bloom.cpp
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	// Copyright (c) 2012-2016 The Bitcoin 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 <hash.h>
	#include <primitives/transaction.h>
	#include <random.h>
	#include <script/script.h>
	#include <script/standard.h>
	#include <streams.h>

	#include <cmath>
	#include <cstdlib>

	#include <algorithm>

	#define LN2SQUARED 0.4804530139182014246671025263266649717305529515945455
	#define LN2 0.6931471805599453094172321214581765680755001343602552

	/**
	* 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
	*
	* 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.
	*/
	CBloomFilter::CBloomFilter(const uint32_t nElements, const double nFPRate,
	const uint32_t nTweakIn, uint8_t nFlagsIn)
	: vData(std::min<uint32_t>(-1 / LN2SQUARED * nElements * log(nFPRate),
	MAX_BLOOM_FILTER_SIZE * 8) /
	8),
	nHashFuncs(std::min<uint32_t>(vData.size() * 8 / nElements * LN2,
	MAX_HASH_FUNCS)),
	nTweak(nTweakIn), nFlags(nFlagsIn) {}

	inline uint32_t
	CBloomFilter::Hash(uint32_t nHashNum,
	const std::vector<uint8_t> &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<uint8_t> &vKey) {
	if (vData.empty()) {
	// Avoid divide-by-zero (CVE-2013-5700)
	return;
	}

	for (uint32_t i = 0; i < nHashFuncs; i++) {
	uint32_t nIndex = Hash(i, vKey);
	// Sets bit nIndex of vData
	vData[nIndex >> 3] \|= (1 << (7 & nIndex));
	}
	}

	void CBloomFilter::insert(const COutPoint &outpoint) {
	CDataStream stream(SER_NETWORK, PROTOCOL_VERSION);
	stream << outpoint;
	std::vector<uint8_t> data(stream.begin(), stream.end());
	insert(data);
	}

	void CBloomFilter::insert(const uint256 &hash) {
	std::vector<uint8_t> data(hash.begin(), hash.end());
	insert(data);
	}

	bool CBloomFilter::contains(const std::vector<uint8_t> &vKey) const {
	if (vData.empty()) {
	// Avoid divide-by-zero (CVE-2013-5700)
	return true;
	}
	for (uint32_t i = 0; i < nHashFuncs; i++) {
	uint32_t 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<uint8_t> data(stream.begin(), stream.end());
	return contains(data);
	}

	bool CBloomFilter::contains(const uint256 &hash) const {
	std::vector<uint8_t> data(hash.begin(), hash.end());
	return contains(data);
	}

	bool CBloomFilter::IsWithinSizeConstraints() const {
	return vData.size() <= MAX_BLOOM_FILTER_SIZE &&
	nHashFuncs <= MAX_HASH_FUNCS;
	}

	bool CBloomFilter::MatchAndInsertOutputs(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 (vData.empty()) {
	// zero-size = "match-all" filter
	return true;
	}

	const TxId &txid = tx.GetId();
	if (contains(txid)) {
	fFound = true;
	}

	for (size_t 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<uint8_t> 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(txid, i));
	} else if ((nFlags & BLOOM_UPDATE_MASK) ==
	BLOOM_UPDATE_P2PUBKEY_ONLY) {
	std::vector<std::vector<uint8_t>> vSolutions;
	TxoutType type = Solver(txout.scriptPubKey, vSolutions);
	if (type == TxoutType::PUBKEY \|\|
	type == TxoutType::MULTISIG) {
	insert(COutPoint(txid, i));
	}
	}
	break;
	}
	}
	}

	return fFound;
	}

	bool CBloomFilter::MatchInputs(const CTransaction &tx) {
	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<uint8_t> 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;
	}

	CRollingBloomFilter::CRollingBloomFilter(const uint32_t 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(uint32_t nHashNum, uint32_t nTweak,
	const std::vector<uint8_t> &vDataToHash) {
	return MurmurHash3(nHashNum * 0xFBA4C795 + nTweak, vDataToHash);
	}

	// A replacement for x % n. This assumes that x and n are 32bit integers, and x
	// is a uniformly random distributed 32bit value which should be the case for a
	// good hash. See
	// https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
	static inline uint32_t FastMod(uint32_t x, size_t n) {
	return (uint64_t(x) * uint64_t(n)) >> 32;
	}

	void CRollingBloomFilter::insert(const std::vector<uint8_t> &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;
	/* FastMod works with the upper bits of h, so it is safe to ignore that
	* the lower bits of h are already used for bit. */
	uint32_t pos = FastMod(h, 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<uint8_t> vData(hash.begin(), hash.end());
	insert(vData);
	}

	bool CRollingBloomFilter::contains(const std::vector<uint8_t> &vKey) const {
	for (int n = 0; n < nHashFuncs; n++) {
	uint32_t h = RollingBloomHash(n, nTweak, vKey);
	int bit = h & 0x3F;
	uint32_t pos = FastMod(h, 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<uint8_t> vData(hash.begin(), hash.end());
	return contains(vData);
	}

	void CRollingBloomFilter::reset() {
	nTweak = GetRand(std::numeric_limits<unsigned int>::max());
	nEntriesThisGeneration = 0;
	nGeneration = 1;
	std::fill(data.begin(), data.end(), 0);
	}

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