Add CPartialMerkleTree

This adds a compact representation for a subset of a merkle tree's
nodes.

src/main.h

@@ -1110,11 +1110,101 @@ public:
 
 
 
+/** Data structure that represents a partial merkle tree.
+ *
+ * It respresents a subset of the txid's of a known block, in a way that
+ * allows recovery of the list of txid's and the merkle root, in an
+ * authenticated way.
+ *
+ * The encoding works as follows: we traverse the tree in depth-first order,
+ * storing a bit for each traversed node, signifying whether the node is the
+ * parent of at least one matched leaf txid (or a matched txid itself). In
+ * case we are at the leaf level, or this bit is 0, its merkle node hash is
+ * stored, and its children are not explorer further. Otherwise, no hash is
+ * stored, but we recurse into both (or the only) child branch. During
+ * decoding, the same depth-first traversal is performed, consuming bits and
+ * hashes as they written during encoding.
+ *
+ * The serialization is fixed and provides a hard guarantee about the
+ * encoded size:
+ *
+ *   SIZE <= 10 + ceil(32.25*N)
+ *
+ * Where N represents the number of leaf nodes of the partial tree. N itself
+ * is bounded by:
+ *
+ *   N <= total_transactions
+ *   N <= 1 + matched_transactions*tree_height
+ *
+ * The serialization format:
+ *  - uint32     total_transactions (4 bytes)
+ *  - varint     number of hashes   (1-3 bytes)
+ *  - uint256[]  hashes in depth-first order (<= 32*N bytes)
+ *  - varint     number of bytes of flag bits (1-3 bytes)
+ *  - byte[]     flag bits, packed per 8 in a byte, least significant bit first (<= 2*N-1 bits)
+ * The size constraints follow from this.
+ */
+class CPartialMerkleTree
+{
+protected:
+    // the total number of transactions in the block
+    unsigned int nTransactions;
 
+    // node-is-parent-of-matched-txid bits
+    std::vector<bool> vBits;
 
+    // txids and internal hashes
+    std::vector<uint256> vHash;
 
+    // flag set when encountering invalid data
+    bool fBad;
 
+    // helper function to efficiently calculate the number of nodes at given height in the merkle tree
+    unsigned int CalcTreeWidth(int height) {
+        return (nTransactions+(1 << height)-1) >> height;
+    }
 
+    // calculate the hash of a node in the merkle tree (at leaf level: the txid's themself)
+    uint256 CalcHash(int height, unsigned int pos, const std::vector<uint256> &vTxid);
+
+    // recursive function that traverses tree nodes, storing the data as bits and hashes
+    void TraverseAndBuild(int height, unsigned int pos, const std::vector<uint256> &vTxid, const std::vector<bool> &vMatch);
+
+    // recursive function that traverses tree nodes, consuming the bits and hashes produced by TraverseAndBuild.
+    // it returns the hash of the respective node.
+    uint256 TraverseAndExtract(int height, unsigned int pos, unsigned int &nBitsUsed, unsigned int &nHashUsed, std::vector<uint256> &vMatch);
+
+public:
+
+    // serialization implementation
+    IMPLEMENT_SERIALIZE(
+        READWRITE(nTransactions);
+        READWRITE(vHash);
+        std::vector<unsigned char> vBytes;
+        if (fRead) {
+            READWRITE(vBytes);
+            CPartialMerkleTree &us = *(const_cast<CPartialMerkleTree*>(this));
+            us.vBits.resize(vBytes.size() * 8);
+            for (unsigned int p = 0; p < us.vBits.size(); p++)
+                us.vBits[p] = (vBytes[p / 8] & (1 << (p % 8))) != 0;
+            us.fBad = false;
+        } else {
+            vBytes.resize((vBits.size()+7)/8);
+            for (unsigned int p = 0; p < vBits.size(); p++)
+                vBytes[p / 8] |= vBits[p] << (p % 8);
+            READWRITE(vBytes);
+        }
+    )
+
+    // Construct a partial merkle tree from a list of transaction id's, and a mask that selects a subset of them
+    CPartialMerkleTree(const std::vector<uint256> &vTxid, const std::vector<bool> &vMatch);
+
+    CPartialMerkleTree();
+
+    // extract the matching txid's represented by this partial merkle tree.
+    // returns the merkle root, or 0 in case of failure
+    uint256 ExtractMatches(std::vector<uint256> &vMatch);
+};
 
 
 /** Nodes collect new transactions into a block, hash them into a hash tree,