Export of internal Abseil changes.

--
7a6ff16a85beb730c172d5d25cf1b5e1be885c56 by Laramie Leavitt <lar@google.com>:

Internal change.

PiperOrigin-RevId: 254454546

--
ff8f9bafaefc26d451f576ea4a06d150aed63f6f by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254451562

--
deefc5b651b479ce36f0b4ef203e119c0c8936f2 by CJ Johnson <johnsoncj@google.com>:

Account for subtracting unsigned values from the size of InlinedVector

PiperOrigin-RevId: 254450625

--
3c677316a27bcadc17e41957c809ca472d5fef14 by Andy Soffer <asoffer@google.com>:

Add C++17's std::make_from_tuple to absl/utility/utility.h

PiperOrigin-RevId: 254411573

--
4ee3536a918830eeec402a28fc31a62c7c90b940 by CJ Johnson <johnsoncj@google.com>:

Adds benchmark for the rest of the InlinedVector public API

PiperOrigin-RevId: 254408378

--
e5a21a00700ee83498ff1efbf649169756463ee4 by CJ Johnson <johnsoncj@google.com>:

Updates the definition of InlinedVector::shrink_to_fit() to be exception safe and adds exception safety tests for it.

PiperOrigin-RevId: 254401387

--
2ea82e72b86d82d78b4e4712a63a55981b53c64b by Laramie Leavitt <lar@google.com>:

Use absl::InsecureBitGen in place of std::mt19937
in tests absl/random/...distribution_test.cc

PiperOrigin-RevId: 254289444

--
fa099e02c413a7ffda732415e8105cad26a90337 by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254286334

--
ce34b7f36933b30cfa35b9c9a5697a792b5666e4 by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254273059

--
6f9c473da7c2090c2e85a37c5f00622e8a912a89 by Jorg Brown <jorg@google.com>:

Change absl::container_internal::CompressedTuple to instantiate its
internal Storage class with the name of the type it's holding, rather
than the name of the Tuple.  This is not an externally-visible change,
other than less compiler memory is used and less debug information is
generated.

PiperOrigin-RevId: 254269285

--
8bd3c186bf2fc0c55d8a2dd6f28a5327502c9fba by Andy Soffer <asoffer@google.com>:

Adding short-hand IntervalClosed for IntervalClosedClosed and IntervalOpen for
IntervalOpenOpen.

PiperOrigin-RevId: 254252419

--
ea957f99b6a04fccd42aa05605605f3b44b1ecfd by Abseil Team <absl-team@google.com>:

Do not directly use __SIZEOF_INT128__.

In order to avoid linker errors when building with clang-cl (__fixunsdfti, __udivti3 and __fixunssfti are undefined), this CL uses ABSL_HAVE_INTRINSIC_INT128 which is not defined for clang-cl.

PiperOrigin-RevId: 254250739

--
89ab385cd26b34d64130bce856253aaba96d2345 by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254242321

--
cffc793d93eca6d6bdf7de733847b6ab4a255ae9 by CJ Johnson <johnsoncj@google.com>:

Adds benchmark for InlinedVector::reserve(size_type)

PiperOrigin-RevId: 254199226

--
c90c7a9fa3c8f0c9d5114036979548b055ea2f2a by Gennadiy Rozental <rogeeff@google.com>:

Import of CCTZ from GitHub.

PiperOrigin-RevId: 254072387

--
c4c388beae016c9570ab54ffa1d52660e4a85b7b by Laramie Leavitt <lar@google.com>:

Internal cleanup.

PiperOrigin-RevId: 254062381

--
d3c992e221cc74e5372d0c8fa410170b6a43c062 by Tom Manshreck <shreck@google.com>:

Update distributions.h to Abseil standards

PiperOrigin-RevId: 254054946

--
d15ad0035c34ef11b14fadc5a4a2d3ec415f5518 by CJ Johnson <johnsoncj@google.com>:

Removes functions with only one caller from the implementation details of InlinedVector by manually inlining the definitions

PiperOrigin-RevId: 254005427

--
2f37e807efc3a8ef1f4b539bdd379917d4151520 by Andy Soffer <asoffer@google.com>:

Initial release of Abseil Random

PiperOrigin-RevId: 253999861

--
24ed1694b6430791d781ed533a8f8ccf6cac5856 by CJ Johnson <johnsoncj@google.com>:

Updates the definition of InlinedVector::assign(...)/InlinedVector::operator=(...) to new, exception-safe implementations with exception safety tests to boot

PiperOrigin-RevId: 253993691

--
5613d95f5a7e34a535cfaeadce801441e990843e by CJ Johnson <johnsoncj@google.com>:

Adds benchmarks for InlinedVector::shrink_to_fit()

PiperOrigin-RevId: 253989647

--
2a96ddfdac40bbb8cb6a7f1aeab90917067c6e63 by Abseil Team <absl-team@google.com>:

Initial release of Abseil Random

PiperOrigin-RevId: 253927497

--
bf1aff8fc9ffa921ad74643e9525ecf25b0d8dc1 by Andy Soffer <asoffer@google.com>:

Initial release of Abseil Random

PiperOrigin-RevId: 253920512

--
bfc03f4a3dcda3cf3a4b84bdb84cda24e3394f41 by Laramie Leavitt <lar@google.com>:

Internal change.

PiperOrigin-RevId: 253886486

--
05036cfcc078ca7c5f581a00dfb0daed568cbb69 by Eric Fiselier <ericwf@google.com>:

Don't include `winsock2.h` because it drags in `windows.h` and friends,
and they define awful macros like OPAQUE, ERROR, and more. This has the
potential to break abseil users.

Instead we only forward declare `timeval` and require Windows users
include `winsock2.h` themselves. This is both inconsistent and poor QoI, but so
including 'windows.h' is bad too.

PiperOrigin-RevId: 253852615
GitOrigin-RevId: 7a6ff16a85beb730c172d5d25cf1b5e1be885c56
Change-Id: Icd6aff87da26f29ec8915da856f051129987cef6

1 files changed, 573 insertions, 0 deletions

diff --git a/absl/random/gaussian_distribution_test.cc b/absl/random/gaussian_distribution_test.cc
new file mode 100644
index 00000000..47c2989d
--- /dev/null
+++ b/absl/random/gaussian_distribution_test.cc
@@ -0,0 +1,573 @@
+// 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/random/gaussian_distribution.h"
+
+#include <algorithm>
+#include <cmath>
+#include <cstddef>
+#include <ios>
+#include <iterator>
+#include <random>
+#include <string>
+#include <vector>
+
+#include "gmock/gmock.h"
+#include "gtest/gtest.h"
+#include "absl/base/internal/raw_logging.h"
+#include "absl/base/macros.h"
+#include "absl/random/internal/chi_square.h"
+#include "absl/random/internal/distribution_test_util.h"
+#include "absl/random/internal/sequence_urbg.h"
+#include "absl/random/random.h"
+#include "absl/strings/str_cat.h"
+#include "absl/strings/str_format.h"
+#include "absl/strings/str_replace.h"
+#include "absl/strings/strip.h"
+
+namespace {
+
+using absl::random_internal::kChiSquared;
+
+template <typename RealType>
+class GaussianDistributionInterfaceTest : public ::testing::Test {};
+
+using RealTypes = ::testing::Types<float, double, long double>;
+TYPED_TEST_CASE(GaussianDistributionInterfaceTest, RealTypes);
+
+TYPED_TEST(GaussianDistributionInterfaceTest, SerializeTest) {
+  using param_type =
+      typename absl::gaussian_distribution<TypeParam>::param_type;
+
+  const TypeParam kParams[] = {
+      // Cases around 1.
+      1,                                           //
+      std::nextafter(TypeParam(1), TypeParam(0)),  // 1 - epsilon
+      std::nextafter(TypeParam(1), TypeParam(2)),  // 1 + epsilon
+      // Arbitrary values.
+      TypeParam(1e-8), TypeParam(1e-4), TypeParam(2), TypeParam(1e4),
+      TypeParam(1e8), TypeParam(1e20), TypeParam(2.5),
+      // Boundary cases.
+      std::numeric_limits<TypeParam>::infinity(),
+      std::numeric_limits<TypeParam>::max(),
+      std::numeric_limits<TypeParam>::epsilon(),
+      std::nextafter(std::numeric_limits<TypeParam>::min(),
+                     TypeParam(1)),           // min + epsilon
+      std::numeric_limits<TypeParam>::min(),  // smallest normal
+      // There are some errors dealing with denorms on apple platforms.
+      std::numeric_limits<TypeParam>::denorm_min(),  // smallest denorm
+      std::numeric_limits<TypeParam>::min() / 2,
+      std::nextafter(std::numeric_limits<TypeParam>::min(),
+                     TypeParam(0)),  // denorm_max
+  };
+
+  constexpr int kCount = 1000;
+  absl::InsecureBitGen gen;
+
+  // Use a loop to generate the combinations of {+/-x, +/-y}, and assign x, y to
+  // all values in kParams,
+  for (const auto mod : {0, 1, 2, 3}) {
+    for (const auto x : kParams) {
+      if (!std::isfinite(x)) continue;
+      for (const auto y : kParams) {
+        const TypeParam mean = (mod & 0x1) ? -x : x;
+        const TypeParam stddev = (mod & 0x2) ? -y : y;
+        const param_type param(mean, stddev);
+
+        absl::gaussian_distribution<TypeParam> before(mean, stddev);
+        EXPECT_EQ(before.mean(), param.mean());
+        EXPECT_EQ(before.stddev(), param.stddev());
+
+        {
+          absl::gaussian_distribution<TypeParam> via_param(param);
+          EXPECT_EQ(via_param, before);
+          EXPECT_EQ(via_param.param(), before.param());
+        }
+
+        // Smoke test.
+        auto sample_min = before.max();
+        auto sample_max = before.min();
+        for (int i = 0; i < kCount; i++) {
+          auto sample = before(gen);
+          if (sample > sample_max) sample_max = sample;
+          if (sample < sample_min) sample_min = sample;
+          EXPECT_GE(sample, before.min()) << before;
+          EXPECT_LE(sample, before.max()) << before;
+        }
+        if (!std::is_same<TypeParam, long double>::value) {
+          ABSL_INTERNAL_LOG(
+              INFO, absl::StrFormat("Range{%f, %f}: %f, %f", mean, stddev,
+                                    sample_min, sample_max));
+        }
+
+        std::stringstream ss;
+        ss << before;
+
+        if (!std::isfinite(mean) || !std::isfinite(stddev)) {
+          // Streams do not parse inf/nan.
+          continue;
+        }
+
+        // Validate stream serialization.
+        absl::gaussian_distribution<TypeParam> after(-0.53f, 2.3456f);
+
+        EXPECT_NE(before.mean(), after.mean());
+        EXPECT_NE(before.stddev(), after.stddev());
+        EXPECT_NE(before.param(), after.param());
+        EXPECT_NE(before, after);
+
+        ss >> after;
+
+#if defined(__powerpc64__) || defined(__PPC64__) || defined(__powerpc__) || \
+    defined(__ppc__) || defined(__PPC__)
+        if (std::is_same<TypeParam, long double>::value) {
+          // Roundtripping floating point values requires sufficient precision
+          // to reconstruct the exact value.  It turns out that long double
+          // has some errors doing this on ppc, particularly for values
+          // near {1.0 +/- epsilon}.
+          if (mean <= std::numeric_limits<double>::max() &&
+              mean >= std::numeric_limits<double>::lowest()) {
+            EXPECT_EQ(static_cast<double>(before.mean()),
+                      static_cast<double>(after.mean()))
+                << ss.str();
+          }
+          if (stddev <= std::numeric_limits<double>::max() &&
+              stddev >= std::numeric_limits<double>::lowest()) {
+            EXPECT_EQ(static_cast<double>(before.stddev()),
+                      static_cast<double>(after.stddev()))
+                << ss.str();
+          }
+          continue;
+        }
+#endif
+
+        EXPECT_EQ(before.mean(), after.mean());
+        EXPECT_EQ(before.stddev(), after.stddev())  //
+            << ss.str() << " "                      //
+            << (ss.good() ? "good " : "")           //
+            << (ss.bad() ? "bad " : "")             //
+            << (ss.eof() ? "eof " : "")             //
+            << (ss.fail() ? "fail " : "");
+      }
+    }
+  }
+}
+
+// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
+
+class GaussianModel {
+ public:
+  GaussianModel(double mean, double stddev) : mean_(mean), stddev_(stddev) {}
+
+  double mean() const { return mean_; }
+  double variance() const { return stddev() * stddev(); }
+  double stddev() const { return stddev_; }
+  double skew() const { return 0; }
+  double kurtosis() const { return 3.0; }
+
+  // The inverse CDF, or PercentPoint function.
+  double InverseCDF(double p) {
+    ABSL_ASSERT(p >= 0.0);
+    ABSL_ASSERT(p < 1.0);
+    return mean() + stddev() * -absl::random_internal::InverseNormalSurvival(p);
+  }
+
+ private:
+  const double mean_;
+  const double stddev_;
+};
+
+struct Param {
+  double mean;
+  double stddev;
+  double p_fail;  // Z-Test probability of failure.
+  int trials;     // Z-Test trials.
+};
+
+// GaussianDistributionTests implements a z-test for the gaussian
+// distribution.
+class GaussianDistributionTests : public testing::TestWithParam<Param>,
+                                  public GaussianModel {
+ public:
+  GaussianDistributionTests()
+      : GaussianModel(GetParam().mean, GetParam().stddev) {}
+
+  // SingleZTest provides a basic z-squared test of the mean vs. expected
+  // mean for data generated by the poisson distribution.
+  template <typename D>
+  bool SingleZTest(const double p, const size_t samples);
+
+  // SingleChiSquaredTest provides a basic chi-squared test of the normal
+  // distribution.
+  template <typename D>
+  double SingleChiSquaredTest();
+
+  absl::InsecureBitGen rng_;
+};
+
+template <typename D>
+bool GaussianDistributionTests::SingleZTest(const double p,
+                                            const size_t samples) {
+  D dis(mean(), stddev());
+
+  std::vector<double> data;
+  data.reserve(samples);
+  for (size_t i = 0; i < samples; i++) {
+    const double x = dis(rng_);
+    data.push_back(x);
+  }
+
+  const double max_err = absl::random_internal::MaxErrorTolerance(p);
+  const auto m = absl::random_internal::ComputeDistributionMoments(data);
+  const double z = absl::random_internal::ZScore(mean(), m);
+  const bool pass = absl::random_internal::Near("z", z, 0.0, max_err);
+
+  // NOTE: Informational statistical test:
+  //
+  // Compute the Jarque-Bera test statistic given the excess skewness
+  // and kurtosis. The statistic is drawn from a chi-square(2) distribution.
+  // https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test
+  //
+  // The null-hypothesis (normal distribution) is rejected when
+  // (p = 0.05 => jb > 5.99)
+  // (p = 0.01 => jb > 9.21)
+  // NOTE: JB has a large type-I error rate, so it will reject the
+  // null-hypothesis even when it is true more often than the z-test.
+  //
+  const double jb =
+      static_cast<double>(m.n) / 6.0 *
+      (std::pow(m.skewness, 2.0) + std::pow(m.kurtosis - 3.0, 2.0) / 4.0);
+
+  if (!pass || jb > 9.21) {
+    ABSL_INTERNAL_LOG(
+        INFO, absl::StrFormat("p=%f max_err=%f\n"
+                              " mean=%f vs. %f\n"
+                              " stddev=%f vs. %f\n"
+                              " skewness=%f vs. %f\n"
+                              " kurtosis=%f vs. %f\n"
+                              " z=%f vs. 0\n"
+                              " jb=%f vs. 9.21",
+                              p, max_err, m.mean, mean(), std::sqrt(m.variance),
+                              stddev(), m.skewness, skew(), m.kurtosis,
+                              kurtosis(), z, jb));
+  }
+  return pass;
+}
+
+template <typename D>
+double GaussianDistributionTests::SingleChiSquaredTest() {
+  const size_t kSamples = 10000;
+  const int kBuckets = 50;
+
+  // The InverseCDF is the percent point function of the
+  // distribution, and can be used to assign buckets
+  // roughly uniformly.
+  std::vector<double> cutoffs;
+  const double kInc = 1.0 / static_cast<double>(kBuckets);
+  for (double p = kInc; p < 1.0; p += kInc) {
+    cutoffs.push_back(InverseCDF(p));
+  }
+  if (cutoffs.back() != std::numeric_limits<double>::infinity()) {
+    cutoffs.push_back(std::numeric_limits<double>::infinity());
+  }
+
+  D dis(mean(), stddev());
+
+  std::vector<int32_t> counts(cutoffs.size(), 0);
+  for (int j = 0; j < kSamples; j++) {
+    const double x = dis(rng_);
+    auto it = std::upper_bound(cutoffs.begin(), cutoffs.end(), x);
+    counts[std::distance(cutoffs.begin(), it)]++;
+  }
+
+  // Null-hypothesis is that the distribution is a gaussian distribution
+  // with the provided mean and stddev (not estimated from the data).
+  const int dof = static_cast<int>(counts.size()) - 1;
+
+  // Our threshold for logging is 1-in-50.
+  const double threshold = absl::random_internal::ChiSquareValue(dof, 0.98);
+
+  const double expected =
+      static_cast<double>(kSamples) / static_cast<double>(counts.size());
+
+  double chi_square = absl::random_internal::ChiSquareWithExpected(
+      std::begin(counts), std::end(counts), expected);
+  double p = absl::random_internal::ChiSquarePValue(chi_square, dof);
+
+  // Log if the chi_square value is above the threshold.
+  if (chi_square > threshold) {
+    for (int i = 0; i < cutoffs.size(); i++) {
+      ABSL_INTERNAL_LOG(
+          INFO, absl::StrFormat("%d : (%f) = %d", i, cutoffs[i], counts[i]));
+    }
+
+    ABSL_INTERNAL_LOG(
+        INFO, absl::StrCat("mean=", mean(), " stddev=", stddev(), "\n",   //
+                           " expected ", expected, "\n",                  //
+                           kChiSquared, " ", chi_square, " (", p, ")\n",  //
+                           kChiSquared, " @ 0.98 = ", threshold));
+  }
+  return p;
+}
+
+TEST_P(GaussianDistributionTests, ZTest) {
+  // TODO(absl-team): Run these tests against std::normal_distribution<double>
+  // to validate outcomes are similar.
+  const size_t kSamples = 10000;
+  const auto& param = GetParam();
+  const int expected_failures =
+      std::max(1, static_cast<int>(std::ceil(param.trials * param.p_fail)));
+  const double p = absl::random_internal::RequiredSuccessProbability(
+      param.p_fail, param.trials);
+
+  int failures = 0;
+  for (int i = 0; i < param.trials; i++) {
+    failures +=
+        SingleZTest<absl::gaussian_distribution<double>>(p, kSamples) ? 0 : 1;
+  }
+  EXPECT_LE(failures, expected_failures);
+}
+
+TEST_P(GaussianDistributionTests, ChiSquaredTest) {
+  const int kTrials = 20;
+  int failures = 0;
+
+  for (int i = 0; i < kTrials; i++) {
+    double p_value =
+        SingleChiSquaredTest<absl::gaussian_distribution<double>>();
+    if (p_value < 0.0025) {  // 1/400
+      failures++;
+    }
+  }
+  // There is a 0.05% chance of producing at least one failure, so raise the
+  // failure threshold high enough to allow for a flake rate of less than one in
+  // 10,000.
+  EXPECT_LE(failures, 4);
+}
+
+std::vector<Param> GenParams() {
+  return {
+      // Mean around 0.
+      Param{0.0, 1.0, 0.01, 100},
+      Param{0.0, 1e2, 0.01, 100},
+      Param{0.0, 1e4, 0.01, 100},
+      Param{0.0, 1e8, 0.01, 100},
+      Param{0.0, 1e16, 0.01, 100},
+      Param{0.0, 1e-3, 0.01, 100},
+      Param{0.0, 1e-5, 0.01, 100},
+      Param{0.0, 1e-9, 0.01, 100},
+      Param{0.0, 1e-17, 0.01, 100},
+
+      // Mean around 1.
+      Param{1.0, 1.0, 0.01, 100},
+      Param{1.0, 1e2, 0.01, 100},
+      Param{1.0, 1e-2, 0.01, 100},
+
+      // Mean around 100 / -100
+      Param{1e2, 1.0, 0.01, 100},
+      Param{-1e2, 1.0, 0.01, 100},
+      Param{1e2, 1e6, 0.01, 100},
+      Param{-1e2, 1e6, 0.01, 100},
+
+      // More extreme
+      Param{1e4, 1e4, 0.01, 100},
+      Param{1e8, 1e4, 0.01, 100},
+      Param{1e12, 1e4, 0.01, 100},
+  };
+}
+
+std::string ParamName(const ::testing::TestParamInfo<Param>& info) {
+  const auto& p = info.param;
+  std::string name = absl::StrCat("mean_", absl::SixDigits(p.mean), "__stddev_",
+                                  absl::SixDigits(p.stddev));
+  return absl::StrReplaceAll(name, {{"+", "_"}, {"-", "_"}, {".", "_"}});
+}
+
+INSTANTIATE_TEST_SUITE_P(, GaussianDistributionTests,
+                         ::testing::ValuesIn(GenParams()), ParamName);
+
+// NOTE: absl::gaussian_distribution is not guaranteed to be stable.
+TEST(GaussianDistributionTest, StabilityTest) {
+  // absl::gaussian_distribution stability relies on the underlying zignor
+  // data, absl::random_interna::RandU64ToDouble, std::exp, std::log, and
+  // std::abs.
+  absl::random_internal::sequence_urbg urbg(
+      {0x0003eb76f6f7f755ull, 0xFFCEA50FDB2F953Bull, 0xC332DDEFBE6C5AA5ull,
+       0x6558218568AB9702ull, 0x2AEF7DAD5B6E2F84ull, 0x1521B62829076170ull,
+       0xECDD4775619F1510ull, 0x13CCA830EB61BD96ull, 0x0334FE1EAA0363CFull,
+       0xB5735C904C70A239ull, 0xD59E9E0BCBAADE14ull, 0xEECC86BC60622CA7ull});
+
+  std::vector<int> output(11);
+
+  {
+    absl::gaussian_distribution<double> dist;
+    std::generate(std::begin(output), std::end(output),
+                  [&] { return static_cast<int>(10000000.0 * dist(urbg)); });
+
+    EXPECT_EQ(13, urbg.invocations());
+    EXPECT_THAT(output,  //
+                testing::ElementsAre(1494, 25518841, 9991550, 1351856,
+                                     -20373238, 3456682, 333530, -6804981,
+                                     -15279580, -16459654, 1494));
+  }
+
+  urbg.reset();
+  {
+    absl::gaussian_distribution<float> dist;
+    std::generate(std::begin(output), std::end(output),
+                  [&] { return static_cast<int>(1000000.0f * dist(urbg)); });
+
+    EXPECT_EQ(13, urbg.invocations());
+    EXPECT_THAT(
+        output,  //
+        testing::ElementsAre(149, 2551884, 999155, 135185, -2037323, 345668,
+                             33353, -680498, -1527958, -1645965, 149));
+  }
+}
+
+// This is an implementation-specific test. If any part of the implementation
+// changes, then it is likely that this test will change as well.
+// Also, if dependencies of the distribution change, such as RandU64ToDouble,
+// then this is also likely to change.
+TEST(GaussianDistributionTest, AlgorithmBounds) {
+  absl::gaussian_distribution<double> dist;
+
+  // In ~95% of cases, a single value is used to generate the output.
+  // for all inputs where |x| < 0.750461021389 this should be the case.
+  //
+  // The exact constraints are based on the ziggurat tables, and any
+  // changes to the ziggurat tables may require adjusting these bounds.
+  //
+  // for i in range(0, len(X)-1):
+  //   print i, X[i+1]/X[i], (X[i+1]/X[i] > 0.984375)
+  //
+  // 0.125 <= |values| <= 0.75
+  const uint64_t kValues[] = {
+      0x1000000000000100ull, 0x2000000000000100ull, 0x3000000000000100ull,
+      0x4000000000000100ull, 0x5000000000000100ull, 0x6000000000000100ull,
+      // negative values
+      0x9000000000000100ull, 0xa000000000000100ull, 0xb000000000000100ull,
+      0xc000000000000100ull, 0xd000000000000100ull, 0xe000000000000100ull};
+
+  // 0.875 <= |values| <= 0.984375
+  const uint64_t kExtraValues[] = {
+      0x7000000000000100ull, 0x7800000000000100ull,  //
+      0x7c00000000000100ull, 0x7e00000000000100ull,  //
+      // negative values
+      0xf000000000000100ull, 0xf800000000000100ull,  //
+      0xfc00000000000100ull, 0xfe00000000000100ull};
+
+  auto make_box = [](uint64_t v, uint64_t box) {
+    return (v & 0xffffffffffffff80ull) | box;
+  };
+
+  // The box is the lower 7 bits of the value. When the box == 0, then
+  // the algorithm uses an escape hatch to select the result for large
+  // outputs.
+  for (uint64_t box = 0; box < 0x7f; box++) {
+    for (const uint64_t v : kValues) {
+      // Extra values are added to the sequence to attempt to avoid
+      // infinite loops from rejection sampling on bugs/errors.
+      absl::random_internal::sequence_urbg urbg(
+          {make_box(v, box), 0x0003eb76f6f7f755ull, 0x5FCEA50FDB2F953Bull});
+
+      auto a = dist(urbg);
+      EXPECT_EQ(1, urbg.invocations()) << box << " " << std::hex << v;
+      if (v & 0x8000000000000000ull) {
+        EXPECT_LT(a, 0.0) << box << " " << std::hex << v;
+      } else {
+        EXPECT_GT(a, 0.0) << box << " " << std::hex << v;
+      }
+    }
+    if (box > 10 && box < 100) {
+      // The center boxes use the fast algorithm for more
+      // than 98.4375% of values.
+      for (const uint64_t v : kExtraValues) {
+        absl::random_internal::sequence_urbg urbg(
+            {make_box(v, box), 0x0003eb76f6f7f755ull, 0x5FCEA50FDB2F953Bull});
+
+        auto a = dist(urbg);
+        EXPECT_EQ(1, urbg.invocations()) << box << " " << std::hex << v;
+        if (v & 0x8000000000000000ull) {
+          EXPECT_LT(a, 0.0) << box << " " << std::hex << v;
+        } else {
+          EXPECT_GT(a, 0.0) << box << " " << std::hex << v;
+        }
+      }
+    }
+  }
+
+  // When the box == 0, the fallback algorithm uses a ratio of uniforms,
+  // which consumes 2 additional values from the urbg.
+  // Fallback also requires that the initial value be > 0.9271586026096681.
+  auto make_fallback = [](uint64_t v) { return (v & 0xffffffffffffff80ull); };
+
+  double tail[2];
+  {
+    // 0.9375
+    absl::random_internal::sequence_urbg urbg(
+        {make_fallback(0x7800000000000000ull), 0x13CCA830EB61BD96ull,
+         0x00000076f6f7f755ull});
+    tail[0] = dist(urbg);
+    EXPECT_EQ(3, urbg.invocations());
+    EXPECT_GT(tail[0], 0);
+  }
+  {
+    // -0.9375
+    absl::random_internal::sequence_urbg urbg(
+        {make_fallback(0xf800000000000000ull), 0x13CCA830EB61BD96ull,
+         0x00000076f6f7f755ull});
+    tail[1] = dist(urbg);
+    EXPECT_EQ(3, urbg.invocations());
+    EXPECT_LT(tail[1], 0);
+  }
+  EXPECT_EQ(tail[0], -tail[1]);
+  EXPECT_EQ(418610, static_cast<int64_t>(tail[0] * 100000.0));
+
+  // When the box != 0, the fallback algorithm computes a wedge function.
+  // Depending on the box, the threshold for varies as high as
+  // 0.991522480228.
+  {
+    // 0.9921875, 0.875
+    absl::random_internal::sequence_urbg urbg(
+        {make_box(0x7f00000000000000ull, 120), 0xe000000000000001ull,
+         0x13CCA830EB61BD96ull});
+    tail[0] = dist(urbg);
+    EXPECT_EQ(2, urbg.invocations());
+    EXPECT_GT(tail[0], 0);
+  }
+  {
+    // -0.9921875, 0.875
+    absl::random_internal::sequence_urbg urbg(
+        {make_box(0xff00000000000000ull, 120), 0xe000000000000001ull,
+         0x13CCA830EB61BD96ull});
+    tail[1] = dist(urbg);
+    EXPECT_EQ(2, urbg.invocations());
+    EXPECT_LT(tail[1], 0);
+  }
+  EXPECT_EQ(tail[0], -tail[1]);
+  EXPECT_EQ(61948, static_cast<int64_t>(tail[0] * 100000.0));
+
+  // Fallback rejected, try again.
+  {
+    // -0.9921875, 0.0625
+    absl::random_internal::sequence_urbg urbg(
+        {make_box(0xff00000000000000ull, 120), 0x1000000000000001,
+         make_box(0x1000000000000100ull, 50), 0x13CCA830EB61BD96ull});
+    dist(urbg);
+    EXPECT_EQ(3, urbg.invocations());
+  }
+}
+
+}  // namespace