#pragma once #include "Types.h" #include <math.h> #include <vector> #include <map> #include <algorithm> // for std::sort #include <string.h> // for memset #include <stdio.h> // for printf double calcScore ( const int * bins, const int bincount, const int ballcount ); void plot ( double n ); inline double ExpectedCollisions ( double balls, double bins ) { return balls - bins + bins * pow(1 - 1/bins,balls); } double chooseK ( int b, int k ); double chooseUpToK ( int n, int k ); //----------------------------------------------------------------------------- inline uint32_t f3mix ( uint32_t k ) { k ^= k >> 16; k *= 0x85ebca6b; k ^= k >> 13; k *= 0xc2b2ae35; k ^= k >> 16; return k; } //----------------------------------------------------------------------------- // Sort the hash list, count the total number of collisions and return // the first N collisions for further processing template< typename hashtype > int FindCollisions ( std::vector<hashtype> & hashes, HashSet<hashtype> & collisions, int maxCollisions ) { int collcount = 0; std::sort(hashes.begin(),hashes.end()); for(size_t i = 1; i < hashes.size(); i++) { if(hashes[i] == hashes[i-1]) { collcount++; if((int)collisions.size() < maxCollisions) { collisions.insert(hashes[i]); } } } return collcount; } //----------------------------------------------------------------------------- template < class keytype, typename hashtype > int PrintCollisions ( hashfunc<hashtype> hash, std::vector<keytype> & keys ) { int collcount = 0; typedef std::map<hashtype,keytype> htab; htab tab; for(size_t i = 1; i < keys.size(); i++) { keytype & k1 = keys[i]; hashtype h = hash(&k1,sizeof(keytype),0); typename htab::iterator it = tab.find(h); if(it != tab.end()) { keytype & k2 = (*it).second; printf("A: "); printbits(&k1,sizeof(keytype)); printf("B: "); printbits(&k2,sizeof(keytype)); } else { tab.insert( std::make_pair(h,k1) ); } } return collcount; } //---------------------------------------------------------------------------- // Measure the distribution "score" for each possible N-bit span up to 20 bits template< typename hashtype > double TestDistribution ( std::vector<hashtype> & hashes, bool drawDiagram ) { printf("Testing distribution - "); if(drawDiagram) printf("\n"); const int hashbits = sizeof(hashtype) * 8; int maxwidth = 20; // We need at least 5 keys per bin to reliably test distribution biases // down to 1%, so don't bother to test sparser distributions than that while(double(hashes.size()) / double(1 << maxwidth) < 5.0) { maxwidth--; } std::vector<int> bins; bins.resize(1 << maxwidth); double worst = 0; int worstStart = -1; int worstWidth = -1; for(int start = 0; start < hashbits; start++) { int width = maxwidth; int bincount = (1 << width); memset(&bins[0],0,sizeof(int)*bincount); for(size_t j = 0; j < hashes.size(); j++) { hashtype & hash = hashes[j]; uint32_t index = window(&hash,sizeof(hash),start,width); bins[index]++; } // Test the distribution, then fold the bins in half, // repeat until we're down to 256 bins if(drawDiagram) printf("["); while(bincount >= 256) { double n = calcScore(&bins[0],bincount,(int)hashes.size()); if(drawDiagram) plot(n); if(n > worst) { worst = n; worstStart = start; worstWidth = width; } width--; bincount /= 2; if(width < 8) break; for(int i = 0; i < bincount; i++) { bins[i] += bins[i+bincount]; } } if(drawDiagram) printf("]\n"); } double pct = worst * 100.0; printf("Worst bias is the %3d-bit window at bit %3d - %5.3f%%",worstWidth,worstStart,pct); if(pct >= 1.0) printf(" !!!!! "); printf("\n"); return worst; } //---------------------------------------------------------------------------- template < typename hashtype > bool TestHashList ( std::vector<hashtype> & hashes, std::vector<hashtype> & collisions, bool testDist, bool drawDiagram ) { bool result = true; { size_t count = hashes.size(); double expected = (double(count) * double(count-1)) / pow(2.0,double(sizeof(hashtype) * 8 + 1)); printf("Testing collisions - Expected %8.2f, ",expected); double collcount = 0; HashSet<hashtype> collisions; collcount = FindCollisions(hashes,collisions,1000); printf("actual %8.2f (%5.2fx)",collcount, collcount / expected); if(sizeof(hashtype) == sizeof(uint32_t)) { // 2x expected collisions = fail // #TODO - collision failure cutoff needs to be expressed as a standard deviation instead // of a scale factor, otherwise we fail erroneously if there are a small expected number // of collisions if(double(collcount) / double(expected) > 2.0) { printf(" !!!!! "); result = false; } } else { // For all hashes larger than 32 bits, _any_ collisions are a failure. if(collcount > 0) { printf(" !!!!! "); result = false; } } printf("\n"); } //---------- if(testDist) { TestDistribution(hashes,drawDiagram); } return result; } //---------- template < typename hashtype > bool TestHashList ( std::vector<hashtype> & hashes, bool /*testColl*/, bool testDist, bool drawDiagram ) { std::vector<hashtype> collisions; return TestHashList(hashes,collisions,testDist,drawDiagram); } //----------------------------------------------------------------------------- template < class keytype, typename hashtype > bool TestKeyList ( hashfunc<hashtype> hash, std::vector<keytype> & keys, bool testColl, bool testDist, bool drawDiagram ) { int keycount = (int)keys.size(); std::vector<hashtype> hashes; hashes.resize(keycount); printf("Hashing"); for(int i = 0; i < keycount; i++) { if(i % (keycount / 10) == 0) printf("."); keytype & k = keys[i]; hash(&k,sizeof(k),0,&hashes[i]); } printf("\n"); bool result = TestHashList(hashes,testColl,testDist,drawDiagram); printf("\n"); return result; } //----------------------------------------------------------------------------- // Bytepair test - generate 16-bit indices from all possible non-overlapping // 8-bit sections of the hash value, check distribution on all of them. // This is a very good test for catching weak intercorrelations between bits - // much harder to pass than the normal distribution test. However, it doesn't // really model the normal usage of hash functions in hash table lookup, so // I'm not sure it's that useful (and hash functions that fail this test but // pass the normal distribution test still work well in practice) template < typename hashtype > double TestDistributionBytepairs ( std::vector<hashtype> & hashes, bool drawDiagram ) { const int nbytes = sizeof(hashtype); const int hashbits = nbytes * 8; const int nbins = 65536; std::vector<int> bins(nbins,0); double worst = 0; for(int a = 0; a < hashbits; a++) { if(drawDiagram) if((a % 8 == 0) && (a > 0)) printf("\n"); if(drawDiagram) printf("["); for(int b = 0; b < hashbits; b++) { if(drawDiagram) if((b % 8 == 0) && (b > 0)) printf(" "); bins.clear(); bins.resize(nbins,0); for(size_t i = 0; i < hashes.size(); i++) { hashtype & hash = hashes[i]; uint32_t pa = window(&hash,sizeof(hash),a,8); uint32_t pb = window(&hash,sizeof(hash),b,8); bins[pa | (pb << 8)]++; } double s = calcScore(bins,bins.size(),hashes.size()); if(drawDiagram) plot(s); if(s > worst) { worst = s; } } if(drawDiagram) printf("]\n"); } return worst; } //----------------------------------------------------------------------------- // Simplified test - only check 64k distributions, and only on byte boundaries template < typename hashtype > void TestDistributionFast ( std::vector<hashtype> & hashes, double & dworst, double & davg ) { const int hashbits = sizeof(hashtype) * 8; const int nbins = 65536; std::vector<int> bins(nbins,0); dworst = -1.0e90; davg = 0; for(int start = 0; start < hashbits; start += 8) { bins.clear(); bins.resize(nbins,0); for(size_t j = 0; j < hashes.size(); j++) { hashtype & hash = hashes[j]; uint32_t index = window(&hash,sizeof(hash),start,16); bins[index]++; } double n = calcScore(&bins.front(),(int)bins.size(),(int)hashes.size()); davg += n; if(n > dworst) dworst = n; } davg /= double(hashbits/8); } //-----------------------------------------------------------------------------