fasthash-sys-fork 0.4.2

//-----------------------------------------------------------------------------
// Keyset tests generate various sorts of difficult-to-hash keysets and compare
// the distribution and collision frequency of the hash results against an
// ideal random distribution

// The sanity checks are also in this cpp/h

#pragma once

#include "Types.h"
#include "Stats.h"
#include "Random.h"   // for rand_p
#include "Hashes.h"

#include <stdint.h>
#include <inttypes.h>
#include <assert.h>

#include <algorithm>  // for std::swap
#include <string>
#if NCPU > 1 // disable with -DNCPU=0 or 1
#include <thread>
#include <chrono>
#endif

#undef MAX
#define MAX(x,  y)   (((x) > (y)) ? (x) : (y))
//-----------------------------------------------------------------------------
// Sanity tests

bool VerificationTest   ( HashInfo *info, bool verbose );
bool SanityTest         ( pfHash hash, const int hashbits );
void AppendedZeroesTest ( pfHash hash, const int hashbits );

static void printKey(const void* key, size_t len)
{
    const unsigned char* const p = (const unsigned char*)key;
    size_t s;
    printf("\n0x");
    for (s=0; s<len; s++) printf("%02X", p[s]);
    printf("\n  ");
    for (s=0; s<len; s+=8) printf("%-16zu", s);
}

//-----------------------------------------------------------------------------
// Keyset 'Prng'


template< typename hashtype >
void Prn_gen (int nbRn, pfHash hash, std::vector<hashtype> & hashes )
{
  assert(nbRn > 0);

  printf("Generating %i random numbers : \n", nbRn);

  hashtype hcopy;
  memset(&hcopy, 0, sizeof(hcopy));

  // a generated random number becomes the input for the next one
  for (int i=0; i< nbRn; i++) {
      hashtype h;
      hash(&hcopy, sizeof(hcopy), 0, &h);
      hashes.push_back(h);
      memcpy(&hcopy, &h, sizeof(h));
  }
}


template< typename hashtype >
bool PrngTest ( hashfunc<hashtype> hash,
                bool testColl, bool testDist, bool drawDiagram )
{

  if (sizeof(hashtype) < 8) {
      printf("The PRNG test is designed for hashes >= 64-bit \n");
      return true;
  }

  //----------

  std::vector<hashtype> hashes;
  Prn_gen(32 << 20, hash, hashes);

  //----------
  bool result = TestHashList(hashes,drawDiagram,testColl,testDist);

  return result;
}

//-----------------------------------------------------------------------------
// Find bad seeds, and test against the known secrets/bad seeds.

// A more thourough test for a known secret. vary keys and key len
template< typename hashtype >
bool TestSecret ( const HashInfo* info, const uint64_t secret ) {
  bool result = true;
  static hashtype zero;
  pfHash hash = info->hash;
  uint8_t key[128];
  printf("0x%" PRIx64 " ", secret);
  Hash_Seed_init (hash, secret);
  for (int len : std::vector<int> {1,2,4,8,12,16,32,64,128}) {
    std::vector<hashtype> hashes;
    for (int c : std::vector<int> {0,32,'0',127,128,255}) {
      hashtype h;
      memset(&key, c, len);
      hash(key, len, secret, &h);
      if (h == 0 && c == 0) {
        printf("Broken seed 0x%" PRIx64 " => 0 with key[%d] of all %d bytes confirmed => hash 0\n",
               secret, len, c);
        hashes.push_back(h);
        result = false;
      }
      else
        hashes.push_back(h);
    }
    if (!TestHashList(hashes, false, true, false, false, false, false)) {
      printf(" Bad seed 0x%" PRIx64 " for len %d confirmed ", secret, len);
#if !defined __clang__ && !defined _MSC_VER
      printf("=> hashes: ");
      for (hashtype x : hashes) printf ("%lx ", x);
#endif
      printf ("\n");
      TestHashList(hashes, false);
      result = false;
    }
  }
  return result;
}

// Process part of a 2^32 range, split into NCPU threads
template< typename hashtype >
void TestSecretRangeThread ( const HashInfo* info, const uint64_t hi,
                             const uint32_t start, const uint32_t len, bool &result )
{
  pfHash hash = info->hash;
  std::vector<hashtype> hashes;
  int fails = 0;
  hashes.resize(4);
  result = true;
  printf("at %lx ", hi | start);
  size_t end = start + len;
  for (size_t y=start; y < end; y++) {
    static hashtype zero;
    uint64_t seed = hi | y;
    if ((seed & UINT64_C(0x1ffffff)) == UINT64_C(0x1ffffff))
      printf ("%" PRIx64 " ", seed);
    hashes.clear();
    Hash_Seed_init (hash, seed);
    for (int x : std::vector<int> {0,32,127,255}) {
      hashtype h;
      uint8_t key[64]; // for crc32_pclmul, otherwie we would need only 16 byte
      memset(&key, x, sizeof(key));
      hash(key, 16, seed, &h);
      if (h == 0 && x == 0) {
        printf("Broken seed 0x%" PRIx64 " => 0 with key[16] of all %d bytes\n", seed, x);
        hashes.push_back(h);
        fails++;
        result = false;
      }
      else {
        hashes.push_back(h);
      }
    }
    if (!TestHashList(hashes, false, true, false, false, false, false)) {
      fails++;
      printf("Bad seed 0x%" PRIx64 "\n", seed);
      if (fails < 32) // don't print too many lines
        TestHashList(hashes, false);
      result = false;
    }
    if (fails > 300) {
      fprintf(stderr, "Too many bad seeds, aborting\n");
      exit(1);
    }
  }
  fflush(NULL);
  //printf("\n");
  return;
}

// Test the full 2^32 range [hi + 0, hi + 0xffffffff], the hi part
template< typename hashtype >
bool TestSecret32 ( const HashInfo* info, const uint64_t hi ) {
  bool result = true;
#if NCPU > 1
  // split into NCPU threads
  const uint64_t len = 0x100000000UL / NCPU;
  const uint32_t len32 = (const uint32_t)(len & 0xffffffff);
  static std::thread t[NCPU];
  bool *results = (bool*)calloc (NCPU, sizeof(bool));
  printf("%d threads starting...\n", NCPU);
  for (int i=0; i < NCPU; i++) {
    const uint32_t start = i * len;
    t[i] = std::thread {TestSecretRangeThread<hashtype>, info, hi, start, len32, std::ref(results[i])};
    // pin it? moves around a lot. but the result is fair
  }
  std::this_thread::sleep_for(std::chrono::seconds(30));
  for (int i=0; i < NCPU; i++) {
    t[i].join();
  }
  printf("All %d threads ended\n", NCPU);
  for (int i=0; i < NCPU; i++) {
    result &= results[i];
  }
  free(results);
#else
  TestSecretRangeThread<hashtype>(info, hi, 0x0, 0xffffffff, result);
  printf("\n");
#endif
  return result;
}

template< typename hashtype >
bool BadSeedsTest ( HashInfo* info, bool testAll ) {
  bool result = true;
  bool have_lower = false;
#ifdef HAVE_INT64
  const std::vector<uint64_t> secrets = info->secrets;
#else
  const std::vector<size_t> secrets = info->secrets;
#endif
#if !defined __arm__ && !defined __aarch64__
  printf("Testing %lu internal secrets:\n", (unsigned long)secrets.size());
#endif
  for (auto secret : secrets) {
    result &= TestSecret<hashtype>(info, secret);
    if (sizeof(hashtype) == 8 && secret <= 0xffffffff) { // check the upper hi mask also
      uint64_t s = secret << 32;
      have_lower = true;
      result &= TestSecret<hashtype>(info, s);
    }
  }
  if (!secrets.size())
    result &= TestSecret<hashtype>(info, 0x0);
  if (getenv("SEED")) {
    const char *s = getenv("SEED");
    size_t seed = strtol(s, NULL, 0);
    printf("\nTesting SEED=0x%" PRIx64 " ", seed);
    //if (*s && s[1] && *s == '0' && s[1] == 'x')
    //  seed = strtol(&s[2], NULL, 16);
    if (seed || secrets.size())
      result &= TestSecret<hashtype>(info, seed);
  }
  if (result)
    printf("PASS\n");
  if (testAll == false || info->quality == SKIP)
    return result;

  // many days with >= 64 bit hashes
  printf("Testing the first 0xffffffff seeds ...\n");
  result &= TestSecret32<hashtype>(info, UINT64_C(0x0));
#ifdef HAVE_INT64
  if (sizeof(hashtype) > 4) { // and the upper half 32bit range
    if (have_lower) {
      for (auto secret : secrets) {
        if (secret <= 0xffffffff) {
          uint64_t s = secret;
          s = s << 32;
          printf("Suspect the 0x%" PRIx64 " seeds ...\n", s);
          result &= TestSecret32<hashtype>(info, s);
        }
      }
    }
    printf("And the last 0xffffffff00000000 seeds ...\n");
    result &= TestSecret32<hashtype>(info, UINT64_C(0xffffffff00000000));
  }
#endif
  if (result)
    printf("PASS\n");
  else
    printf("FAIL\nEnsure to add these bad seeds to the list of secrets in main.cpp\n");
  fflush(NULL);
  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Perlin Noise' - X,Y coordinates on input & seed


template< typename hashtype >
void PerlinNoiseTest (int Xbits, int Ybits,
                      int inputLen, int step,
                      pfHash hash, std::vector<hashtype> & hashes )
{
  assert(0 < Ybits && Ybits < 31);
  assert(0 < Xbits && Xbits < 31);
  assert(inputLen*8 > Xbits);  // enough space to run the test

  int const xMax = (1 << Xbits);
  int const yMax = (1 << Ybits);

  assert(Xbits + Ybits < 31);

#define INPUT_LEN_MAX 256
  assert(inputLen <= INPUT_LEN_MAX);
  char key[INPUT_LEN_MAX] = {0};

  printf("Testing %i coordinates (L%i) : \n", xMax * yMax, inputLen);

  for(uint64_t x = 0; x < xMax; x++) {
      memcpy(key, &x, inputLen);  // Note : only works with Little Endian
      for (size_t y=0; y < yMax; y++) {
          hashtype h;
          Hash_Seed_init (hash, y);
          hash(key, inputLen, y, &h);
          hashes.push_back(h);
      }
  }
}


template< typename hashtype >
bool PerlinNoise ( hashfunc<hashtype> hash, int inputLen,
                   bool testColl, bool testDist, bool drawDiagram )
{
  //----------

  std::vector<hashtype> hashes;

  PerlinNoiseTest(12, 12, inputLen, 1, hash, hashes);

  //----------

  bool result = TestHashList(hashes,drawDiagram,testColl,testDist);
  printf("\n");

  return result;
}


//-----------------------------------------------------------------------------
// Keyset 'Combination' - all possible combinations of input blocks

template< typename hashtype, class blocktype >
void CombinationKeygenRecurse ( blocktype * key, int len, int maxlen,
                                blocktype * blocks, int blockcount,
                                pfHash hash, std::vector<hashtype> & hashes )
{
  if(len == maxlen) return;  // end recursion

  for(int i = 0; i < blockcount; i++)
  {
    key[len] = blocks[i];

    hashtype h;
    hash(key, (len+1) * sizeof(blocktype), 0, &h);
    hashes.push_back(h);

    CombinationKeygenRecurse(key,len+1,maxlen,blocks,blockcount,hash,hashes);
  }
}

typedef struct { char c[16]; } block16;
typedef struct { char c[32]; } block32;
typedef struct { char c[64]; } block64;
typedef struct { char c[128]; } block128;

template< typename hashtype, typename blocktype >
bool CombinationKeyTest ( hashfunc<hashtype> hash, int maxlen, blocktype* blocks,
                          int blockcount, bool testColl, bool testDist, bool drawDiagram )
{
  printf("Keyset 'Combination' - up to %d blocks from a set of %d - ",maxlen,blockcount);

  //----------

  std::vector<hashtype> hashes;

  blocktype * key = new blocktype[maxlen];

  CombinationKeygenRecurse(key,0,maxlen,blocks,blockcount,hash,hashes);

  delete [] key;

  printf("%d keys\n",(int)hashes.size());

  //----------

  bool result = TestHashList(hashes,drawDiagram,testColl,testDist);
  printf("\n");

  return result;
}



//----------------------------------------------------------------------------
// Keyset 'Permutation' - given a set of 32-bit blocks, generate keys
// consisting of all possible permutations of those blocks

template< typename hashtype >
void PermutationKeygenRecurse ( pfHash hash, uint32_t * blocks, int blockcount, int k, std::vector<hashtype> & hashes )
{
  if(k == blockcount-1)
  {
    hashtype h;

    hash(blocks,blockcount * sizeof(uint32_t),0,&h);

    hashes.push_back(h);

    return;
  }

  for(int i = k; i < blockcount; i++)
  {
    std::swap(blocks[k],blocks[i]);

    PermutationKeygenRecurse(hash,blocks,blockcount,k+1,hashes);

    std::swap(blocks[k],blocks[i]);
  }
}

template< typename hashtype >
bool PermutationKeyTest ( hashfunc<hashtype> hash, uint32_t * blocks, int blockcount, bool testColl, bool testDist, bool drawDiagram )
{
  printf("Keyset 'Permutation' - %d blocks - ",blockcount);

  //----------

  std::vector<hashtype> hashes;

  PermutationKeygenRecurse<hashtype>(hash,blocks,blockcount,0,hashes);

  printf("%d keys\n",(int)hashes.size());

  //----------
  bool result = TestHashList<hashtype>(hashes,drawDiagram,testColl,testDist);
  printf("\n");

  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Sparse' - generate all possible N-bit keys with up to K bits set

static void printSparseKey(const void* buffer, size_t size)
{
    const char* const p = (const char*)buffer;
    size_t s;
    printf("bits:");
    for (s=0; s<size; s++) {
        int b;
        for (b=0; b<8; b++) {
            if ((p[s] >> b) & 1)
                printf(" %2u.%2i,", (unsigned)s, b);
        }
    }
}

template < typename keytype, typename hashtype >
void SparseKeygenRecurse ( pfHash hash, int start, int bitsleft, bool inclusive, keytype & k, std::vector<hashtype> & hashes )
{
  const int nbytes = sizeof(keytype);
  const int nbits = nbytes * 8;

  hashtype h;

  for(int i = start; i < nbits; i++)
  {
    flipbit(&k, nbytes, i);

    if(inclusive || (bitsleft == 1))
    {
      hash(&k, sizeof(keytype), 0, &h);
      hashes.push_back(h);
    }

    if(bitsleft > 1)
    {
      SparseKeygenRecurse(hash, i+1, bitsleft-1, inclusive, k, hashes);
    }

    flipbit(&k, nbytes, i);
  }
}

//----------

template < int keybits, typename hashtype >
bool SparseKeyTest ( hashfunc<hashtype> hash, const int setbits, bool inclusive,
                     bool testColl, bool testDist, bool drawDiagram )
{
  printf("Keyset 'Sparse' - %d-bit keys with %s %d bits set - ",keybits,
         inclusive ? "up to" : "exactly", setbits);

  typedef Blob<keybits> keytype;

  std::vector<hashtype> hashes;

  keytype k;
  memset(&k,0,sizeof(k));

  if(inclusive)
  {
    hashes.resize(1);
    hash(&k,sizeof(keytype),0,&hashes[0]);
  }

  SparseKeygenRecurse(hash,0,setbits,inclusive,k,hashes);

  printf("%d keys\n",(int)hashes.size());

  bool result = TestHashList<hashtype>(hashes,drawDiagram,testColl,testDist);
  printf("\n");

  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Window' - for all possible N-bit windows of a K-bit key, generate
// all possible keys with bits set in that window

template < typename keytype, typename hashtype >
bool WindowedKeyTest ( hashfunc<hashtype> hash, int windowbits,
                       bool testCollision, bool testDistribution, bool drawDiagram )
{
  const int keybits = sizeof(keytype) * 8;
  // calc keycount to expect min. 0.5 collisions: EstimateNbCollisions, except for 64++bit.
  // there limit to 2^25 = 33554432 keys
  int keycount = 1 << windowbits;
  while (EstimateNbCollisions(keycount, sizeof(hashtype) * 8) < 0.5 && windowbits < 25) {
    if ((int)log2(2.0 * keycount) < 0) // overflow
      break;
    keycount *= 2;
    windowbits = (int)log2(1.0 * keycount);
    //printf (" enlarge windowbits to %d (%d keys)\n", windowbits, keycount);
    //fflush (NULL);
  }

  std::vector<hashtype> hashes;
  hashes.resize(keycount);

  bool result = true;
  int testcount = keybits;

  printf("Keyset 'Window' - %3d-bit key, %3d-bit window - %d tests, %d keys per test\n",
         keybits,windowbits,testcount,keycount);

  for(int j = 0; j <= testcount; j++)
  {
    int minbit = j;
    keytype key;

    for(int i = 0; i < keycount; i++)
    {
      key = i;
      //key = key << minbit;
      lrot(&key,sizeof(keytype),minbit);
      hash(&key,sizeof(keytype),0,&hashes[i]);
    }

    printf("Window at %3d - ",j);
    result &= TestHashList(hashes, drawDiagram, testCollision, testDistribution,
                           /* do not test high/low bits (to not clobber the screen) */
                           false, false);
    //printf("\n");
  }

  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Cyclic' - generate keys that consist solely of N repetitions of M
// bytes.

// (This keyset type is designed to make MurmurHash2 fail)

template < typename hashtype >
bool CyclicKeyTest ( pfHash hash, int cycleLen, int cycleReps, const int keycount, bool drawDiagram )
{
  printf("Keyset 'Cyclic' - %d cycles of %d bytes - %d keys\n",cycleReps,cycleLen,keycount);

  Rand r(483723);

  std::vector<hashtype> hashes;
  hashes.resize(keycount);

  int keyLen = cycleLen * cycleReps;

  uint8_t * cycle = new uint8_t[cycleLen + 16];
  uint8_t * key = new uint8_t[keyLen];

  //----------

  for(int i = 0; i < keycount; i++)
  {
    r.rand_p(cycle,cycleLen);

    *(uint32_t*)cycle = f3mix(i ^ 0x746a94f1);

    for(int j = 0; j < keyLen; j++)
    {
      key[j] = cycle[j % cycleLen];
    }

    hash(key,keyLen,0,&hashes[i]);
  }

  //----------

  bool result = TestHashList(hashes,drawDiagram);
  printf("\n");

  delete [] key;
  delete [] cycle;

  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'TwoBytes' - generate all keys up to length N with two non-zero bytes

void TwoBytesKeygen ( int maxlen, KeyCallback & c );

template < typename hashtype >
bool TwoBytesTest2 ( pfHash hash, int maxlen, bool drawDiagram )
{
  std::vector<hashtype> hashes;

  HashCallback<hashtype> c(hash,hashes);

  TwoBytesKeygen(maxlen,c);

  bool result = TestHashList(hashes,drawDiagram);
  printf("\n");

  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Text' - generate all keys of the form "prefix"+"core"+"suffix",
// where "core" consists of all possible combinations of the given character
// set of length N.

template < typename hashtype >
bool TextKeyTest ( hashfunc<hashtype> hash, const char * prefix, const char * coreset, const int corelen, const char * suffix, bool drawDiagram )
{
  const int prefixlen = (int)strlen(prefix);
  const int suffixlen = (int)strlen(suffix);
  const int corecount = (int)strlen(coreset);

  const int keybytes = prefixlen + corelen + suffixlen;
  long keycount = (long)pow(double(corecount),double(corelen));
  if (keycount > INT32_MAX / 8)
    keycount = INT32_MAX / 8;

  printf("Keyset 'Text' - keys of form \"%s",prefix);
  for(int i = 0; i < corelen; i++) printf("X");
  printf("%s\" - %ld keys\n",suffix,keycount);

  uint8_t * key = new uint8_t[std::min(keybytes+1, 64)];

  key[keybytes] = 0;

  memcpy(key,prefix,prefixlen);
  memcpy(key+prefixlen+corelen,suffix,suffixlen);

  //----------

  std::vector<hashtype> hashes;
  hashes.resize(keycount);

  for(int i = 0; i < (int)keycount; i++)
  {
    int t = i;

    for(int j = 0; j < corelen; j++)
    {
      key[prefixlen+j] = coreset[t % corecount]; t /= corecount;
    }

    hash(key,keybytes,0,&hashes[i]);
  }

  //----------
  bool result = TestHashList(hashes,drawDiagram);
  printf("\n");

  delete [] key;
  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Words' - pick random chars from coreset (alnum or password chars)

template < typename hashtype >
bool WordsKeyTest ( hashfunc<hashtype> hash, const long keycount,
                    const int minlen, const int maxlen,
                    const char * coreset,
                    const char* name, bool drawDiagram )
{
  const int corecount = (int)strlen(coreset);
  printf("Keyset 'Words' - %ld random keys of len %d-%d from %s charset\n", keycount, minlen, maxlen, name);
  assert (minlen >= 0);
  assert (maxlen > minlen);

  HashSet<std::string> words; // need to be unique, otherwise we report collisions
  std::vector<hashtype> hashes;
  hashes.resize(keycount);
  Rand r(483723);

  char* key = new char[std::min(maxlen+1, 64)];
  std::string key_str;

  for(long i = 0; i < keycount; i++)
  {
    const int len = minlen + (r.rand_u32() % (maxlen - minlen));
    key[len] = 0;
    for(int j = 0; j < len; j++)
    {
      key[j] = coreset[r.rand_u32() % corecount];
    }
    key_str = key;
    if (words.count(key_str) > 0) { // not unique
      i--;
      continue;
    }
    words.insert(key_str);

    hash(key,len,0,&hashes[i]);

#if 0 && defined DEBUG
    uint64_t h;
    memcpy(&h, &hashes[i], MAX(sizeof(hashtype),8));
    printf("%d %s %lx\n", i, (char*)key, h);
#endif
  }
  delete [] key;

  //----------
  bool result = TestHashList(hashes,drawDiagram);
  printf("\n");

  return result;
}

template < typename hashtype >
bool WordsStringTest ( hashfunc<hashtype> hash, std::vector<std::string> & words,
                       bool drawDiagram )
{
  long wordscount = words.size();
  printf("Keyset 'Words' - %ld dict words\n", wordscount);

  std::vector<hashtype> hashes;
  hashes.resize(wordscount);
  Rand r(483723);
  HashSet<std::string> wordset; // need to be unique, otherwise we report collisions

  for(int i = 0; i < (int)wordscount; i++)
  {
    if (wordset.count(words[i]) > 0) { // not unique
      i--;
      continue;
    }
    if (need_minlen64_align16(hash) && words[i].capacity() < 64)
      words[i].resize(64);
    wordset.insert(words[i]);
    const int len = words[i].length();
    const char *key = words[i].c_str();
    hash(key, len, 0, &hashes[i]);
  }

  //----------
  bool result = TestHashList(hashes,drawDiagram);
  printf("\n");

  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Zeroes' - keys consisting of all zeroes, differing only in length

// We reuse one block of empty bytes, otherwise the RAM cost is enormous.

template < typename hashtype >
bool ZeroKeyTest ( pfHash hash, bool drawDiagram )
{
  int keycount = 200*1024;

  printf("Keyset 'Zeroes' - %d keys\n",keycount);

  unsigned char * nullblock = new unsigned char[keycount];
  memset(nullblock,0,keycount);

  //----------

  std::vector<hashtype> hashes;

  hashes.resize(keycount);

  for(int i = 0; i < keycount; i++)
  {
    hash(nullblock,i,0,&hashes[i]);
  }

  bool result = TestHashList(hashes,drawDiagram);
  printf("\n");

  delete [] nullblock;

  return result;
}

//-----------------------------------------------------------------------------
// Keyset 'Seed' - hash "the quick brown fox..." using different seeds

template < typename hashtype >
bool SeedTest ( pfHash hash, int keycount, bool drawDiagram )
{
  printf("Keyset 'Seed' - %d keys\n",keycount);

  const char text[64] = "The quick brown fox jumps over the lazy dog";
  const int len = (int)strlen(text);

  //----------

  std::vector<hashtype> hashes;

  hashes.resize(keycount);

  for(int i = 0; i < keycount; i++)
  {
    Hash_Seed_init (hash, i);
    hash(text,len,i,&hashes[i]);
  }

  bool result = TestHashList(hashes,drawDiagram);
  printf("\n");

  return result;
}

//-----------------------------------------------------------------------------

void ReportCollisions ( pfHash hash );