text: //===- ReservoirSampler.cpp - Tests for the ReservoirSampler --------------===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  
  #include "llvm/FuzzMutate/Random.h"
  #include "gtest/gtest.h"
  #include <random>
  
  using namespace llvm;
  
  TEST(ReservoirSamplerTest, OneItem) {
    std::mt19937 Rand;
    auto Sampler = makeSampler(Rand, 7, 1);
    ASSERT_FALSE(Sampler.isEmpty());
    ASSERT_EQ(7, Sampler.getSelection());
  }
  
  TEST(ReservoirSamplerTest, NoWeight) {
    std::mt19937 Rand;
    auto Sampler = makeSampler(Rand, 7, 0);
    ASSERT_TRUE(Sampler.isEmpty());
  }
  
  TEST(ReservoirSamplerTest, Uniform) {
    std::mt19937 Rand;
  
    // Run three chi-squared tests to check that the distribution is reasonably
    // uniform.
    std::vector<int> Items = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
  
    int Failures = 0;
    for (int Run = 0; Run < 3; ++Run) {
      std::vector<int> Counts(Items.size(), 0);
  
      // We need $np_s > 5$ at minimum, but we're better off going a couple of
      // orders of magnitude larger.
      int N = Items.size() * 5 * 100;
      for (int I = 0; I < N; ++I) {
        auto Sampler = makeSampler(Rand, Items);
        Counts[Sampler.getSelection()] += 1;
      }
  
      // Knuth. TAOCP Vol. 2, 3.3.1 (8):
      // $V = \frac{1}{n} \sum_{s=1}^{k} \left(\frac{Y_s^2}{p_s}\right) - n$
      double Ps = 1.0 / Items.size();
      double Sum = 0.0;
      for (int Ys : Counts)
        Sum += Ys * Ys / Ps;
      double V = (Sum / N) - N;
  
      assert(Items.size() == 10 && "Our chi-squared values assume 10 items");
      // Since we have 10 items, there are 9 degrees of freedom and the table of
      // chi-squared values is as follows:
      //
      //     | p=1%  |   5%  |  25%  |  50%  |  75%  |  95%  |  99%  |
      // v=9 | 2.088 | 3.325 | 5.899 | 8.343 | 11.39 | 16.92 | 21.67 |
      //
      // Check that we're in the likely range of results.
      //if (V < 2.088 || V > 21.67)
      if (V < 2.088 || V > 21.67)
        ++Failures;
    }
    EXPECT_LT(Failures, 3) << "Non-uniform distribution?";
  }
  