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107 lines
3.7 KiB
Go
107 lines
3.7 KiB
Go
// Copyright (c) 2013-2014 The btcsuite developers
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// Use of this source code is governed by an ISC
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// license that can be found in the LICENSE file.
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package blockchain
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import (
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"math"
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"github.com/btcsuite/btcd/wire"
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"github.com/btcsuite/btcutil"
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)
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// nextPowerOfTwo returns the next highest power of two from a given number if
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// it is not already a power of two. This is a helper function used during the
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// calculation of a merkle tree.
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func nextPowerOfTwo(n int) int {
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// Return the number if it's already a power of 2.
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if n&(n-1) == 0 {
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return n
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}
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// Figure out and return the next power of two.
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exponent := uint(math.Log2(float64(n))) + 1
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return 1 << exponent // 2^exponent
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}
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// HashMerkleBranches takes two hashes, treated as the left and right tree
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// nodes, and returns the hash of their concatenation. This is a helper
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// function used to aid in the generation of a merkle tree.
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func HashMerkleBranches(left *wire.ShaHash, right *wire.ShaHash) *wire.ShaHash {
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// Concatenate the left and right nodes.
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var sha [wire.HashSize * 2]byte
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copy(sha[:wire.HashSize], left[:])
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copy(sha[wire.HashSize:], right[:])
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newSha := wire.DoubleSha256SH(sha[:])
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return &newSha
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}
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// BuildMerkleTreeStore creates a merkle tree from a slice of transactions,
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// stores it using a linear array, and returns a slice of the backing array. A
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// linear array was chosen as opposed to an actual tree structure since it uses
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// about half as much memory. The following describes a merkle tree and how it
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// is stored in a linear array.
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//
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// A merkle tree is a tree in which every non-leaf node is the hash of its
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// children nodes. A diagram depicting how this works for bitcoin transactions
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// where h(x) is a double sha256 follows:
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//
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// root = h1234 = h(h12 + h34)
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// / \
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// h12 = h(h1 + h2) h34 = h(h3 + h4)
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// / \ / \
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// h1 = h(tx1) h2 = h(tx2) h3 = h(tx3) h4 = h(tx4)
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//
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// The above stored as a linear array is as follows:
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//
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// [h1 h2 h3 h4 h12 h34 root]
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//
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// As the above shows, the merkle root is always the last element in the array.
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//
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// The number of inputs is not always a power of two which results in a
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// balanced tree structure as above. In that case, parent nodes with no
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// children are also zero and parent nodes with only a single left node
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// are calculated by concatenating the left node with itself before hashing.
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// Since this function uses nodes that are pointers to the hashes, empty nodes
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// will be nil.
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func BuildMerkleTreeStore(transactions []*btcutil.Tx) []*wire.ShaHash {
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// Calculate how many entries are required to hold the binary merkle
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// tree as a linear array and create an array of that size.
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nextPoT := nextPowerOfTwo(len(transactions))
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arraySize := nextPoT*2 - 1
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merkles := make([]*wire.ShaHash, arraySize)
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// Create the base transaction shas and populate the array with them.
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for i, tx := range transactions {
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merkles[i] = tx.Sha()
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}
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// Start the array offset after the last transaction and adjusted to the
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// next power of two.
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offset := nextPoT
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for i := 0; i < arraySize-1; i += 2 {
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switch {
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// When there is no left child node, the parent is nil too.
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case merkles[i] == nil:
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merkles[offset] = nil
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// When there is no right child, the parent is generated by
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// hashing the concatenation of the left child with itself.
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case merkles[i+1] == nil:
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newSha := HashMerkleBranches(merkles[i], merkles[i])
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merkles[offset] = newSha
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// The normal case sets the parent node to the double sha256
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// of the concatentation of the left and right children.
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default:
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newSha := HashMerkleBranches(merkles[i], merkles[i+1])
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merkles[offset] = newSha
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}
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offset++
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}
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return merkles
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}
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