libstdc++-v3/testsuite/20_util/hash/chi2_quality.cc

   1 // { dg-options "-std=gnu++0x" }
   2
   3 // Use smaller statistics when running on simulators, so it takes less time.
   4 // { dg-options "-std=gnu++0x -DSAMPLES=30000" { target simulator } }
   5
   6 // Copyright (C) 2010-2013 Free Software Foundation, Inc.
   7 //
   8 // This file is part of the GNU ISO C++ Library.  This library is free
   9 // software; you can redistribute it and/or modify it under the
  10 // terms of the GNU General Public License as published by the
  11 // Free Software Foundation; either version 3, or (at your option)
  12 // any later version.
  13 //
  14 // This library is distributed in the hope that it will be useful,
  15 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  16 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  17 // GNU General Public License for more details.
  18 //
  19 // You should have received a copy of the GNU General Public License
  20 // along with this library; see the file COPYING3.  If not see
  21 // <http://www.gnu.org/licenses/>.
  22
  23 // This file uses the chi^2 test to measure the quality of a hash
  24 // function, by computing the uniformity with which it distributes a set
  25 // of N strings into k buckets (where k is significantly greater than N).
  26 //
  27 // Each bucket has B[i] strings in it. The expected value of each bucket
  28 // for a uniform distribution is z = N/k, so
  29 //   chi^2 = Sum_i (B[i] - z)^2 / z.
  30 //
  31 // We check whether chi^2 is small enough to be consistent with the
  32 // hypothesis of a uniform distribution. If F(chi^2, k-1) is close to
  33 // 0 (where F is the cumulative probability distribution), we can
  34 // reject that hypothesis. So we don't want F to be too small, which
  35 // for large k, means we want chi^2 to be not too much larger than k.
  36 //
  37 // We use the chi^2 test for several sets of strings. Any non-horrible
  38 // hash function should do well with purely random strings. A really
  39 // good hash function will also do well with more structured sets,
  40 // including ones where the strings differ by only a few bits.
  41
  42 #include <algorithm>
  43 #include <cstdlib>
  44 #include <cstdio>
  45 #include <fstream>
  46 #include <functional>
  47 #include <iostream>
  48 #include <iterator>
  49 #include <string>
  50 #include <unordered_set>
  51 #include <vector>
  52 #include <testsuite_hooks.h>
  53
  54 #ifndef SAMPLES
  55 #define SAMPLES 300000
  56 #endif
  57
  58 template <typename Container>
  59   double
  60   chi2_hash(const Container& c, long buckets)
  61   {
  62     std::vector<int> counts(buckets);
  63     std::hash<std::string> hasher;
  64     double elements = 0;
  65     for (auto i = c.begin(); i != c.end(); ++i)
  66       {
  67         ++counts[hasher(*i) % buckets];
  68         ++elements;
  69       }
  70
  71     const double z = elements / buckets;
  72     double sum = 0;
  73     for (long i = 0; i < buckets; ++i)
  74       {
  75         double delta = counts[i] - z;
  76         sum += delta*delta;
  77       }
  78     return sum/z;
  79   }
  80
  81 // Tests chi^2 for a distribution of uniformly generated random strings.
  82 void
  83 test_uniform_random()
  84 {
  85   bool test __attribute__((unused)) = true;
  86   std::srand(137);
  87   std::unordered_set<std::string> set;
  88   std::string s;
  89   const unsigned long N = SAMPLES;
  90   const unsigned long k = N/100;
  91   const unsigned int len = 25;
  92   while (set.size() < N)
  93     {
  94       s.clear();
  95       for (unsigned int i = 0; i < len; ++i)
  96         s.push_back(rand() % 128);
  97       set.insert(s);
  98     }
  99
 100   double chi2 = chi2_hash(set, k);
 101   VERIFY( chi2 < k*1.1 );
 102 }
 103
 104 // Tests chi^2 for a distribution of strings that differ from each
 105 // other by only a few bits. We start with an arbitrary base string, and
 106 // flip three random bits for each member of the set.
 107 void
 108 test_bit_flip_set()
 109 {
 110   bool test __attribute__((unused)) = true;
 111   const unsigned long N = SAMPLES;
 112   const unsigned long k = N/100;
 113   const unsigned int len = 67;
 114   const unsigned int bitlen = len * 8;
 115   const unsigned int bits_to_flip = 3;
 116   const char base[len+1] = "abcdefghijklmnopqrstuvwxyz"
 117                            "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
 118                            "0123456789!@#$%";
 119
 120   std::unordered_set<std::string> set;
 121   while (set.size() < N)
 122     {
 123       std::string s(base, base+len);
 124       for (unsigned int i = 0; i < bits_to_flip; ++i)
 125         {
 126           int bit = rand() % bitlen;
 127           s[bit/8] ^= (1 << (bit%8));
 128         }
 129       set.insert(s);
 130     }
 131
 132   double chi2 = chi2_hash(set, k);
 133   VERIFY( chi2 < k*1.1 );
 134 }
 135
 136 // Tests chi^2 of a set of strings that all have a similar pattern,
 137 // intended to mimic some sort of ID string.
 138 void
 139 test_numeric_pattern_set()
 140 {
 141   bool test __attribute__((unused)) = true;
 142   const unsigned long N = SAMPLES;
 143   const unsigned long k = N/100;
 144   std::vector<std::string> set;
 145   for (unsigned long i = 0; i < N; ++i)
 146     {
 147       long i1 = i % 100000;
 148       long i2 = i / 100000;
 149       char buf[16];
 150       std::sprintf(buf, "XX-%05lu-%05lu", i1, i2);
 151       set.push_back(buf);
 152     }
 153
 154   double chi2 = chi2_hash(set, k);
 155   VERIFY( chi2 < k*1.1 );
 156 }
 157
 158 // Tests chi^2 for a set of strings that all consist of '1' and '0'.
 159 void
 160 test_bit_string_set()
 161 {
 162   bool test __attribute__((unused)) = true;
 163   const unsigned long N = SAMPLES;
 164   const unsigned long k = N/100;
 165   std::vector<std::string> set;
 166   std::string s;
 167   for (unsigned long i = 0; i < N; ++i)
 168     {
 169       s.clear();
 170       for (unsigned int j = 0; j < sizeof(unsigned long) * 8; ++j)
 171         {
 172           const bool bit = (1UL << j) & i;
 173           s.push_back(bit ? '1' : '0');
 174         }
 175       set.push_back(s);
 176     }
 177
 178   double chi2 = chi2_hash(set, k);
 179   VERIFY( chi2 < k*1.1 );
 180 }
 181
 182 // Tests chi^2 for a set of words taken from a document written in English.
 183 void
 184 test_document_words()
 185 {
 186   // That file is 187587 single-word lines.  To avoid a timeout, just skip
 187   // this part, which would take up to 95% of the program runtime (with
 188   // SAMPLES == 10000), if we're not supposed to run anywhere that long.
 189 #if SAMPLES >= 100000
 190   bool test __attribute__((unused)) = true;
 191   const std::string f_name = "thirty_years_among_the_dead_preproc.txt";
 192   std::ifstream in(f_name);
 193   VERIFY( in.is_open() );
 194   std::vector<std::string> words;
 195   words.assign(std::istream_iterator<std::string>(in),
 196                std::istream_iterator<std::string>());
 197   VERIFY( words.size() > 100000 );
 198   std::sort(words.begin(), words.end());
 199   auto it = std::unique(words.begin(), words.end());
 200   words.erase(it, words.end());
 201   VERIFY( words.size() > 5000 );
 202
 203   const unsigned long k = words.size() / 20;
 204   double chi2 = chi2_hash(words, k);
 205   VERIFY( chi2 < k*1.1 );
 206 #endif
 207 }
 208
 209 int
 210 main()
 211 {
 212   test_uniform_random();
 213   test_bit_flip_set();
 214   test_numeric_pattern_set();
 215   test_bit_string_set();
 216   test_document_words();
 217   return 0;
 218 }