 6, '_', "_12345"},
+      // left adjustment
+      {absl::uint128(9), std::ios::dec | std::ios::left, 6, '_', "9_____"},
+      {absl::uint128(12345), std::ios::dec | std::ios::left, 6, '_', "12345_"},
+  };
+  for (const auto& test_case : cases) {
+    std::ostringstream os;
+    os.flags(test_case.flags);
+    os.width(test_case.width);
+    os.fill(test_case.fill);
+    os << test_case.val;
+    EXPECT_EQ(test_case.rep, os.str());
+  }
+}
+
+}  // namespace