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// { dg-options "-std=gnu++0x" }

// Use smaller statistics when running on simulators, so it takes less time.

// { dg-options "-std=gnu++0x -DSAMPLES=10000" { target simulator } }

// Copyright (C) 2010, 2011 Free Software Foundation, Inc.

//

// This file is part of the GNU ISO C++ Library.  This library is free

// software; you can redistribute it and/or modify it under the

// terms of the GNU General Public License as published by the

// Free Software Foundation; either version 3, or (at your option)

// any later version.

//

// This library is distributed in the hope that it will be useful,

// but WITHOUT ANY WARRANTY; without even the implied warranty of

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

// GNU General Public License for more details.

//

// You should have received a copy of the GNU General Public License

// along with this library; see the file COPYING3.  If not see

// <http://www.gnu.org/licenses/>.

// This file uses the chi^2 test to measure the quality of a hash

// function, by computing the uniformity with which it distributes a set

// of N strings into k buckets (where k is significantly greater than N).

//

// Each bucket has B[i] strings in it. The expected value of each bucket

// for a uniform distribution is z = N/k, so

//   chi^2 = Sum_i (B[i] - z)^2 / z.

//

// We check whether chi^2 is small enough to be consistent with the

// hypothesis of a uniform distribution. If F(chi^2, k-1) is close to

// 0 (where F is the cumulative probability distribution), we can

// reject that hypothesis. So we don't want F to be too small, which

// for large k, means we want chi^2 to be not too much larger than k.

//

// We use the chi^2 test for several sets of strings. Any non-horrible

// hash function should do well with purely random strings. A really

// good hash function will also do well with more structured sets,

// including ones where the strings differ by only a few bits.

#include <algorithm>

#include <cstdlib>

#include <cstdio>

#include <fstream>

#include <functional>

#include <iostream>

#include <iterator>

#include <string>

#include <unordered_set>

#include <vector>

#include <testsuite_hooks.h>

#ifndef SAMPLES

#define SAMPLES 300000

#endif

template <typename Container>

  double

  chi2_hash(const Container& c, long buckets)

  {

    std::vector<int> counts(buckets);

    std::hash<std::string> hasher;

    double elements = 0;

    for (auto i = c.begin(); i != c.end(); ++i)

      {

        ++counts[hasher(*i) % buckets];

        ++elements;

      }

    const double z = elements / buckets;

    double sum = 0;

    for (long i = 0; i < buckets; ++i)

      {

        double delta = counts[i] - z;

        sum += delta*delta;

      }

    return sum/z;

  }

// Tests chi^2 for a distribution of uniformly generated random strings.

void

test_uniform_random()

{

  bool test __attribute__((unused)) = true;

  std::srand(137);

  std::unordered_set<std::string> set;

  std::string s;

  const unsigned long N = SAMPLES;

  const unsigned long k = N/100;

  const unsigned int len = 25;

  while (set.size() < N)

    {

      s.clear();

      for (unsigned int i = 0; i < len; ++i)

        s.push_back(rand() % 128);

      set.insert(s);

    }

  double chi2 = chi2_hash(set, k);

  VERIFY( chi2 < k*1.1 );

}

// Tests chi^2 for a distribution of strings that differ from each

// other by only a few bits. We start with an arbitrary base string, and

// flip three random bits for each member of the set.

void

test_bit_flip_set()

{

  bool test __attribute__((unused)) = true;

  const unsigned long N = SAMPLES;

  const unsigned long k = N/100;

  const unsigned int len = 67;

  const unsigned int bitlen = len * 8;

  const unsigned int bits_to_flip = 3;

  const char base[len+1] = "abcdefghijklmnopqrstuvwxyz"

                           "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

                           "0123456789!@#$%";

  std::unordered_set<std::string> set;

  while (set.size() < N)

    {

      std::string s(base, base+len);

      for (unsigned int i = 0; i < bits_to_flip; ++i)

        {

          int bit = rand() % bitlen;

          s[bit/8] ^= (1 << (bit%8));

        }

      set.insert(s);

    }

  double chi2 = chi2_hash(set, k);

  VERIFY( chi2 < k*1.1 );

}

// Tests chi^2 of a set of strings that all have a similar pattern,

// intended to mimic some sort of ID string.

void

test_numeric_pattern_set()

{

  bool test __attribute__((unused)) = true;

  const unsigned long N = SAMPLES;

  const unsigned long k = N/100;

  std::vector<std::string> set;

  for (unsigned long i = 0; i < N; ++i)

    {

      long i1 = i % 100000;

      long i2 = i / 100000;

      char buf[16];

      std::sprintf(buf, "XX-%05lu-%05lu", i1, i2);

      set.push_back(buf);

    }

  double chi2 = chi2_hash(set, k);

  VERIFY( chi2 < k*1.1 );

}

// Tests chi^2 for a set of strings that all consist of '1' and '0'.

void

test_bit_string_set()

{

  bool test __attribute__((unused)) = true;

  const unsigned long N = SAMPLES;

  const unsigned long k = N/100;

  std::vector<std::string> set;

  std::string s;

  for (unsigned long i = 0; i < N; ++i)

    {

      s.clear();

      for (unsigned int j = 0; j < sizeof(unsigned long) * 8; ++j)

        {

          const bool bit = (1UL << j) & i;

          s.push_back(bit ? '1' : '0');

        }

      set.push_back(s);

    }

  double chi2 = chi2_hash(set, k);

  VERIFY( chi2 < k*1.1 );

}

// Tests chi^2 for a set of words taken from a document written in English.

void

test_document_words()

{

  // That file is 187587 single-word lines.  To avoid a timeout, just skip

  // this part, which would take up to 95% of the program runtime (with

  // SAMPLES == 10000), if we're not supposed to run anywhere that long.

#if SAMPLES >= 100000

  bool test __attribute__((unused)) = true;

  const std::string f_name = "thirty_years_among_the_dead_preproc.txt";

  std::ifstream in(f_name);

  VERIFY( in.is_open() );

  std::vector<std::string> words;

  words.assign(std::istream_iterator<std::string>(in),

               std::istream_iterator<std::string>());

  VERIFY( words.size() > 100000 );

  std::sort(words.begin(), words.end());

  auto it = std::unique(words.begin(), words.end());

  words.erase(it, words.end());

  VERIFY( words.size() > 5000 );

  const unsigned long k = words.size() / 20;

  double chi2 = chi2_hash(words, k);

  VERIFY( chi2 < k*1.1 );

#endif

}

int

main()

{

  test_uniform_random();

  test_bit_flip_set();

  test_numeric_pattern_set();

  test_bit_string_set();

  test_document_words();

  return 0;

}