feat(merkle): Add merkle with repetitions

Author: mpolitzer

internal/merkle/repetitions.go

@@ -0,0 +1,77 @@
+// (c) Cartesi and individual authors (see AUTHORS)
+// SPDX-License-Identifier: Apache-2.0 (see LICENSE)
+
+package merkle
+
+import (
+	"cmp"
+	"fmt"
+	"slices"
+
+	"github.com/ethereum/go-ethereum/common"
+	"github.com/ethereum/go-ethereum/crypto"
+)
+
+type Node struct {
+	hash  common.Hash
+	until uint64 // (count of) elements to the left
+}
+
+func nodeCmp(x Node, until uint64) int {
+	return cmp.Compare(x.until, until)
+}
+
+func Append(xs []Node, hash common.Hash, reps uint64) []Node {
+	if len(xs) == 0 {
+		return []Node{{hash, reps}}
+	}
+
+	latest := &xs[len(xs)-1]
+	if latest.hash == hash { // reuse previous Node when repeating the hash
+		xs[len(xs)-1].until += reps
+		return xs
+	}
+	return append(xs, Node{hash, latest.until + reps})
+}
+
+// Merkle with repetitions receives an ORDERED array of nodes, log2size and a
+// stride to compute the root hash of subtree in the range `a` - `b`.
+//
+//	      .       |
+//	     / \      |
+//	    /   \     |
+//	   /     \    |
+//	  /       \   |
+//	 /  /\     \  |
+//	+--/--\-----+ v  log2size
+//	0  1  2  3  4 <- stride
+//	   a--b
+func GetRootHash(nodes []Node, log2size uint64, stride uint64) (common.Hash, error) {
+	zero := common.Hash{}
+
+	aIndex := (1 << log2size) * stride
+	bIndex := (1 << log2size) * (stride + 1)
+
+	limit := nodes[len(nodes)-1].until
+	if limit < bIndex {
+		return zero, fmt.Errorf("Index out of bounds: %v out of %v.", bIndex, limit)
+	}
+
+	aCell, _ := slices.BinarySearchFunc(nodes, aIndex, nodeCmp)
+	bCell, _ := slices.BinarySearchFunc(nodes, bIndex, nodeCmp)
+	if aCell == bCell {
+		return repeatedMerkleRoot(nodes[aCell].hash, log2size)
+	}
+
+	lhs, _ := GetRootHash(nodes[aCell:bCell], log2size-1, 2*stride)
+	rhs, _ := GetRootHash(nodes[aCell:bCell], log2size-1, 2*stride+1)
+	return crypto.Keccak256Hash(lhs[:], rhs[:]), nil
+}
+
+// level is a power of 2
+func repeatedMerkleRoot(hash common.Hash, log2level uint64) (common.Hash, error) {
+	for range log2level {
+		hash = crypto.Keccak256Hash(hash[:], hash[:])
+	}
+	return hash, nil
+}