Add 'third_party/abseil_cpp/' from commit '768eb2ca28'

git-subtree-dir: third_party/abseil_cpp
git-subtree-mainline: ffb2ae54be
git-subtree-split: 768eb2ca28

third_party/abseil_cpp/absl/numeric/BUILD.bazel

@@ -0,0 +1,73 @@
+# Copyright 2018 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.
+
+load("@rules_cc//cc:defs.bzl", "cc_library", "cc_test")
+load(
+    "//absl:copts/configure_copts.bzl",
+    "ABSL_DEFAULT_COPTS",
+    "ABSL_DEFAULT_LINKOPTS",
+    "ABSL_TEST_COPTS",
+)
+
+package(default_visibility = ["//visibility:public"])
+
+licenses(["notice"])  # Apache 2.0
+
+cc_library(
+    name = "int128",
+    srcs = [
+        "int128.cc",
+        "int128_have_intrinsic.inc",
+        "int128_no_intrinsic.inc",
+    ],
+    hdrs = ["int128.h"],
+    copts = ABSL_DEFAULT_COPTS,
+    linkopts = ABSL_DEFAULT_LINKOPTS,
+    deps = [
+        "//absl/base:config",
+        "//absl/base:core_headers",
+    ],
+)
+
+cc_test(
+    name = "int128_test",
+    size = "small",
+    srcs = [
+        "int128_stream_test.cc",
+        "int128_test.cc",
+    ],
+    copts = ABSL_TEST_COPTS,
+    linkopts = ABSL_DEFAULT_LINKOPTS,
+    deps = [
+        ":int128",
+        "//absl/base",
+        "//absl/base:core_headers",
+        "//absl/hash:hash_testing",
+        "//absl/meta:type_traits",
+        "@com_google_googletest//:gtest_main",
+    ],
+)
+
+cc_test(
+    name = "int128_benchmark",
+    srcs = ["int128_benchmark.cc"],
+    copts = ABSL_TEST_COPTS,
+    linkopts = ABSL_DEFAULT_LINKOPTS,
+    tags = ["benchmark"],
+    deps = [
+        ":int128",
+        "//absl/base:config",
+        "@com_github_google_benchmark//:benchmark_main",
+    ],
+)

third_party/abseil_cpp/absl/numeric/CMakeLists.txt

@@ -0,0 +1,60 @@
+#
+# 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.
+#
+
+absl_cc_library(
+  NAME
+    int128
+  HDRS
+    "int128.h"
+  SRCS
+    "int128.cc"
+    "int128_have_intrinsic.inc"
+    "int128_no_intrinsic.inc"
+  COPTS
+    ${ABSL_DEFAULT_COPTS}
+  DEPS
+    absl::config
+    absl::core_headers
+  PUBLIC
+)
+
+absl_cc_test(
+  NAME
+    int128_test
+  SRCS
+    "int128_stream_test.cc"
+    "int128_test.cc"
+  COPTS
+    ${ABSL_TEST_COPTS}
+  DEPS
+    absl::int128
+    absl::base
+    absl::core_headers
+    absl::hash_testing
+    absl::type_traits
+    gmock_main
+)
+
+# component target
+absl_cc_library(
+  NAME
+    numeric
+  COPTS
+    ${ABSL_DEFAULT_COPTS}
+  DEPS
+    absl::int128
+  PUBLIC
+)

third_party/abseil_cpp/absl/numeric/int128.cc

@@ -0,0 +1,404 @@
+// 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.
+
+#include "absl/numeric/int128.h"
+
+#include <stddef.h>
+#include <cassert>
+#include <iomanip>
+#include <ostream>  // NOLINT(readability/streams)
+#include <sstream>
+#include <string>
+#include <type_traits>
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+
+ABSL_DLL 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:
+// https://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 MakeUint128FromFloat(T v) {
+  static_assert(std::is_floating_point<T>::value, "");
+
+  // Rounding behavior is towards zero, same as for built-in types.
+
+  // Undefined behavior if v is NaN or cannot fit into uint128.
+  assert(std::isfinite(v) && v > -1 &&
+         (std::numeric_limits<T>::max_exponent <= 128 ||
+          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));
+}
+
+#if defined(__clang__) && !defined(__SSE3__)
+// Workaround for clang bug: https://bugs.llvm.org/show_bug.cgi?id=38289
+// Casting from long double to uint64_t is miscompiled and drops bits.
+// It is more work, so only use when we need the workaround.
+uint128 MakeUint128FromFloat(long double v) {
+  // Go 50 bits at a time, that fits in a double
+  static_assert(std::numeric_limits<double>::digits >= 50, "");
+  static_assert(std::numeric_limits<long double>::digits <= 150, "");
+  // Undefined behavior if v is not finite or cannot fit into uint128.
+  assert(std::isfinite(v) && v > -1 && v < std::ldexp(1.0L, 128));
+
+  v = std::ldexp(v, -100);
+  uint64_t w0 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
+  v = std::ldexp(v - static_cast<double>(w0), 50);
+  uint64_t w1 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
+  v = std::ldexp(v - static_cast<double>(w1), 50);
+  uint64_t w2 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
+  return (static_cast<uint128>(w0) << 100) | (static_cast<uint128>(w1) << 50) |
+         static_cast<uint128>(w2);
+}
+#endif  // __clang__ && !__SSE3__
+}  // namespace
+
+uint128::uint128(float v) : uint128(MakeUint128FromFloat(v)) {}
+uint128::uint128(double v) : uint128(MakeUint128FromFloat(v)) {}
+uint128::uint128(long double v) : uint128(MakeUint128FromFloat(v)) {}
+
+uint128 operator/(uint128 lhs, uint128 rhs) {
+#if defined(ABSL_HAVE_INTRINSIC_INT128)
+  return static_cast<unsigned __int128>(lhs) /
+         static_cast<unsigned __int128>(rhs);
+#else  // ABSL_HAVE_INTRINSIC_INT128
+  uint128 quotient = 0;
+  uint128 remainder = 0;
+  DivModImpl(lhs, rhs, &quotient, &remainder);
+  return quotient;
+#endif  // ABSL_HAVE_INTRINSIC_INT128
+}
+uint128 operator%(uint128 lhs, uint128 rhs) {
+#if defined(ABSL_HAVE_INTRINSIC_INT128)
+  return static_cast<unsigned __int128>(lhs) %
+         static_cast<unsigned __int128>(rhs);
+#else  // ABSL_HAVE_INTRINSIC_INT128
+  uint128 quotient = 0;
+  uint128 remainder = 0;
+  DivModImpl(lhs, rhs, &quotient, &remainder);
+  return remainder;
+#endif  // ABSL_HAVE_INTRINSIC_INT128
+}
+
+namespace {
+
+std::string Uint128ToFormattedString(uint128 v, std::ios_base::fmtflags 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 = v;
+  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);
+  return os.str();
+}
+
+}  // namespace
+
+std::ostream& operator<<(std::ostream& os, uint128 v) {
+  std::ios_base::fmtflags flags = os.flags();
+  std::string rep = Uint128ToFormattedString(v, flags);
+
+  // Add the requisite padding.
+  std::streamsize width = os.width(0);
+  if (static_cast<size_t>(width) > rep.size()) {
+    std::ios::fmtflags adjustfield = flags & std::ios::adjustfield;
+    if (adjustfield == std::ios::left) {
+      rep.append(width - rep.size(), os.fill());
+    } else if (adjustfield == std::ios::internal &&
+               (flags & std::ios::showbase) &&
+               (flags & std::ios::basefield) == std::ios::hex && v != 0) {
+      rep.insert(2, width - rep.size(), os.fill());
+    } else {
+      rep.insert(0, width - rep.size(), os.fill());
+    }
+  }
+
+  return os << rep;
+}
+
+namespace {
+
+uint128 UnsignedAbsoluteValue(int128 v) {
+  // Cast to uint128 before possibly negating because -Int128Min() is undefined.
+  return Int128High64(v) < 0 ? -uint128(v) : uint128(v);
+}
+
+}  // namespace
+
+#if !defined(ABSL_HAVE_INTRINSIC_INT128)
+namespace {
+
+template <typename T>
+int128 MakeInt128FromFloat(T v) {
+  // Conversion when v is NaN or cannot fit into int128 would be undefined
+  // behavior if using an intrinsic 128-bit integer.
+  assert(std::isfinite(v) && (std::numeric_limits<T>::max_exponent <= 127 ||
+                              (v >= -std::ldexp(static_cast<T>(1), 127) &&
+                               v < std::ldexp(static_cast<T>(1), 127))));
+
+  // We must convert the absolute value and then negate as needed, because
+  // floating point types are typically sign-magnitude. Otherwise, the
+  // difference between the high and low 64 bits when interpreted as two's
+  // complement overwhelms the precision of the mantissa.
+  uint128 result = v < 0 ? -MakeUint128FromFloat(-v) : MakeUint128FromFloat(v);
+  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(result)),
+                    Uint128Low64(result));
+}
+
+}  // namespace
+
+int128::int128(float v) : int128(MakeInt128FromFloat(v)) {}
+int128::int128(double v) : int128(MakeInt128FromFloat(v)) {}
+int128::int128(long double v) : int128(MakeInt128FromFloat(v)) {}
+
+int128 operator/(int128 lhs, int128 rhs) {
+  assert(lhs != Int128Min() || rhs != -1);  // UB on two's complement.
+
+  uint128 quotient = 0;
+  uint128 remainder = 0;
+  DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
+             &quotient, &remainder);
+  if ((Int128High64(lhs) < 0) != (Int128High64(rhs) < 0)) quotient = -quotient;
+  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(quotient)),
+                    Uint128Low64(quotient));
+}
+
+int128 operator%(int128 lhs, int128 rhs) {
+  assert(lhs != Int128Min() || rhs != -1);  // UB on two's complement.
+
+  uint128 quotient = 0;
+  uint128 remainder = 0;
+  DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
+             &quotient, &remainder);
+  if (Int128High64(lhs) < 0) remainder = -remainder;
+  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(remainder)),
+                    Uint128Low64(remainder));
+}
+#endif  // ABSL_HAVE_INTRINSIC_INT128
+
+std::ostream& operator<<(std::ostream& os, int128 v) {
+  std::ios_base::fmtflags flags = os.flags();
+  std::string rep;
+
+  // Add the sign if needed.
+  bool print_as_decimal =
+      (flags & std::ios::basefield) == std::ios::dec ||
+      (flags & std::ios::basefield) == std::ios_base::fmtflags();
+  if (print_as_decimal) {
+    if (Int128High64(v) < 0) {
+      rep = "-";
+    } else if (flags & std::ios::showpos) {
+      rep = "+";
+    }
+  }
+
+  rep.append(Uint128ToFormattedString(
+      print_as_decimal ? UnsignedAbsoluteValue(v) : uint128(v), os.flags()));
+
+  // Add the requisite padding.
+  std::streamsize width = os.width(0);
+  if (static_cast<size_t>(width) > rep.size()) {
+    switch (flags & std::ios::adjustfield) {
+      case std::ios::left:
+        rep.append(width - rep.size(), os.fill());
+        break;
+      case std::ios::internal:
+        if (print_as_decimal && (rep[0] == '+' || rep[0] == '-')) {
+          rep.insert(1, width - rep.size(), os.fill());
+        } else if ((flags & std::ios::basefield) == std::ios::hex &&
+                   (flags & std::ios::showbase) && v != 0) {
+          rep.insert(2, width - rep.size(), os.fill());
+        } else {
+          rep.insert(0, width - rep.size(), os.fill());
+        }
+        break;
+      default:  // std::ios::right
+        rep.insert(0, width - rep.size(), os.fill());
+        break;
+    }
+  }
+
+  return os << rep;
+}
+
+ABSL_NAMESPACE_END
+}  // namespace absl
+
+namespace std {
+constexpr bool numeric_limits<absl::uint128>::is_specialized;
+constexpr bool numeric_limits<absl::uint128>::is_signed;
+constexpr bool numeric_limits<absl::uint128>::is_integer;
+constexpr bool numeric_limits<absl::uint128>::is_exact;
+constexpr bool numeric_limits<absl::uint128>::has_infinity;
+constexpr bool numeric_limits<absl::uint128>::has_quiet_NaN;
+constexpr bool numeric_limits<absl::uint128>::has_signaling_NaN;
+constexpr float_denorm_style numeric_limits<absl::uint128>::has_denorm;
+constexpr bool numeric_limits<absl::uint128>::has_denorm_loss;
+constexpr float_round_style numeric_limits<absl::uint128>::round_style;
+constexpr bool numeric_limits<absl::uint128>::is_iec559;
+constexpr bool numeric_limits<absl::uint128>::is_bounded;
+constexpr bool numeric_limits<absl::uint128>::is_modulo;
+constexpr int numeric_limits<absl::uint128>::digits;
+constexpr int numeric_limits<absl::uint128>::digits10;
+constexpr int numeric_limits<absl::uint128>::max_digits10;
+constexpr int numeric_limits<absl::uint128>::radix;
+constexpr int numeric_limits<absl::uint128>::min_exponent;
+constexpr int numeric_limits<absl::uint128>::min_exponent10;
+constexpr int numeric_limits<absl::uint128>::max_exponent;
+constexpr int numeric_limits<absl::uint128>::max_exponent10;
+constexpr bool numeric_limits<absl::uint128>::traps;
+constexpr bool numeric_limits<absl::uint128>::tinyness_before;
+
+constexpr bool numeric_limits<absl::int128>::is_specialized;
+constexpr bool numeric_limits<absl::int128>::is_signed;
+constexpr bool numeric_limits<absl::int128>::is_integer;
+constexpr bool numeric_limits<absl::int128>::is_exact;
+constexpr bool numeric_limits<absl::int128>::has_infinity;
+constexpr bool numeric_limits<absl::int128>::has_quiet_NaN;
+constexpr bool numeric_limits<absl::int128>::has_signaling_NaN;
+constexpr float_denorm_style numeric_limits<absl::int128>::has_denorm;
+constexpr bool numeric_limits<absl::int128>::has_denorm_loss;
+constexpr float_round_style numeric_limits<absl::int128>::round_style;
+constexpr bool numeric_limits<absl::int128>::is_iec559;
+constexpr bool numeric_limits<absl::int128>::is_bounded;
+constexpr bool numeric_limits<absl::int128>::is_modulo;
+constexpr int numeric_limits<absl::int128>::digits;
+constexpr int numeric_limits<absl::int128>::digits10;
+constexpr int numeric_limits<absl::int128>::max_digits10;
+constexpr int numeric_limits<absl::int128>::radix;
+constexpr int numeric_limits<absl::int128>::min_exponent;
+constexpr int numeric_limits<absl::int128>::min_exponent10;
+constexpr int numeric_limits<absl::int128>::max_exponent;
+constexpr int numeric_limits<absl::int128>::max_exponent10;
+constexpr bool numeric_limits<absl::int128>::traps;
+constexpr bool numeric_limits<absl::int128>::tinyness_before;
+}  // namespace std

third_party/abseil_cpp/absl/numeric/int128_benchmark.cc

@@ -0,0 +1,221 @@
+// 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.
+
+#include "absl/numeric/int128.h"
+
+#include <algorithm>
+#include <cstdint>
+#include <random>
+#include <vector>
+
+#include "benchmark/benchmark.h"
+#include "absl/base/config.h"
+
+namespace {
+
+constexpr size_t kSampleSize = 1000000;
+
+std::mt19937 MakeRandomEngine() {
+  std::random_device r;
+  std::seed_seq seed({r(), r(), r(), r(), r(), r(), r(), r()});
+  return std::mt19937(seed);
+}
+
+std::vector<std::pair<absl::uint128, absl::uint128>>
+GetRandomClass128SampleUniformDivisor() {
+  std::vector<std::pair<absl::uint128, absl::uint128>> values;
+  std::mt19937 random = MakeRandomEngine();
+  std::uniform_int_distribution<uint64_t> uniform_uint64;
+  values.reserve(kSampleSize);
+  for (size_t i = 0; i < kSampleSize; ++i) {
+    absl::uint128 a =
+        absl::MakeUint128(uniform_uint64(random), uniform_uint64(random));
+    absl::uint128 b =
+        absl::MakeUint128(uniform_uint64(random), uniform_uint64(random));
+    values.emplace_back(std::max(a, b),
+                        std::max(absl::uint128(2), std::min(a, b)));
+  }
+  return values;
+}
+
+void BM_DivideClass128UniformDivisor(benchmark::State& state) {
+  auto values = GetRandomClass128SampleUniformDivisor();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first / pair.second);
+    }
+  }
+}
+BENCHMARK(BM_DivideClass128UniformDivisor);
+
+std::vector<std::pair<absl::uint128, uint64_t>>
+GetRandomClass128SampleSmallDivisor() {
+  std::vector<std::pair<absl::uint128, uint64_t>> values;
+  std::mt19937 random = MakeRandomEngine();
+  std::uniform_int_distribution<uint64_t> uniform_uint64;
+  values.reserve(kSampleSize);
+  for (size_t i = 0; i < kSampleSize; ++i) {
+    absl::uint128 a =
+        absl::MakeUint128(uniform_uint64(random), uniform_uint64(random));
+    uint64_t b = std::max(uint64_t{2}, uniform_uint64(random));
+    values.emplace_back(std::max(a, absl::uint128(b)), b);
+  }
+  return values;
+}
+
+void BM_DivideClass128SmallDivisor(benchmark::State& state) {
+  auto values = GetRandomClass128SampleSmallDivisor();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first / pair.second);
+    }
+  }
+}
+BENCHMARK(BM_DivideClass128SmallDivisor);
+
+std::vector<std::pair<absl::uint128, absl::uint128>> GetRandomClass128Sample() {
+  std::vector<std::pair<absl::uint128, absl::uint128>> values;
+  std::mt19937 random = MakeRandomEngine();
+  std::uniform_int_distribution<uint64_t> uniform_uint64;
+  values.reserve(kSampleSize);
+  for (size_t i = 0; i < kSampleSize; ++i) {
+    values.emplace_back(
+        absl::MakeUint128(uniform_uint64(random), uniform_uint64(random)),
+        absl::MakeUint128(uniform_uint64(random), uniform_uint64(random)));
+  }
+  return values;
+}
+
+void BM_MultiplyClass128(benchmark::State& state) {
+  auto values = GetRandomClass128Sample();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first * pair.second);
+    }
+  }
+}
+BENCHMARK(BM_MultiplyClass128);
+
+void BM_AddClass128(benchmark::State& state) {
+  auto values = GetRandomClass128Sample();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first + pair.second);
+    }
+  }
+}
+BENCHMARK(BM_AddClass128);
+
+#ifdef ABSL_HAVE_INTRINSIC_INT128
+
+// Some implementations of <random> do not support __int128 when it is
+// available, so we make our own uniform_int_distribution-like type.
+class UniformIntDistribution128 {
+ public:
+  // NOLINTNEXTLINE: mimicking std::uniform_int_distribution API
+  unsigned __int128 operator()(std::mt19937& generator) {
+    return (static_cast<unsigned __int128>(dist64_(generator)) << 64) |
+           dist64_(generator);
+  }
+
+ private:
+  std::uniform_int_distribution<uint64_t> dist64_;
+};
+
+std::vector<std::pair<unsigned __int128, unsigned __int128>>
+GetRandomIntrinsic128SampleUniformDivisor() {
+  std::vector<std::pair<unsigned __int128, unsigned __int128>> values;
+  std::mt19937 random = MakeRandomEngine();
+  UniformIntDistribution128 uniform_uint128;
+  values.reserve(kSampleSize);
+  for (size_t i = 0; i < kSampleSize; ++i) {
+    unsigned __int128 a = uniform_uint128(random);
+    unsigned __int128 b = uniform_uint128(random);
+    values.emplace_back(
+        std::max(a, b),
+        std::max(static_cast<unsigned __int128>(2), std::min(a, b)));
+  }
+  return values;
+}
+
+void BM_DivideIntrinsic128UniformDivisor(benchmark::State& state) {
+  auto values = GetRandomIntrinsic128SampleUniformDivisor();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first / pair.second);
+    }
+  }
+}
+BENCHMARK(BM_DivideIntrinsic128UniformDivisor);
+
+std::vector<std::pair<unsigned __int128, uint64_t>>
+GetRandomIntrinsic128SampleSmallDivisor() {
+  std::vector<std::pair<unsigned __int128, uint64_t>> values;
+  std::mt19937 random = MakeRandomEngine();
+  UniformIntDistribution128 uniform_uint128;
+  std::uniform_int_distribution<uint64_t> uniform_uint64;
+  values.reserve(kSampleSize);
+  for (size_t i = 0; i < kSampleSize; ++i) {
+    unsigned __int128 a = uniform_uint128(random);
+    uint64_t b = std::max(uint64_t{2}, uniform_uint64(random));
+    values.emplace_back(std::max(a, static_cast<unsigned __int128>(b)), b);
+  }
+  return values;
+}
+
+void BM_DivideIntrinsic128SmallDivisor(benchmark::State& state) {
+  auto values = GetRandomIntrinsic128SampleSmallDivisor();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first / pair.second);
+    }
+  }
+}
+BENCHMARK(BM_DivideIntrinsic128SmallDivisor);
+
+std::vector<std::pair<unsigned __int128, unsigned __int128>>
+      GetRandomIntrinsic128Sample() {
+  std::vector<std::pair<unsigned __int128, unsigned __int128>> values;
+  std::mt19937 random = MakeRandomEngine();
+  UniformIntDistribution128 uniform_uint128;
+  values.reserve(kSampleSize);
+  for (size_t i = 0; i < kSampleSize; ++i) {
+    values.emplace_back(uniform_uint128(random), uniform_uint128(random));
+  }
+  return values;
+}
+
+void BM_MultiplyIntrinsic128(benchmark::State& state) {
+  auto values = GetRandomIntrinsic128Sample();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first * pair.second);
+    }
+  }
+}
+BENCHMARK(BM_MultiplyIntrinsic128);
+
+void BM_AddIntrinsic128(benchmark::State& state) {
+  auto values = GetRandomIntrinsic128Sample();
+  while (state.KeepRunningBatch(values.size())) {
+    for (const auto& pair : values) {
+      benchmark::DoNotOptimize(pair.first + pair.second);
+    }
+  }
+}
+BENCHMARK(BM_AddIntrinsic128);
+
+#endif  // ABSL_HAVE_INTRINSIC_INT128
+
+}  // namespace

third_party/abseil_cpp/absl/numeric/int128_have_intrinsic.inc

@@ -0,0 +1,302 @@
+//
+// 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.
+
+// This file contains :int128 implementation details that depend on internal
+// representation when ABSL_HAVE_INTRINSIC_INT128 is defined. This file is
+// included by int128.h and relies on ABSL_INTERNAL_WCHAR_T being defined.
+
+namespace int128_internal {
+
+// Casts from unsigned to signed while preserving the underlying binary
+// representation.
+constexpr __int128 BitCastToSigned(unsigned __int128 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 and GCC
+  // optimize this to a no-op on x86-64.
+  return v & (static_cast<unsigned __int128>(1) << 127)
+             ? ~static_cast<__int128>(~v)
+             : static_cast<__int128>(v);
+}
+
+}  // namespace int128_internal
+
+inline int128& int128::operator=(__int128 v) {
+  v_ = v;
+  return *this;
+}
+
+constexpr uint64_t Int128Low64(int128 v) {
+  return static_cast<uint64_t>(v.v_ & ~uint64_t{0});
+}
+
+constexpr int64_t Int128High64(int128 v) {
+  // Initially cast to unsigned to prevent a right shift on a negative value.
+  return int128_internal::BitCastToSigned(
+      static_cast<uint64_t>(static_cast<unsigned __int128>(v.v_) >> 64));
+}
+
+constexpr int128::int128(int64_t high, uint64_t low)
+    // Initially cast to unsigned to prevent a left shift that overflows.
+    : v_(int128_internal::BitCastToSigned(static_cast<unsigned __int128>(high)
+                                           << 64) |
+         low) {}
+
+
+constexpr int128::int128(int v) : v_{v} {}
+
+constexpr int128::int128(long v) : v_{v} {}       // NOLINT(runtime/int)
+
+constexpr int128::int128(long long v) : v_{v} {}  // NOLINT(runtime/int)
+
+constexpr int128::int128(__int128 v) : v_{v} {}
+
+constexpr int128::int128(unsigned int v) : v_{v} {}
+
+constexpr int128::int128(unsigned long v) : v_{v} {}  // NOLINT(runtime/int)
+
+// NOLINTNEXTLINE(runtime/int)
+constexpr int128::int128(unsigned long long v) : v_{v} {}
+
+constexpr int128::int128(unsigned __int128 v) : v_{static_cast<__int128>(v)} {}
+
+inline int128::int128(float v) {
+  v_ = static_cast<__int128>(v);
+}
+
+inline int128::int128(double v) {
+  v_ = static_cast<__int128>(v);
+}
+
+inline int128::int128(long double v) {
+  v_ = static_cast<__int128>(v);
+}
+
+constexpr int128::int128(uint128 v) : v_{static_cast<__int128>(v)} {}
+
+constexpr int128::operator bool() const { return static_cast<bool>(v_); }
+
+constexpr int128::operator char() const { return static_cast<char>(v_); }
+
+constexpr int128::operator signed char() const {
+  return static_cast<signed char>(v_);
+}
+
+constexpr int128::operator unsigned char() const {
+  return static_cast<unsigned char>(v_);
+}
+
+constexpr int128::operator char16_t() const {
+  return static_cast<char16_t>(v_);
+}
+
+constexpr int128::operator char32_t() const {
+  return static_cast<char32_t>(v_);
+}
+
+constexpr int128::operator ABSL_INTERNAL_WCHAR_T() const {
+  return static_cast<ABSL_INTERNAL_WCHAR_T>(v_);
+}
+
+constexpr int128::operator short() const {  // NOLINT(runtime/int)
+  return static_cast<short>(v_);            // NOLINT(runtime/int)
+}
+
+constexpr int128::operator unsigned short() const {  // NOLINT(runtime/int)
+  return static_cast<unsigned short>(v_);            // NOLINT(runtime/int)
+}
+
+constexpr int128::operator int() const {
+  return static_cast<int>(v_);
+}
+
+constexpr int128::operator unsigned int() const {
+  return static_cast<unsigned int>(v_);
+}
+
+constexpr int128::operator long() const {  // NOLINT(runtime/int)
+  return static_cast<long>(v_);            // NOLINT(runtime/int)
+}
+
+constexpr int128::operator unsigned long() const {  // NOLINT(runtime/int)
+  return static_cast<unsigned long>(v_);            // NOLINT(runtime/int)
+}
+
+constexpr int128::operator long long() const {  // NOLINT(runtime/int)
+  return static_cast<long long>(v_);            // NOLINT(runtime/int)
+}
+
+constexpr int128::operator unsigned long long() const {  // NOLINT(runtime/int)
+  return static_cast<unsigned long long>(v_);            // NOLINT(runtime/int)
+}
+
+constexpr int128::operator __int128() const { return v_; }
+
+constexpr int128::operator unsigned __int128() const {
+  return static_cast<unsigned __int128>(v_);
+}
+
+// Clang on PowerPC sometimes produces incorrect __int128 to floating point
+// conversions. In that case, we do the conversion with a similar implementation
+// to the conversion operators in int128_no_intrinsic.inc.
+#if defined(__clang__) && !defined(__ppc64__)
+inline int128::operator float() const { return static_cast<float>(v_); }
+
+inline int128::operator double () const { return static_cast<double>(v_); }
+
+inline int128::operator long double() const {
+  return static_cast<long double>(v_);
+}
+
+#else  // Clang on PowerPC
+// Forward declaration for conversion operators to floating point types.
+int128 operator-(int128 v);
+bool operator!=(int128 lhs, int128 rhs);
+
+inline int128::operator float() const {
+  // We must convert the absolute value and then negate as needed, because
+  // floating point types are typically sign-magnitude. Otherwise, the
+  // difference between the high and low 64 bits when interpreted as two's
+  // complement overwhelms the precision of the mantissa.
+  //
+  // Also check to make sure we don't negate Int128Min()
+  return v_ < 0 && *this != Int128Min()
+             ? -static_cast<float>(-*this)
+             : static_cast<float>(Int128Low64(*this)) +
+                   std::ldexp(static_cast<float>(Int128High64(*this)), 64);
+}
+
+inline int128::operator double() const {
+  // See comment in int128::operator float() above.
+  return v_ < 0 && *this != Int128Min()
+             ? -static_cast<double>(-*this)
+             : static_cast<double>(Int128Low64(*this)) +
+                   std::ldexp(static_cast<double>(Int128High64(*this)), 64);
+}
+
+inline int128::operator long double() const {
+  // See comment in int128::operator float() above.
+  return v_ < 0 && *this != Int128Min()
+             ? -static_cast<long double>(-*this)
+             : static_cast<long double>(Int128Low64(*this)) +
+                   std::ldexp(static_cast<long double>(Int128High64(*this)),
+                              64);
+}
+#endif  // Clang on PowerPC
+
+// Comparison operators.
+
+inline bool operator==(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) == static_cast<__int128>(rhs);
+}
+
+inline bool operator!=(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) != static_cast<__int128>(rhs);
+}
+
+inline bool operator<(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) < static_cast<__int128>(rhs);
+}
+
+inline bool operator>(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) > static_cast<__int128>(rhs);
+}
+
+inline bool operator<=(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) <= static_cast<__int128>(rhs);
+}
+
+inline bool operator>=(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) >= static_cast<__int128>(rhs);
+}
+
+// Unary operators.
+
+inline int128 operator-(int128 v) {
+  return -static_cast<__int128>(v);
+}
+
+inline bool operator!(int128 v) {
+  return !static_cast<__int128>(v);
+}
+
+inline int128 operator~(int128 val) {
+  return ~static_cast<__int128>(val);
+}
+
+// Arithmetic operators.
+
+inline int128 operator+(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) + static_cast<__int128>(rhs);
+}
+
+inline int128 operator-(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) - static_cast<__int128>(rhs);
+}
+
+inline int128 operator*(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) * static_cast<__int128>(rhs);
+}
+
+inline int128 operator/(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) / static_cast<__int128>(rhs);
+}
+
+inline int128 operator%(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) % static_cast<__int128>(rhs);
+}
+
+inline int128 int128::operator++(int) {
+  int128 tmp(*this);
+  ++v_;
+  return tmp;
+}
+
+inline int128 int128::operator--(int) {
+  int128 tmp(*this);
+  --v_;
+  return tmp;
+}
+
+inline int128& int128::operator++() {
+  ++v_;
+  return *this;
+}
+
+inline int128& int128::operator--() {
+  --v_;
+  return *this;
+}
+
+inline int128 operator|(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) | static_cast<__int128>(rhs);
+}
+
+inline int128 operator&(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) & static_cast<__int128>(rhs);
+}
+
+inline int128 operator^(int128 lhs, int128 rhs) {
+  return static_cast<__int128>(lhs) ^ static_cast<__int128>(rhs);
+}
+
+inline int128 operator<<(int128 lhs, int amount) {
+  return static_cast<__int128>(lhs) << amount;
+}
+
+inline int128 operator>>(int128 lhs, int amount) {
+  return static_cast<__int128>(lhs) >> amount;
+}

third_party/abseil_cpp/absl/numeric/int128_no_intrinsic.inc

@@ -0,0 +1,308 @@
+//
+// 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.
+
+// This file contains :int128 implementation details that depend on internal
+// representation when ABSL_HAVE_INTRINSIC_INT128 is *not* defined. This file
+// is included by int128.h and relies on ABSL_INTERNAL_WCHAR_T being defined.
+
+constexpr uint64_t Int128Low64(int128 v) { return v.lo_; }
+
+constexpr int64_t Int128High64(int128 v) { return v.hi_; }
+
+#if defined(ABSL_IS_LITTLE_ENDIAN)
+
+constexpr int128::int128(int64_t high, uint64_t low) :
+    lo_(low), hi_(high) {}
+
+constexpr int128::int128(int v)
+    : lo_{static_cast<uint64_t>(v)}, hi_{v < 0 ? ~int64_t{0} : 0} {}
+constexpr int128::int128(long v)  // NOLINT(runtime/int)
+    : lo_{static_cast<uint64_t>(v)}, hi_{v < 0 ? ~int64_t{0} : 0} {}
+constexpr int128::int128(long long v)  // NOLINT(runtime/int)
+    : lo_{static_cast<uint64_t>(v)}, hi_{v < 0 ? ~int64_t{0} : 0} {}
+
+constexpr int128::int128(unsigned int v) : lo_{v}, hi_{0} {}
+// NOLINTNEXTLINE(runtime/int)
+constexpr int128::int128(unsigned long v) : lo_{v}, hi_{0} {}
+// NOLINTNEXTLINE(runtime/int)
+constexpr int128::int128(unsigned long long v) : lo_{v}, hi_{0} {}
+
+constexpr int128::int128(uint128 v)
+    : lo_{Uint128Low64(v)}, hi_{static_cast<int64_t>(Uint128High64(v))} {}
+
+#elif defined(ABSL_IS_BIG_ENDIAN)
+
+constexpr int128::int128(int64_t high, uint64_t low) :
+    hi_{high}, lo_{low} {}
+
+constexpr int128::int128(int v)
+    : hi_{v < 0 ? ~int64_t{0} : 0}, lo_{static_cast<uint64_t>(v)} {}
+constexpr int128::int128(long v)  // NOLINT(runtime/int)
+    : hi_{v < 0 ? ~int64_t{0} : 0}, lo_{static_cast<uint64_t>(v)} {}
+constexpr int128::int128(long long v)  // NOLINT(runtime/int)
+    : hi_{v < 0 ? ~int64_t{0} : 0}, lo_{static_cast<uint64_t>(v)} {}
+
+constexpr int128::int128(unsigned int v) : hi_{0}, lo_{v} {}
+// NOLINTNEXTLINE(runtime/int)
+constexpr int128::int128(unsigned long v) : hi_{0}, lo_{v} {}
+// NOLINTNEXTLINE(runtime/int)
+constexpr int128::int128(unsigned long long v) : hi_{0}, lo_{v} {}
+
+constexpr int128::int128(uint128 v)
+    : hi_{static_cast<int64_t>(Uint128High64(v))}, lo_{Uint128Low64(v)} {}
+
+#else  // byte order
+#error "Unsupported byte order: must be little-endian or big-endian."
+#endif  // byte order
+
+constexpr int128::operator bool() const { return lo_ || hi_; }
+
+constexpr int128::operator char() const {
+  // NOLINTNEXTLINE(runtime/int)
+  return static_cast<char>(static_cast<long long>(*this));
+}
+
+constexpr int128::operator signed char() const {
+  // NOLINTNEXTLINE(runtime/int)
+  return static_cast<signed char>(static_cast<long long>(*this));
+}
+
+constexpr int128::operator unsigned char() const {
+  return static_cast<unsigned char>(lo_);
+}
+
+constexpr int128::operator char16_t() const {
+  return static_cast<char16_t>(lo_);
+}
+
+constexpr int128::operator char32_t() const {
+  return static_cast<char32_t>(lo_);
+}
+
+constexpr int128::operator ABSL_INTERNAL_WCHAR_T() const {
+  // NOLINTNEXTLINE(runtime/int)
+  return static_cast<ABSL_INTERNAL_WCHAR_T>(static_cast<long long>(*this));
+}
+
+constexpr int128::operator short() const {  // NOLINT(runtime/int)
+  // NOLINTNEXTLINE(runtime/int)
+  return static_cast<short>(static_cast<long long>(*this));
+}
+
+constexpr int128::operator unsigned short() const {  // NOLINT(runtime/int)
+  return static_cast<unsigned short>(lo_);           // NOLINT(runtime/int)
+}
+
+constexpr int128::operator int() const {
+  // NOLINTNEXTLINE(runtime/int)
+  return static_cast<int>(static_cast<long long>(*this));
+}
+
+constexpr int128::operator unsigned int() const {
+  return static_cast<unsigned int>(lo_);
+}
+
+constexpr int128::operator long() const {  // NOLINT(runtime/int)
+  // NOLINTNEXTLINE(runtime/int)
+  return static_cast<long>(static_cast<long long>(*this));
+}
+
+constexpr int128::operator unsigned long() const {  // NOLINT(runtime/int)
+  return static_cast<unsigned long>(lo_);           // NOLINT(runtime/int)
+}
+
+constexpr int128::operator long long() const {  // NOLINT(runtime/int)
+  // We don't bother checking the value of hi_. If *this < 0, lo_'s high bit
+  // must be set in order for the value to fit into a long long. Conversely, if
+  // lo_'s high bit is set, *this must be < 0 for the value to fit.
+  return int128_internal::BitCastToSigned(lo_);
+}
+
+constexpr int128::operator unsigned long long() const {  // NOLINT(runtime/int)
+  return static_cast<unsigned long long>(lo_);           // NOLINT(runtime/int)
+}
+
+// Forward declaration for conversion operators to floating point types.
+int128 operator-(int128 v);
+bool operator!=(int128 lhs, int128 rhs);
+
+inline int128::operator float() const {
+  // We must convert the absolute value and then negate as needed, because
+  // floating point types are typically sign-magnitude. Otherwise, the
+  // difference between the high and low 64 bits when interpreted as two's
+  // complement overwhelms the precision of the mantissa.
+  //
+  // Also check to make sure we don't negate Int128Min()
+  return hi_ < 0 && *this != Int128Min()
+             ? -static_cast<float>(-*this)
+             : static_cast<float>(lo_) +
+                   std::ldexp(static_cast<float>(hi_), 64);
+}
+
+inline int128::operator double() const {
+  // See comment in int128::operator float() above.
+  return hi_ < 0 && *this != Int128Min()
+             ? -static_cast<double>(-*this)
+             : static_cast<double>(lo_) +
+                   std::ldexp(static_cast<double>(hi_), 64);
+}
+
+inline int128::operator long double() const {
+  // See comment in int128::operator float() above.
+  return hi_ < 0 && *this != Int128Min()
+             ? -static_cast<long double>(-*this)
+             : static_cast<long double>(lo_) +
+                   std::ldexp(static_cast<long double>(hi_), 64);
+}
+
+// Comparison operators.
+
+inline bool operator==(int128 lhs, int128 rhs) {
+  return (Int128Low64(lhs) == Int128Low64(rhs) &&
+          Int128High64(lhs) == Int128High64(rhs));
+}
+
+inline bool operator!=(int128 lhs, int128 rhs) {
+  return !(lhs == rhs);
+}
+
+inline bool operator<(int128 lhs, int128 rhs) {
+  return (Int128High64(lhs) == Int128High64(rhs))
+             ? (Int128Low64(lhs) < Int128Low64(rhs))
+             : (Int128High64(lhs) < Int128High64(rhs));
+}
+
+inline bool operator>(int128 lhs, int128 rhs) {
+  return (Int128High64(lhs) == Int128High64(rhs))
+             ? (Int128Low64(lhs) > Int128Low64(rhs))
+             : (Int128High64(lhs) > Int128High64(rhs));
+}
+
+inline bool operator<=(int128 lhs, int128 rhs) {
+  return !(lhs > rhs);
+}
+
+inline bool operator>=(int128 lhs, int128 rhs) {
+  return !(lhs < rhs);
+}
+
+// Unary operators.
+
+inline int128 operator-(int128 v) {
+  int64_t hi = ~Int128High64(v);
+  uint64_t lo = ~Int128Low64(v) + 1;
+  if (lo == 0) ++hi;  // carry
+  return MakeInt128(hi, lo);
+}
+
+inline bool operator!(int128 v) {
+  return !Int128Low64(v) && !Int128High64(v);
+}
+
+inline int128 operator~(int128 val) {
+  return MakeInt128(~Int128High64(val), ~Int128Low64(val));
+}
+
+// Arithmetic operators.
+
+inline int128 operator+(int128 lhs, int128 rhs) {
+  int128 result = MakeInt128(Int128High64(lhs) + Int128High64(rhs),
+                             Int128Low64(lhs) + Int128Low64(rhs));
+  if (Int128Low64(result) < Int128Low64(lhs)) {  // check for carry
+    return MakeInt128(Int128High64(result) + 1, Int128Low64(result));
+  }
+  return result;
+}
+
+inline int128 operator-(int128 lhs, int128 rhs) {
+  int128 result = MakeInt128(Int128High64(lhs) - Int128High64(rhs),
+                             Int128Low64(lhs) - Int128Low64(rhs));
+  if (Int128Low64(lhs) < Int128Low64(rhs)) {  // check for carry
+    return MakeInt128(Int128High64(result) - 1, Int128Low64(result));
+  }
+  return result;
+}
+
+inline int128 operator*(int128 lhs, int128 rhs) {
+  uint128 result = uint128(lhs) * rhs;
+  return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(result)),
+                    Uint128Low64(result));
+}
+
+inline int128 int128::operator++(int) {
+  int128 tmp(*this);
+  *this += 1;
+  return tmp;
+}
+
+inline int128 int128::operator--(int) {
+  int128 tmp(*this);
+  *this -= 1;
+  return tmp;
+}
+
+inline int128& int128::operator++() {
+  *this += 1;
+  return *this;
+}
+
+inline int128& int128::operator--() {
+  *this -= 1;
+  return *this;
+}
+
+inline int128 operator|(int128 lhs, int128 rhs) {
+  return MakeInt128(Int128High64(lhs) | Int128High64(rhs),
+                    Int128Low64(lhs) | Int128Low64(rhs));
+}
+
+inline int128 operator&(int128 lhs, int128 rhs) {
+  return MakeInt128(Int128High64(lhs) & Int128High64(rhs),
+                    Int128Low64(lhs) & Int128Low64(rhs));
+}
+
+inline int128 operator^(int128 lhs, int128 rhs) {
+  return MakeInt128(Int128High64(lhs) ^ Int128High64(rhs),
+                    Int128Low64(lhs) ^ Int128Low64(rhs));
+}
+
+inline int128 operator<<(int128 lhs, int amount) {
+  // uint64_t shifts of >= 64 are undefined, so we need some special-casing.
+  if (amount < 64) {
+    if (amount != 0) {
+      return MakeInt128(
+          (Int128High64(lhs) << amount) |
+              static_cast<int64_t>(Int128Low64(lhs) >> (64 - amount)),
+          Int128Low64(lhs) << amount);
+    }
+    return lhs;
+  }
+  return MakeInt128(static_cast<int64_t>(Int128Low64(lhs) << (amount - 64)), 0);
+}
+
+inline int128 operator>>(int128 lhs, int amount) {
+  // uint64_t shifts of >= 64 are undefined, so we need some special-casing.
+  if (amount < 64) {
+    if (amount != 0) {
+      return MakeInt128(
+          Int128High64(lhs) >> amount,
+          (Int128Low64(lhs) >> amount) |
+              (static_cast<uint64_t>(Int128High64(lhs)) << (64 - amount)));
+    }
+    return lhs;
+  }
+  return MakeInt128(0,
+                    static_cast<uint64_t>(Int128High64(lhs) >> (amount - 64)));
+}