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+// 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