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main.go
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main.go
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// Copyright 2019 Google LLC. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// A binary to produce LaTeX documents representing Merkle trees.
// The generated document should be fed into xelatex, and the Forest package
// must be available.
//
// Usage: go run main.go | xelatex
// This should generate a PDF file called treetek.pdf containing a drawing of
// the tree.
//
package main
import (
"flag"
"fmt"
"log"
"math/bits"
"strings"
"github.com/google/trillian/merkle"
"github.com/google/trillian/merkle/compact"
)
const (
preamble = `
% Hash-tree
% Author: treetex
\documentclass[convert]{standalone}
\usepackage[dvipsnames]{xcolor}
\usepackage{forest}
\begin{document}
% Change colours here:
\definecolor{proof}{rgb}{1,0.5,0.5}
\definecolor{proof_ephemeral}{rgb}{1,0.7,0.7}
\definecolor{perfect}{rgb}{1,0.9,0.5}
\definecolor{target}{rgb}{0.5,0.5,0.9}
\definecolor{target_path}{rgb}{0.7,0.7,0.9}
\definecolor{mega}{rgb}{0.9,0.9,0.9}
\definecolor{target0}{rgb}{0.1,0.9,0.1}
\definecolor{target1}{rgb}{0.1,0.1,0.9}
\definecolor{target2}{rgb}{0.9,0.1,0.9}
\definecolor{range0}{rgb}{0.3,0.9,0.3}
\definecolor{range1}{rgb}{0.3,0.3,0.9}
\definecolor{range2}{rgb}{0.9,0.3,0.9}
\forestset{
% This defines a new "edge" style for drawing the perfect subtrees.
% Rather than simply drawing a line representing an edge, this draws a
% triangle between the labelled anchors on the given nodes.
% See "Anchors" section in the Forest manual for more details:
% http://mirrors.ibiblio.org/CTAN/graphics/pgf/contrib/forest/forest-doc.pdf
perfect/.style={edge path={%
\noexpand\path[fill=mega, \forestoption{edge}]
(.parent first)--(!u.children)--(.parent last)--cycle
\forestoption{edge label};
}
},
}
\begin{forest}
`
postfix = `\end{forest}
\end{document}
`
// Maximum number of ranges to allow.
maxRanges = 3
)
var (
treeSize = flag.Uint64("tree_size", 23, "Size of tree to produce")
leafData = flag.String("leaf_data", "", "Comma separated list of leaf data text (setting this overrides --tree_size")
nodeFormat = flag.String("node_format", "address", "Format for internal node text, one of: address, hash")
inclusion = flag.Int64("inclusion", -1, "Leaf index to show inclusion proof")
megaMode = flag.Uint("megamode_threshold", 4, "Treat perfect trees larger than this many layers as a single entity")
ranges = flag.String("ranges", "", "Comma-separated Open-Closed ranges of the form L:R")
attrPerfectRoot = flag.String("attr_perfect_root", "", "Latex treatment for perfect root nodes (e.g. 'line width=3pt')")
attrEphemeralNode = flag.String("attr_ephemeral_node", "draw, dotted", "Latex treatment for ephemeral nodes")
// nInfo holds nodeInfo data for the tree.
nInfo = make(map[compact.NodeID]nodeInfo)
)
// nodeInfo represents the style to be applied to a tree node.
// TODO(al): separate out leafdata bits from here.
type nodeInfo struct {
proof bool
incPath bool
target bool
perfectRoot bool
ephemeral bool
leaf bool
dataRangeIndices []int
rangeIndices []int
}
type nodeTextFunc func(id compact.NodeID) string
// String returns a string containing Forest attributes suitable for
// rendering the node, given its type.
func (n nodeInfo) String() string {
attr := make([]string, 0, 4)
// Figure out which colour to fill with:
fill := "white"
if n.perfectRoot {
attr = append(attr, *attrPerfectRoot)
}
if n.proof {
fill = "proof"
if n.ephemeral {
fill = "proof_ephemeral"
}
}
if n.leaf {
if l := len(n.dataRangeIndices); l == 1 {
fill = fmt.Sprintf("target%d!50", n.dataRangeIndices[0])
} else if l > 1 {
// Otherwise, we need to be a bit cleverer, and use the shading feature.
for i, ri := range n.dataRangeIndices {
pos := []string{"left", "right", "middle"}[i]
attr = append(attr, fmt.Sprintf("%s color=target%d!50", pos, ri))
}
}
} else {
if l := len(n.rangeIndices); l == 1 {
fill = fmt.Sprintf("range%d!50", n.rangeIndices[0])
} else if l > 1 {
for i, pi := range n.rangeIndices {
pos := []string{"left", "right", "middle"}[i]
attr = append(attr, fmt.Sprintf("%s color=range%d!50", pos, pi))
}
}
}
if n.target {
fill = "target"
}
if n.incPath {
fill = "target_path"
}
attr = append(attr, "fill="+fill)
if !n.ephemeral {
attr = append(attr, "draw")
} else {
attr = append(attr, *attrEphemeralNode)
}
if !n.leaf {
attr = append(attr, "circle, minimum size=3em, align=center")
} else {
attr = append(attr, "minimum size=1.5em, align=center, base=bottom")
}
return strings.Join(attr, ", ")
}
// modifyNodeInfo applies f to the nodeInfo associated with node id.
func modifyNodeInfo(id compact.NodeID, f func(*nodeInfo)) {
n := nInfo[id] // Note: Returns an empty nodeInfo if id is not found.
f(&n)
nInfo[id] = n
}
// perfectMega renders a large perfect subtree as a single entity.
func perfectMega(prefix string, height uint, leafIndex uint64) {
stLeaves := uint64(1) << height
stWidth := float32(stLeaves) / float32(*treeSize)
fmt.Printf("%s [%d\\dots%d, edge label={node[midway, above]{%d}}, perfect, tier=leaf, minimum width=%f\\linewidth ]\n", prefix, leafIndex, leafIndex+stLeaves, stLeaves, stWidth)
// Create some hidden nodes to preseve the tier spacings:
fmt.Printf("%s", prefix)
for i := int(height - 2); i > 0; i-- {
fmt.Printf(" [, no edge, tier=%d ", i)
defer fmt.Printf(" ] ")
}
}
// perfect renders a perfect subtree.
func perfect(prefix string, height uint, index uint64, nodeText, dataText nodeTextFunc) {
perfectInner(prefix, height, index, true, nodeText, dataText)
}
// drawLeaf emits TeX code to render a leaf.
func drawLeaf(prefix string, index uint64, leafText, dataText nodeTextFunc) {
id := compact.NewNodeID(0, index)
a := nInfo[id]
// First render the leaf node of the Merkle tree.
if len(a.dataRangeIndices) > 0 {
a.incPath = false
}
fmt.Printf("%s [%s, %s, align=center, tier=leaf\n", prefix, leafText(id), a.String())
// and then a child-node representing the leaf data itself:
a = nInfo[id]
a.leaf = true
a.proof = false // proofs don't include leafdata (just the leaf hash above)
a.incPath, a.target = false, a.incPath // draw the target leaf darker if necessary.
fmt.Printf(" %s [%s, %s, align=center, tier=leafdata]\n]\n", prefix, dataText(id), a.String())
}
// openInnerNode renders TeX code to open an internal node.
// The caller may emit any number of child nodes before calling the returned
// func to close the node.
// Returns a func to be called to close the node.
func openInnerNode(prefix string, id compact.NodeID, nodeText nodeTextFunc) func() {
attr := nInfo[id].String()
fmt.Printf("%s [%s, %s, tier=%d\n", prefix, nodeText(id), attr, id.Level)
return func() { fmt.Printf("%s ]\n", prefix) }
}
// perfectInner renders the nodes of a perfect internal subtree.
func perfectInner(prefix string, level uint, index uint64, top bool, nodeText nodeTextFunc, dataText nodeTextFunc) {
id := compact.NewNodeID(level, index)
modifyNodeInfo(id, func(n *nodeInfo) {
n.perfectRoot = top
})
if level == 0 {
drawLeaf(prefix, index, nodeText, dataText)
return
}
c := openInnerNode(prefix, id, nodeText)
childIndex := index << 1
if level > *megaMode {
perfectMega(prefix, level, index<<level)
} else {
perfectInner(prefix+" ", level-1, childIndex, false, nodeText, dataText)
perfectInner(prefix+" ", level-1, childIndex+1, false, nodeText, dataText)
}
c()
}
// renderTree renders a tree node and recurses if necessary.
func renderTree(prefix string, treeSize, index uint64, nodeText, dataText nodeTextFunc) {
if treeSize == 0 {
return
}
// Look at the bit of the treeSize corresponding to the current level:
height := uint(bits.Len64(treeSize) - 1)
b := uint64(1) << height
rest := treeSize - b
// left child is a perfect subtree.
// if there's a right-hand child, then we'll emit this node to be the
// parent. (Otherwise we'll just keep quiet, and recurse down - this is how
// we arrange for leaves to always be on the bottom level.)
if rest > 0 {
childHeight := height + 1
id := compact.NewNodeID(childHeight, index>>childHeight)
modifyNodeInfo(id, func(n *nodeInfo) { n.ephemeral = true })
c := openInnerNode(prefix, id, nodeText)
defer c()
}
perfect(prefix+" ", height, index>>height, nodeText, dataText)
index += b
renderTree(prefix+" ", rest, index, nodeText, dataText)
}
// parseRanges parses and validates a string of comma-separates open-closed
// ranges of the form L:R.
// Returns the parsed ranges, or an error if there's a problem.
func parseRanges(ranges string, treeSize uint64) ([][2]uint64, error) {
rangePairs := strings.Split(ranges, ",")
numRanges := len(rangePairs)
if num, max := numRanges, maxRanges; num > max {
return nil, fmt.Errorf("too many ranges %d, must be %d or fewer", num, max)
}
ret := make([][2]uint64, 0, numRanges)
for _, rng := range rangePairs {
lr := strings.Split(rng, ":")
if len(lr) != 2 {
return nil, fmt.Errorf("specified range %q is invalid", rng)
}
var l, r uint64
if _, err := fmt.Sscanf(rng, "%d:%d", &l, &r); err != nil {
return nil, fmt.Errorf("range %q is malformed: %s", rng, err)
}
switch {
case r > treeSize:
return nil, fmt.Errorf("range %q extends past end of tree (%d)", lr, treeSize)
case l > r:
return nil, fmt.Errorf("range elements in %q are out of order", rng)
}
ret = append(ret, [2]uint64{l, r})
}
return ret, nil
}
// modifyRangeNodeInfo sets style info for nodes affected by ranges.
// This includes leaves and perfect subtree roots.
// TODO(al): Figure out what, if anything, to do to make this show ranges
// which are inside the perfect meganodes.
func modifyRangeNodeInfo() error {
rng, err := parseRanges(*ranges, *treeSize)
if err != nil {
return err
}
for ri, lr := range rng {
l, r := lr[0], lr[1]
// Set leaves:
for i := l; i < r; i++ {
id := compact.NewNodeID(0, i)
modifyNodeInfo(id, func(n *nodeInfo) {
n.dataRangeIndices = append(n.dataRangeIndices, ri)
})
}
for _, id := range compact.RangeNodes(l, r) {
modifyNodeInfo(id, func(n *nodeInfo) {
n.rangeIndices = append(n.rangeIndices, ri)
})
}
}
return nil
}
var dataFormat = func(id compact.NodeID) string {
return fmt.Sprintf("{$leaf_{%d}$}", id.Index)
}
var nodeFormats = map[string]nodeTextFunc{
"address": func(id compact.NodeID) string {
return fmt.Sprintf("%d.%d", id.Level, id.Index)
},
"hash": func(id compact.NodeID) string {
// For "hash" format node text, levels >=1 need a different format
// [H=H(childL|childR)]from the base level (H=H(leafN)].
if id.Level >= 1 {
childLevel := id.Level - 1
leftChild := id.Index * 2
return fmt.Sprintf("{$H_{%d.%d} =$ \\\\ $H(H_{%d.%d} || H_{%d.%d})$}", id.Level, id.Index, childLevel, leftChild, childLevel, leftChild+1)
}
return fmt.Sprintf("{$H_{%d.%d} =$ \\\\ $H(leaf_{%[2]d})$}", id.Level, id.Index)
},
}
// Whee - here we go!
func main() {
// TODO(al): check flag validity.
flag.Parse()
height := uint(bits.Len64(*treeSize-1)) + 1
innerNodeText := nodeFormats[*nodeFormat]
if innerNodeText == nil {
log.Fatalf("unknown --node_format %s", *nodeFormat)
}
nodeText := innerNodeText
if len(*leafData) > 0 {
leaves := strings.Split(*leafData, ",")
*treeSize = uint64(len(leaves))
log.Printf("Overriding treeSize to %d since --leaf_data was set", *treeSize)
dataFormat = func(id compact.NodeID) string {
return leaves[id.Index]
}
}
if *inclusion > 0 {
leafID := compact.NewNodeID(0, uint64(*inclusion))
modifyNodeInfo(leafID, func(n *nodeInfo) { n.incPath = true })
nf, err := merkle.CalcInclusionProofNodeAddresses(int64(*treeSize), *inclusion, int64(*treeSize))
if err != nil {
log.Fatalf("Failed to calculate inclusion proof addresses: %s", err)
}
for _, n := range nf {
modifyNodeInfo(n.ID, func(n *nodeInfo) { n.proof = true })
}
for h, i := uint(0), leafID.Index; h < height; h, i = h+1, i>>1 {
id := compact.NewNodeID(h, i)
modifyNodeInfo(id, func(n *nodeInfo) { n.incPath = true })
}
}
if len(*ranges) > 0 {
if err := modifyRangeNodeInfo(); err != nil {
log.Fatalf("Failed to modify range node styles: %s", err)
}
}
// TODO(al): structify this into a util, and add ability to output to an
// arbitrary stream.
fmt.Print(preamble)
renderTree("", *treeSize, 0, nodeText, dataFormat)
fmt.Print(postfix)
}