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chi2_quality.cc: New.

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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
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Matt Austern 2010-09-28 10:35:53 +00:00 • committed by Paolo Carlini
parent 4c11650506
commit 2e9c3ef354
3 changed files with 391 additions and 0 deletions
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5
libstdc++-v3/ChangeLog
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@ -1,3 +1,8 @@
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,

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libstdc++-v3/testsuite/20_util/hash/chi2_quality.cc Normal file
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// { 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;
}

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// { 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;
}