text: // Copyright (c) 2012-2016 The Vritzcoin Core developers
  // Distributed under the MIT software license, see the accompanying
  // file COPYING or http://www.opensource.org/licenses/mit-license.php.
  
  #include <bloom.h>
  
  #include <primitives/transaction.h>
  #include <hash.h>
  #include <script/script.h>
  #include <script/standard.h>
  #include <random.h>
  #include <streams.h>
  
  #include <math.h>
  #include <stdlib.h>
  
  
  #define LN2SQUARED 0.4804530139182014246671025263266649717305529515945455
  #define LN2 0.6931471805599453094172321214581765680755001343602552
  
  CBloomFilter::CBloomFilter(const unsigned int nElements, const double nFPRate, const unsigned int nTweakIn, unsigned char nFlagsIn) :
      /**
       * The ideal size for a bloom filter with a given number of elements and false positive rate is:
       * - nElements * log(fp rate) / ln(2)^2
       * We ignore filter parameters which will create a bloom filter larger than the protocol limits
       */
      vData(std::min((unsigned int)(-1  / LN2SQUARED * nElements * log(nFPRate)), MAX_BLOOM_FILTER_SIZE * 8) / 8),
      /**
       * The ideal number of hash functions is filter size * ln(2) / number of elements
       * Again, we ignore filter parameters which will create a bloom filter with more hash functions than the protocol limits
       * See https://en.wikipedia.org/wiki/Bloom_filter for an explanation of these formulas
       */
      isFull(false),
      isEmpty(true),
      nHashFuncs(std::min((unsigned int)(vData.size() * 8 / nElements * LN2), MAX_HASH_FUNCS)),
      nTweak(nTweakIn),
      nFlags(nFlagsIn)
  {
  }
  
  // Private constructor used by CRollingBloomFilter
  CBloomFilter::CBloomFilter(const unsigned int nElements, const double nFPRate, const unsigned int nTweakIn) :
      vData((unsigned int)(-1  / LN2SQUARED * nElements * log(nFPRate)) / 8),
      isFull(false),
      isEmpty(true),
      nHashFuncs((unsigned int)(vData.size() * 8 / nElements * LN2)),
      nTweak(nTweakIn),
      nFlags(BLOOM_UPDATE_NONE)
  {
  }
  
  inline unsigned int CBloomFilter::Hash(unsigned int nHashNum, const std::vector<unsigned char>& vDataToHash) const
  {
      // 0xFBA4C795 chosen as it guarantees a reasonable bit difference between nHashNum values.
      return MurmurHash3(nHashNum * 0xFBA4C795 + nTweak, vDataToHash) % (vData.size() * 8);
  }
  
  void CBloomFilter::insert(const std::vector<unsigned char>& vKey)
  {
      if (isFull)
          return;
      for (unsigned int i = 0; i < nHashFuncs; i++)
      {
          unsigned int nIndex = Hash(i, vKey);
          // Sets bit nIndex of vData
          vData[nIndex >> 3] |= (1 << (7 & nIndex));
      }
      isEmpty = false;
  }
  
  void CBloomFilter::insert(const COutPoint& outpoint)
  {
      CDataStream stream(SER_NETWORK, PROTOCOL_VERSION);
      stream << outpoint;
      std::vector<unsigned char> data(stream.begin(), stream.end());
      insert(data);
  }
  
  void CBloomFilter::insert(const uint256& hash)
  {
      std::vector<unsigned char> data(hash.begin(), hash.end());
      insert(data);
  }
  
  bool CBloomFilter::contains(const std::vector<unsigned char>& vKey) const
  {
      if (isFull)
          return true;
      if (isEmpty)
          return false;
      for (unsigned int i = 0; i < nHashFuncs; i++)
      {
          unsigned int nIndex = Hash(i, vKey);
          // Checks bit nIndex of vData
          if (!(vData[nIndex >> 3] & (1 << (7 & nIndex))))
              return false;
      }
      return true;
  }
  
  bool CBloomFilter::contains(const COutPoint& outpoint) const
  {
      CDataStream stream(SER_NETWORK, PROTOCOL_VERSION);
      stream << outpoint;
      std::vector<unsigned char> data(stream.begin(), stream.end());
      return contains(data);
  }
  
  bool CBloomFilter::contains(const uint256& hash) const
  {
      std::vector<unsigned char> data(hash.begin(), hash.end());
      return contains(data);
  }
  
  void CBloomFilter::clear()
  {
      vData.assign(vData.size(),0);
      isFull = false;
      isEmpty = true;
  }
  
  void CBloomFilter::reset(const unsigned int nNewTweak)
  {
      clear();
      nTweak = nNewTweak;
  }
  
  bool CBloomFilter::IsWithinSizeConstraints() const
  {
      return vData.size() <= MAX_BLOOM_FILTER_SIZE && nHashFuncs <= MAX_HASH_FUNCS;
  }
  
  bool CBloomFilter::IsRelevantAndUpdate(const CTransaction& tx)
  {
      bool fFound = false;
      // Match if the filter contains the hash of tx
      //  for finding tx when they appear in a block
      if (isFull)
          return true;
      if (isEmpty)
          return false;
      const uint256& hash = tx.GetHash();
      if (contains(hash))
          fFound = true;
  
      for (unsigned int i = 0; i < tx.vout.size(); i++)
      {
          const CTxOut& txout = tx.vout[i];
          // Match if the filter contains any arbitrary script data element in any scriptPubKey in tx
          // If this matches, also add the specific output that was matched.
          // This means clients don't have to update the filter themselves when a new relevant tx 
          // is discovered in order to find spending transactions, which avoids round-tripping and race conditions.
          CScript::const_iterator pc = txout.scriptPubKey.begin();
          std::vector<unsigned char> data;
          while (pc < txout.scriptPubKey.end())
          {
              opcodetype opcode;
              if (!txout.scriptPubKey.GetOp(pc, opcode, data))
                  break;
              if (data.size() != 0 && contains(data))
              {
                  fFound = true;
                  if ((nFlags & BLOOM_UPDATE_MASK) == BLOOM_UPDATE_ALL)
                      insert(COutPoint(hash, i));
                  else if ((nFlags & BLOOM_UPDATE_MASK) == BLOOM_UPDATE_P2PUBKEY_ONLY)
                  {
                      txnouttype type;
                      std::vector<std::vector<unsigned char> > vSolutions;
                      if (Solver(txout.scriptPubKey, type, vSolutions) &&
                              (type == TX_PUBKEY || type == TX_MULTISIG))
                          insert(COutPoint(hash, i));
                  }
                  break;
              }
          }
      }
  
      if (fFound)
          return true;
  
      for (const CTxIn& txin : tx.vin)
      {
          // Match if the filter contains an outpoint tx spends
          if (contains(txin.prevout))
              return true;
  
          // Match if the filter contains any arbitrary script data element in any scriptSig in tx
          CScript::const_iterator pc = txin.scriptSig.begin();
          std::vector<unsigned char> data;
          while (pc < txin.scriptSig.end())
          {
              opcodetype opcode;
              if (!txin.scriptSig.GetOp(pc, opcode, data))
                  break;
              if (data.size() != 0 && contains(data))
                  return true;
          }
      }
  
      return false;
  }
  
  void CBloomFilter::UpdateEmptyFull()
  {
      bool full = true;
      bool empty = true;
      for (unsigned int i = 0; i < vData.size(); i++)
      {
          full &= vData[i] == 0xff;
          empty &= vData[i] == 0;
      }
      isFull = full;
      isEmpty = empty;
  }
  
  CRollingBloomFilter::CRollingBloomFilter(const unsigned int nElements, const double fpRate)
  {
      double logFpRate = log(fpRate);
      /* The optimal number of hash functions is log(fpRate) / log(0.5), but
       * restrict it to the range 1-50. */
      nHashFuncs = std::max(1, std::min((int)round(logFpRate / log(0.5)), 50));
      /* In this rolling bloom filter, we'll store between 2 and 3 generations of nElements / 2 entries. */
      nEntriesPerGeneration = (nElements + 1) / 2;
      uint32_t nMaxElements = nEntriesPerGeneration * 3;
      /* The maximum fpRate = pow(1.0 - exp(-nHashFuncs * nMaxElements / nFilterBits), nHashFuncs)
       * =>          pow(fpRate, 1.0 / nHashFuncs) = 1.0 - exp(-nHashFuncs * nMaxElements / nFilterBits)
       * =>          1.0 - pow(fpRate, 1.0 / nHashFuncs) = exp(-nHashFuncs * nMaxElements / nFilterBits)
       * =>          log(1.0 - pow(fpRate, 1.0 / nHashFuncs)) = -nHashFuncs * nMaxElements / nFilterBits
       * =>          nFilterBits = -nHashFuncs * nMaxElements / log(1.0 - pow(fpRate, 1.0 / nHashFuncs))
       * =>          nFilterBits = -nHashFuncs * nMaxElements / log(1.0 - exp(logFpRate / nHashFuncs))
       */
      uint32_t nFilterBits = (uint32_t)ceil(-1.0 * nHashFuncs * nMaxElements / log(1.0 - exp(logFpRate / nHashFuncs)));
      data.clear();
      /* For each data element we need to store 2 bits. If both bits are 0, the
       * bit is treated as unset. If the bits are (01), (10), or (11), the bit is
       * treated as set in generation 1, 2, or 3 respectively.
       * These bits are stored in separate integers: position P corresponds to bit
       * (P & 63) of the integers data[(P >> 6) * 2] and data[(P >> 6) * 2 + 1]. */
      data.resize(((nFilterBits + 63) / 64) << 1);
      reset();
  }
  
  /* Similar to CBloomFilter::Hash */
  static inline uint32_t RollingBloomHash(unsigned int nHashNum, uint32_t nTweak, const std::vector<unsigned char>& vDataToHash) {
      return MurmurHash3(nHashNum * 0xFBA4C795 + nTweak, vDataToHash);
  }
  
  void CRollingBloomFilter::insert(const std::vector<unsigned char>& vKey)
  {
      if (nEntriesThisGeneration == nEntriesPerGeneration) {
          nEntriesThisGeneration = 0;
          nGeneration++;
          if (nGeneration == 4) {
              nGeneration = 1;
          }
          uint64_t nGenerationMask1 = 0 - (uint64_t)(nGeneration & 1);
          uint64_t nGenerationMask2 = 0 - (uint64_t)(nGeneration >> 1);
          /* Wipe old entries that used this generation number. */
          for (uint32_t p = 0; p < data.size(); p += 2) {
              uint64_t p1 = data[p], p2 = data[p + 1];
              uint64_t mask = (p1 ^ nGenerationMask1) | (p2 ^ nGenerationMask2);
              data[p] = p1 & mask;
              data[p + 1] = p2 & mask;
          }
      }
      nEntriesThisGeneration++;
  
      for (int n = 0; n < nHashFuncs; n++) {
          uint32_t h = RollingBloomHash(n, nTweak, vKey);
          int bit = h & 0x3F;
          uint32_t pos = (h >> 6) % data.size();
          /* The lowest bit of pos is ignored, and set to zero for the first bit, and to one for the second. */
          data[pos & ~1] = (data[pos & ~1] & ~(((uint64_t)1) << bit)) | ((uint64_t)(nGeneration & 1)) << bit;
          data[pos | 1] = (data[pos | 1] & ~(((uint64_t)1) << bit)) | ((uint64_t)(nGeneration >> 1)) << bit;
      }
  }
  
  void CRollingBloomFilter::insert(const uint256& hash)
  {
      std::vector<unsigned char> vData(hash.begin(), hash.end());
      insert(vData);
  }
  
  bool CRollingBloomFilter::contains(const std::vector<unsigned char>& vKey) const
  {
      for (int n = 0; n < nHashFuncs; n++) {
          uint32_t h = RollingBloomHash(n, nTweak, vKey);
          int bit = h & 0x3F;
          uint32_t pos = (h >> 6) % data.size();
          /* If the relevant bit is not set in either data[pos & ~1] or data[pos | 1], the filter does not contain vKey */
          if (!(((data[pos & ~1] | data[pos | 1]) >> bit) & 1)) {
              return false;
          }
      }
      return true;
  }
  
  bool CRollingBloomFilter::contains(const uint256& hash) const
  {
      std::vector<unsigned char> vData(hash.begin(), hash.end());
      return contains(vData);
  }
  
  void CRollingBloomFilter::reset()
  {
      nTweak = GetRand(std::numeric_limits<unsigned int>::max());
      nEntriesThisGeneration = 0;
      nGeneration = 1;
      for (std::vector<uint64_t>::iterator it = data.begin(); it != data.end(); it++) {
          *it = 0;
      }
  }
  