Creation of LTS branch "lts_2020_02_25"20200225

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GitOrigin-RevId: 0033c9ea91a52ade7c6b725aa2ef3cbe15463421
Change-Id: I8a2b70063cb3ab40c6943a6db0fe40cae71ed8d7

1 files changed, 199 insertions, 0 deletions

diff --git a/absl/base/internal/exponential_biased_test.cc b/absl/base/internal/exponential_biased_test.cc
new file mode 100644
index 00000000..90a482d2
--- /dev/null
+++ b/absl/base/internal/exponential_biased_test.cc
@@ -0,0 +1,199 @@
+// Copyright 2019 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/base/internal/exponential_biased.h"
+
+#include <stddef.h>
+
+#include <cmath>
+#include <cstdint>
+#include <vector>
+
+#include "gmock/gmock.h"
+#include "gtest/gtest.h"
+#include "absl/strings/str_cat.h"
+
+using ::testing::Ge;
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+namespace base_internal {
+
+MATCHER_P2(IsBetween, a, b,
+           absl::StrCat(std::string(negation ? "isn't" : "is"), " between ", a,
+                        " and ", b)) {
+  return a <= arg && arg <= b;
+}
+
+// Tests of the quality of the random numbers generated
+// This uses the Anderson Darling test for uniformity.
+// See "Evaluating the Anderson-Darling Distribution" by Marsaglia
+// for details.
+
+// Short cut version of ADinf(z), z>0 (from Marsaglia)
+// This returns the p-value for Anderson Darling statistic in
+// the limit as n-> infinity. For finite n, apply the error fix below.
+double AndersonDarlingInf(double z) {
+  if (z < 2) {
+    return exp(-1.2337141 / z) / sqrt(z) *
+           (2.00012 +
+            (0.247105 -
+             (0.0649821 - (0.0347962 - (0.011672 - 0.00168691 * z) * z) * z) *
+                 z) *
+                z);
+  }
+  return exp(
+      -exp(1.0776 -
+           (2.30695 -
+            (0.43424 - (0.082433 - (0.008056 - 0.0003146 * z) * z) * z) * z) *
+               z));
+}
+
+// Corrects the approximation error in AndersonDarlingInf for small values of n
+// Add this to AndersonDarlingInf to get a better approximation
+// (from Marsaglia)
+double AndersonDarlingErrFix(int n, double x) {
+  if (x > 0.8) {
+    return (-130.2137 +
+            (745.2337 -
+             (1705.091 - (1950.646 - (1116.360 - 255.7844 * x) * x) * x) * x) *
+                x) /
+           n;
+  }
+  double cutoff = 0.01265 + 0.1757 / n;
+  if (x < cutoff) {
+    double t = x / cutoff;
+    t = sqrt(t) * (1 - t) * (49 * t - 102);
+    return t * (0.0037 / (n * n) + 0.00078 / n + 0.00006) / n;
+  } else {
+    double t = (x - cutoff) / (0.8 - cutoff);
+    t = -0.00022633 +
+        (6.54034 - (14.6538 - (14.458 - (8.259 - 1.91864 * t) * t) * t) * t) *
+            t;
+    return t * (0.04213 + 0.01365 / n) / n;
+  }
+}
+
+// Returns the AndersonDarling p-value given n and the value of the statistic
+double AndersonDarlingPValue(int n, double z) {
+  double ad = AndersonDarlingInf(z);
+  double errfix = AndersonDarlingErrFix(n, ad);
+  return ad + errfix;
+}
+
+double AndersonDarlingStatistic(const std::vector<double>& random_sample) {
+  int n = random_sample.size();
+  double ad_sum = 0;
+  for (int i = 0; i < n; i++) {
+    ad_sum += (2 * i + 1) *
+              std::log(random_sample[i] * (1 - random_sample[n - 1 - i]));
+  }
+  double ad_statistic = -n - 1 / static_cast<double>(n) * ad_sum;
+  return ad_statistic;
+}
+
+// Tests if the array of doubles is uniformly distributed.
+// Returns the p-value of the Anderson Darling Statistic
+// for the given set of sorted random doubles
+// See "Evaluating the Anderson-Darling Distribution" by
+// Marsaglia and Marsaglia for details.
+double AndersonDarlingTest(const std::vector<double>& random_sample) {
+  double ad_statistic = AndersonDarlingStatistic(random_sample);
+  double p = AndersonDarlingPValue(random_sample.size(), ad_statistic);
+  return p;
+}
+
+TEST(ExponentialBiasedTest, CoinTossDemoWithGetSkipCount) {
+  ExponentialBiased eb;
+  for (int runs = 0; runs < 10; ++runs) {
+    for (int flips = eb.GetSkipCount(1); flips > 0; --flips) {
+      printf("head...");
+    }
+    printf("tail\n");
+  }
+  int heads = 0;
+  for (int i = 0; i < 10000000; i += 1 + eb.GetSkipCount(1)) {
+    ++heads;
+  }
+  printf("Heads = %d (%f%%)\n", heads, 100.0 * heads / 10000000);
+}
+
+TEST(ExponentialBiasedTest, SampleDemoWithStride) {
+  ExponentialBiased eb;
+  int stride = eb.GetStride(10);
+  int samples = 0;
+  for (int i = 0; i < 10000000; ++i) {
+    if (--stride == 0) {
+      ++samples;
+      stride = eb.GetStride(10);
+    }
+  }
+  printf("Samples = %d (%f%%)\n", samples, 100.0 * samples / 10000000);
+}
+
+
+// Testing that NextRandom generates uniform random numbers. Applies the
+// Anderson-Darling test for uniformity
+TEST(ExponentialBiasedTest, TestNextRandom) {
+  for (auto n : std::vector<int>({
+           10,  // Check short-range correlation
+           100, 1000,
+           10000  // Make sure there's no systemic error
+       })) {
+    uint64_t x = 1;
+    // This assumes that the prng returns 48 bit numbers
+    uint64_t max_prng_value = static_cast<uint64_t>(1) << 48;
+    // Initialize.
+    for (int i = 1; i <= 20; i++) {
+      x = ExponentialBiased::NextRandom(x);
+    }
+    std::vector<uint64_t> int_random_sample(n);
+    // Collect samples
+    for (int i = 0; i < n; i++) {
+      int_random_sample[i] = x;
+      x = ExponentialBiased::NextRandom(x);
+    }
+    // First sort them...
+    std::sort(int_random_sample.begin(), int_random_sample.end());
+    std::vector<double> random_sample(n);
+    // Convert them to uniform randoms (in the range [0,1])
+    for (int i = 0; i < n; i++) {
+      random_sample[i] =
+          static_cast<double>(int_random_sample[i]) / max_prng_value;
+    }
+    // Now compute the Anderson-Darling statistic
+    double ad_pvalue = AndersonDarlingTest(random_sample);
+    EXPECT_GT(std::min(ad_pvalue, 1 - ad_pvalue), 0.0001)
+        << "prng is not uniform: n = " << n << " p = " << ad_pvalue;
+  }
+}
+
+// The generator needs to be available as a thread_local and as a static
+// variable.
+TEST(ExponentialBiasedTest, InitializationModes) {
+  ABSL_CONST_INIT static ExponentialBiased eb_static;
+  EXPECT_THAT(eb_static.GetSkipCount(2), Ge(0));
+
+#if ABSL_HAVE_THREAD_LOCAL
+  thread_local ExponentialBiased eb_thread;
+  EXPECT_THAT(eb_thread.GetSkipCount(2), Ge(0));
+#endif
+
+  ExponentialBiased eb_stack;
+  EXPECT_THAT(eb_stack.GetSkipCount(2), Ge(0));
+}
+
+}  // namespace base_internal
+ABSL_NAMESPACE_END
+}  // namespace absl