chi2_quality.cc: New.

2010-09-28  Matt Austern  <austern@google.com>

	* testsuite/20_util/hash/chi2_quality.cc: New.
	* testsuite/20_util/hash/quality.cc: Likewise.

From-SVN: r164682

libstdc++-v3/ChangeLog

+2010-09-28  Matt Austern  <austern@google.com>
+
+	* testsuite/20_util/hash/chi2_quality.cc: New.
+	* testsuite/20_util/hash/quality.cc: Likewise.
+
 2010-09-27  Paolo Carlini  <paolo.carlini@oracle.com>
 
 	* include/bits/allocator.h (allocator_arg_t, allocator_arg,

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

+// { dg-options "-std=gnu++0x" }
+
+// Copyright (C) 2010 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>
+
+// Use smaller statistics when running on simulators, so it takes less time.
+// { dg-options "-DSAMPLES=10000" { target simulator } }
+#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 (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 (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 (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()
+{
+  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 );
+}
+
+int
+main()
+{
+  test_uniform_random();
+  test_bit_flip_set();
+  test_numeric_pattern_set();
+  test_bit_string_set();
+  test_document_words();
+  return 0;
+}

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

+// { dg-options "-std=gnu++0x" }
+
+// Copyright (C) 2010 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/>.
+
+#include <cstdlib>
+#include <unordered_set>
+#include <string>
+#include <functional>
+#include <vector>
+#include <testsuite_hooks.h>
+
+using namespace std;
+
+// { dg-options "-DNTESTS=1 -DNSTRINGS=100 -DSTRSIZE=21" { target simulator } }
+#ifndef NTESTS
+#define NTESTS 5
+#endif
+#ifndef NSTRINGS
+#define NSTRINGS 200
+#endif
+#ifndef STRSIZE
+#define STRSIZE 42
+#endif
+
+const int num_quality_tests = NTESTS;
+const int num_strings_for_quality_tests = NSTRINGS;
+const int string_size = STRSIZE;
+
+vector<string>
+random_strings(int n, int len)
+{
+  string s(len, '\0');
+  unordered_set<string> result_set;
+  while (result_set.size() < n)
+    {
+      result_set.insert(s);
+      unsigned int tmp = rand();
+      tmp %= len * 256;
+      s[tmp / 256] = tmp % 256;
+    }
+  return vector<string>(result_set.begin(), result_set.end());
+}
+
+double
+score_from_varying_position(string s, int index)
+{
+  bool test __attribute__((unused)) = true;
+  int bits_in_hash_code = sizeof(size_t) * 8;
+
+  // We'll iterate through all 256 vals for s[index], leaving the rest
+  // of s fixed.  Then, for example, out of the 128 times that
+  // s[index] has its 3rd bit equal to 0 we would like roughly half 1s
+  // and half 0s in bit 9 of the hash codes.
+  //
+  // Bookkeeping: Conceptually we want a 3D array of ints.  We want to
+  // count the number of times each output position (of which there are
+  // bits_in_hash_code) is 1 for each bit position within s[index] (of 
+  // which there are 8) and value of that bit (of which there are 2).
+  const int jj = 2;
+  const int kk = jj * bits_in_hash_code;
+  const int array_size = 8 * kk;
+  vector<int> ones(array_size, 0);
+
+  for (int i = 0; i < 256; i++)
+    {
+      s[index] = i;
+      size_t h = hash<string>()(s);
+      for (int j = 0; h != 0; j++, h >>= 1)
+        {
+          if (h & 1)
+            {
+              for (int k = 0; k < 8; k++)
+                ++ones[k * kk + j * jj + ((i >> k) & 1)];
+            }
+        }
+    }
+
+  // At most, the innermost statement in the above loop nest can
+  // execute 256 * bits_in_hash_code * 8 times.  If the hash is good,
+  // it'll execute about half that many times, with a pretty even
+  // spread across the elements of ones[].
+  VERIFY( 256 * bits_in_hash_code * 8 / array_size == 128 );
+  int max_ones_possible = 128;
+  int good = 0, bad = 0;
+  for (int bit = 0; bit <= 1; bit++)
+    {
+      for (int j = 0; j < bits_in_hash_code; j++)
+        {
+          for (int bitpos = 0; bitpos < 8; bitpos++)
+            {
+              int z = ones[bitpos * kk + j * jj + bit];
+              if (z <= max_ones_possible / 6
+		  || z >= max_ones_possible * 5 / 6)
+                {
+                  // The hash function screwed up, or was just unlucky,
+                  // as 128 flips of a perfect coin occasionally yield
+                  // far from 64 heads.
+                  bad++;
+                }
+              else
+                good++;
+            }
+        }
+    }
+  return good / (double)(good + bad);
+}
+
+double
+score_from_varying_position(const vector<string>& v, int index)
+{
+  double score = 0;
+  for (int i = 0; i < v.size(); i++)
+    score += score_from_varying_position(v[i], index);
+  return score / v.size();
+}
+
+double
+quality_test(int num_strings, int string_size)
+{
+  // Construct random strings.
+  vector<string> v = random_strings(num_strings, string_size);
+  double sum_of_scores = 0;
+  for (int i = 0; i < string_size; i++)
+    sum_of_scores += score_from_varying_position(v, i);
+
+  // A good hash function should have a score very close to 1, and a bad
+  // hash function will have a score close to 0.
+  return sum_of_scores / string_size;
+}
+
+void
+quality_test()
+{
+  bool test __attribute__((unused)) = true;
+  srand(137);
+  double sum_of_scores = 0;
+  for (int i = 0; i < num_quality_tests; i++)
+    {
+      double score = quality_test(num_strings_for_quality_tests,
+				  string_size);
+      sum_of_scores += score;
+      VERIFY( score > 0.99 );
+    }
+
+  if (num_quality_tests > 1)
+    {
+      double mean_quality = sum_of_scores / num_quality_tests;
+      VERIFY( mean_quality > 0.9999 );
+    }
+}
+
+int
+main()
+{
+  quality_test();
+  return 0;
+}