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swarm/bmt: async section writer interface to BMT (#778) 

- AsyncHasher implements AsyncWriter interface
 - add extra level for zerohashes in pool to lookup empty data hash
 - remove unused segment, hash and depth fields from Tree
 - Hash pkg function -> syncHash moved to test
 - add asyncHash helper func to tests using shuffle
 - add TestAsyncCorrectness to tests
 - add BenchmarkBMTAsync to tests
 - refactor benchmarks using subbenchmarks
 - improved comments
 - preinitialise base hashers on the nodes
This commit is contained in:
Viktor Trón 2018-07-18 12:09:38 +02:00 committed by Anton Evangelatov
parent 526abe2736
commit fd982d3f3b
2 changed files with 463 additions and 184 deletions
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366
swarm/bmt/bmt.go
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@ -14,7 +14,7 @@
// You should have received a copy of the GNU Lesser General Public License // You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>. // along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
// Package bmt provides a binary merkle tree implementation // Package bmt provides a binary merkle tree implementation used for swarm chunk hash
package bmt package bmt
import ( import (
@ -26,16 +26,16 @@ import (
) )
/* /*
Binary Merkle Tree Hash is a hash function over arbitrary datachunks of limited size Binary Merkle Tree Hash is a hash function over arbitrary datachunks of limited size.
It is defined as the root hash of the binary merkle tree built over fixed size segments It is defined as the root hash of the binary merkle tree built over fixed size segments
of the underlying chunk using any base hash function (e.g keccak 256 SHA3). of the underlying chunk using any base hash function (e.g., keccak 256 SHA3).
Chunk with data shorter than the fixed size are hashed as if they had zero padding Chunks with data shorter than the fixed size are hashed as if they had zero padding.
BMT hash is used as the chunk hash function in swarm which in turn is the basis for the BMT hash is used as the chunk hash function in swarm which in turn is the basis for the
128 branching swarm hash http://swarm-guide.readthedocs.io/en/latest/architecture.html#swarm-hash 128 branching swarm hash http://swarm-guide.readthedocs.io/en/latest/architecture.html#swarm-hash
The BMT is optimal for providing compact inclusion proofs, i.e. prove that a The BMT is optimal for providing compact inclusion proofs, i.e. prove that a
segment is a substring of a chunk starting at a particular offset segment is a substring of a chunk starting at a particular offset.
The size of the underlying segments is fixed to the size of the base hash (called the resolution The size of the underlying segments is fixed to the size of the base hash (called the resolution
of the BMT hash), Using Keccak256 SHA3 hash is 32 bytes, the EVM word size to optimize for on-chain BMT verification of the BMT hash), Using Keccak256 SHA3 hash is 32 bytes, the EVM word size to optimize for on-chain BMT verification
as well as the hash size optimal for inclusion proofs in the merkle tree of the swarm hash. as well as the hash size optimal for inclusion proofs in the merkle tree of the swarm hash.
@ -46,11 +46,12 @@ Two implementations are provided:
that is simple to understand that is simple to understand
* Hasher is optimized for speed taking advantage of concurrency with minimalistic * Hasher is optimized for speed taking advantage of concurrency with minimalistic
control structure to coordinate the concurrent routines control structure to coordinate the concurrent routines
It implements the following interfaces
* standard golang hash.Hash BMT Hasher implements the following interfaces
* SwarmHash * standard golang hash.Hash - synchronous, reusable
* io.Writer * SwarmHash - SumWithSpan provided
* TODO: SegmentWriter * io.Writer - synchronous left-to-right datawriter
* AsyncWriter - concurrent section writes and asynchronous Sum call
*/ */
const ( const (
@ -69,7 +70,7 @@ type BaseHasherFunc func() hash.Hash
// Hasher a reusable hasher for fixed maximum size chunks representing a BMT // Hasher a reusable hasher for fixed maximum size chunks representing a BMT
// - implements the hash.Hash interface // - implements the hash.Hash interface
// - reuses a pool of trees for amortised memory allocation and resource control // - reuses a pool of trees for amortised memory allocation and resource control
// - supports order-agnostic concurrent segment writes (TODO:) // - supports order-agnostic concurrent segment writes and section (double segment) writes
// as well as sequential read and write // as well as sequential read and write
// - the same hasher instance must not be called concurrently on more than one chunk // - the same hasher instance must not be called concurrently on more than one chunk
// - the same hasher instance is synchronously reuseable // - the same hasher instance is synchronously reuseable
@ -81,8 +82,7 @@ type Hasher struct {
bmt *tree // prebuilt BMT resource for flowcontrol and proofs bmt *tree // prebuilt BMT resource for flowcontrol and proofs
} }
// New creates a reusable Hasher // New creates a reusable BMT Hasher that
// implements the hash.Hash interface
// pulls a new tree from a resource pool for hashing each chunk // pulls a new tree from a resource pool for hashing each chunk
func New(p *TreePool) *Hasher { func New(p *TreePool) *Hasher {
return &Hasher{ return &Hasher{
@ -90,9 +90,9 @@ func New(p *TreePool) *Hasher {
} }
} }
// TreePool provides a pool of trees used as resources by Hasher // TreePool provides a pool of trees used as resources by the BMT Hasher.
// a tree popped from the pool is guaranteed to have clean state // A tree popped from the pool is guaranteed to have a clean state ready
// for hashing a new chunk // for hashing a new chunk.
type TreePool struct { type TreePool struct {
lock sync.Mutex lock sync.Mutex
c chan *tree // the channel to obtain a resource from the pool c chan *tree // the channel to obtain a resource from the pool
@ -101,7 +101,7 @@ type TreePool struct {
SegmentCount int // the number of segments on the base level of the BMT SegmentCount int // the number of segments on the base level of the BMT
Capacity int // pool capacity, controls concurrency Capacity int // pool capacity, controls concurrency
Depth int // depth of the bmt trees = int(log2(segmentCount))+1 Depth int // depth of the bmt trees = int(log2(segmentCount))+1
Datalength int // the total length of the data (count * size) Size int // the total length of the data (count * size)
count int // current count of (ever) allocated resources count int // current count of (ever) allocated resources
zerohashes [][]byte // lookup table for predictable padding subtrees for all levels zerohashes [][]byte // lookup table for predictable padding subtrees for all levels
} }
@ -112,12 +112,12 @@ func NewTreePool(hasher BaseHasherFunc, segmentCount, capacity int) *TreePool {
// initialises the zerohashes lookup table // initialises the zerohashes lookup table
depth := calculateDepthFor(segmentCount) depth := calculateDepthFor(segmentCount)
segmentSize := hasher().Size() segmentSize := hasher().Size()
zerohashes := make([][]byte, depth) zerohashes := make([][]byte, depth+1)
zeros := make([]byte, segmentSize) zeros := make([]byte, segmentSize)
zerohashes[0] = zeros zerohashes[0] = zeros
h := hasher() h := hasher()
for i := 1; i < depth; i++ { for i := 1; i < depth+1; i++ {
zeros = doHash(h, nil, zeros, zeros) zeros = doSum(h, nil, zeros, zeros)
zerohashes[i] = zeros zerohashes[i] = zeros
} }
return &TreePool{ return &TreePool{
@ -126,7 +126,7 @@ func NewTreePool(hasher BaseHasherFunc, segmentCount, capacity int) *TreePool {
SegmentSize: segmentSize, SegmentSize: segmentSize,
SegmentCount: segmentCount, SegmentCount: segmentCount,
Capacity: capacity, Capacity: capacity,
Datalength: segmentCount * segmentSize, Size: segmentCount * segmentSize,
Depth: depth, Depth: depth,
zerohashes: zerohashes, zerohashes: zerohashes,
} }
@ -155,7 +155,7 @@ func (p *TreePool) reserve() *tree {
select { select {
case t = <-p.c: case t = <-p.c:
default: default:
t = newTree(p.SegmentSize, p.Depth) t = newTree(p.SegmentSize, p.Depth, p.hasher)
p.count++ p.count++
} }
return t return t
@ -173,29 +173,28 @@ func (p *TreePool) release(t *tree) {
// the tree is 'locked' while not in the pool // the tree is 'locked' while not in the pool
type tree struct { type tree struct {
leaves []*node // leaf nodes of the tree, other nodes accessible via parent links leaves []*node // leaf nodes of the tree, other nodes accessible via parent links
cur int // index of rightmost currently open segment cursor int // index of rightmost currently open segment
offset int // offset (cursor position) within currently open segment offset int // offset (cursor position) within currently open segment
segment []byte // the rightmost open segment (not complete)
section []byte // the rightmost open section (double segment) section []byte // the rightmost open section (double segment)
depth int // number of levels
result chan []byte // result channel result chan []byte // result channel
hash []byte // to record the result
span []byte // The span of the data subsumed under the chunk span []byte // The span of the data subsumed under the chunk
} }
// node is a reuseable segment hasher representing a node in a BMT // node is a reuseable segment hasher representing a node in a BMT
type node struct { type node struct {
isLeft bool // whether it is left side of the parent double segment isLeft bool // whether it is left side of the parent double segment
parent *node // pointer to parent node in the BMT parent *node // pointer to parent node in the BMT
state int32 // atomic increment impl concurrent boolean toggle state int32 // atomic increment impl concurrent boolean toggle
left, right []byte // this is where the content segment is set left, right []byte // this is where the two children sections are written
hasher hash.Hash // preconstructed hasher on nodes
} }
// newNode constructs a segment hasher node in the BMT (used by newTree) // newNode constructs a segment hasher node in the BMT (used by newTree)
func newNode(index int, parent *node) *node { func newNode(index int, parent *node, hasher hash.Hash) *node {
return &node{ return &node{
parent: parent, parent: parent,
isLeft: index%2 == 0, isLeft: index%2 == 0,
hasher: hasher,
} }
} }
@ -253,16 +252,21 @@ func (t *tree) draw(hash []byte) string {
// newTree initialises a tree by building up the nodes of a BMT // newTree initialises a tree by building up the nodes of a BMT
// - segment size is stipulated to be the size of the hash // - segment size is stipulated to be the size of the hash
func newTree(segmentSize, depth int) *tree { func newTree(segmentSize, depth int, hashfunc func() hash.Hash) *tree {
n := newNode(0, nil) n := newNode(0, nil, hashfunc())
prevlevel := []*node{n} prevlevel := []*node{n}
// iterate over levels and creates 2^(depth-level) nodes // iterate over levels and creates 2^(depth-level) nodes
// the 0 level is on double segment sections so we start at depth - 2 since
count := 2 count := 2
for level := depth - 2; level >= 0; level-- { for level := depth - 2; level >= 0; level-- {
nodes := make([]*node, count) nodes := make([]*node, count)
for i := 0; i < count; i++ { for i := 0; i < count; i++ {
parent := prevlevel[i/2] parent := prevlevel[i/2]
nodes[i] = newNode(i, parent) var hasher hash.Hash
if level == 0 {
hasher = hashfunc()
}
nodes[i] = newNode(i, parent, hasher)
} }
prevlevel = nodes prevlevel = nodes
count *= 2 count *= 2
@ -270,13 +274,12 @@ func newTree(segmentSize, depth int) *tree {
// the datanode level is the nodes on the last level // the datanode level is the nodes on the last level
return &tree{ return &tree{
leaves: prevlevel, leaves: prevlevel,
result: make(chan []byte, 1), result: make(chan []byte),
segment: make([]byte, segmentSize),
section: make([]byte, 2*segmentSize), section: make([]byte, 2*segmentSize),
} }
} }
// methods needed by hash.Hash // methods needed to implement hash.Hash
// Size returns the size // Size returns the size
func (h *Hasher) Size() int { func (h *Hasher) Size() int {
@ -285,63 +288,40 @@ func (h *Hasher) Size() int {
// BlockSize returns the block size // BlockSize returns the block size
func (h *Hasher) BlockSize() int { func (h *Hasher) BlockSize() int {
return h.pool.SegmentSize return 2 * h.pool.SegmentSize
} }
// Hash hashes the data and the span using the bmt hasher // Sum returns the BMT root hash of the buffer
func Hash(h *Hasher, span, data []byte) []byte { // using Sum presupposes sequential synchronous writes (io.Writer interface)
h.ResetWithLength(span)
h.Write(data)
return h.Sum(nil)
}
// Datalength returns the maximum data size that is hashed by the hasher =
// segment count times segment size
func (h *Hasher) DataLength() int {
return h.pool.Datalength
}
// Sum returns the hash of the buffer
// hash.Hash interface Sum method appends the byte slice to the underlying // hash.Hash interface Sum method appends the byte slice to the underlying
// data before it calculates and returns the hash of the chunk // data before it calculates and returns the hash of the chunk
// caller must make sure Sum is not called concurrently with Write, writeSection // caller must make sure Sum is not called concurrently with Write, writeSection
// and WriteSegment (TODO:) func (h *Hasher) Sum(b []byte) (s []byte) {
func (h *Hasher) Sum(b []byte) (r []byte) { t := h.getTree()
return h.sum(b, true, true) // write the last section with final flag set to true
} go h.writeSection(t.cursor, t.section, true, true)
// wait for the result
// sum implements Sum taking parameters s = <-t.result
// * if the tree is released right away
// * if sequential write is used (can read sections)
func (h *Hasher) sum(b []byte, release, section bool) (r []byte) {
t := h.bmt
bh := h.pool.hasher()
go h.writeSection(t.cur, t.section, true)
bmtHash := <-t.result
span := t.span span := t.span
// fmt.Println(t.draw(bmtHash)) // release the tree resource back to the pool
if release { h.releaseTree()
h.releaseTree()
}
// b + sha3(span + BMT(pure_chunk)) // b + sha3(span + BMT(pure_chunk))
if span == nil { if len(span) == 0 {
return append(b, bmtHash...) return append(b, s...)
} }
return doHash(bh, b, span, bmtHash) return doSum(h.pool.hasher(), b, span, s)
} }
// Hasher implements the SwarmHash interface // methods needed to implement the SwarmHash and the io.Writer interfaces
// Hasher implements the io.Writer interface // Write calls sequentially add to the buffer to be hashed,
// with every full segment calls writeSection in a go routine
// Write fills the buffer to hash,
// with every full segment calls writeSection
func (h *Hasher) Write(b []byte) (int, error) { func (h *Hasher) Write(b []byte) (int, error) {
l := len(b) l := len(b)
if l <= 0 { if l == 0 {
return 0, nil return 0, nil
} }
t := h.bmt t := h.getTree()
secsize := 2 * h.pool.SegmentSize secsize := 2 * h.pool.SegmentSize
// calculate length of missing bit to complete current open section // calculate length of missing bit to complete current open section
smax := secsize - t.offset smax := secsize - t.offset
@ -359,20 +339,21 @@ func (h *Hasher) Write(b []byte) (int, error) {
return l, nil return l, nil
} }
} else { } else {
if t.cur == h.pool.SegmentCount*2 { // if end of a section
if t.cursor == h.pool.SegmentCount*2 {
return 0, nil return 0, nil
} }
} }
// read full segments and the last possibly partial segment from the input buffer // read full sections and the last possibly partial section from the input buffer
for smax < l { for smax < l {
// section complete; push to tree asynchronously // section complete; push to tree asynchronously
go h.writeSection(t.cur, t.section, false) go h.writeSection(t.cursor, t.section, true, false)
// reset section // reset section
t.section = make([]byte, secsize) t.section = make([]byte, secsize)
// copy from imput buffer at smax to right half of section // copy from input buffer at smax to right half of section
copy(t.section, b[smax:]) copy(t.section, b[smax:])
// advance cursor // advance cursor
t.cur++ t.cursor++
// smax here represents successive offsets in the input buffer // smax here represents successive offsets in the input buffer
smax += secsize smax += secsize
} }
@ -382,83 +363,225 @@ func (h *Hasher) Write(b []byte) (int, error) {
// Reset needs to be called before writing to the hasher // Reset needs to be called before writing to the hasher
func (h *Hasher) Reset() { func (h *Hasher) Reset() {
h.getTree() h.releaseTree()
} }
// Hasher implements the SwarmHash interface // methods needed to implement the SwarmHash interface
// ResetWithLength needs to be called before writing to the hasher // ResetWithLength needs to be called before writing to the hasher
// the argument is supposed to be the byte slice binary representation of // the argument is supposed to be the byte slice binary representation of
// the length of the data subsumed under the hash, i.e., span // the length of the data subsumed under the hash, i.e., span
func (h *Hasher) ResetWithLength(span []byte) { func (h *Hasher) ResetWithLength(span []byte) {
h.Reset() h.Reset()
h.bmt.span = span h.getTree().span = span
} }
// releaseTree gives back the Tree to the pool whereby it unlocks // releaseTree gives back the Tree to the pool whereby it unlocks
// it resets tree, segment and index // it resets tree, segment and index
func (h *Hasher) releaseTree() { func (h *Hasher) releaseTree() {
t := h.bmt t := h.bmt
if t != nil { if t == nil {
t.cur = 0 return
}
h.bmt = nil
go func() {
t.cursor = 0
t.offset = 0 t.offset = 0
t.span = nil t.span = nil
t.hash = nil
h.bmt = nil
t.section = make([]byte, h.pool.SegmentSize*2) t.section = make([]byte, h.pool.SegmentSize*2)
t.segment = make([]byte, h.pool.SegmentSize) select {
case <-t.result:
default:
}
h.pool.release(t) h.pool.release(t)
}()
}
// NewAsyncWriter extends Hasher with an interface for concurrent segment/section writes
func (h *Hasher) NewAsyncWriter(double bool) *AsyncHasher {
secsize := h.pool.SegmentSize
if double {
secsize *= 2
}
write := func(i int, section []byte, final bool) {
h.writeSection(i, section, double, final)
}
return &AsyncHasher{
Hasher: h,
double: double,
secsize: secsize,
write: write,
} }
} }
// TODO: writeSegment writes the ith segment into the BMT tree // SectionWriter is an asynchronous segment/section writer interface
// func (h *Hasher) writeSegment(i int, s []byte) { type SectionWriter interface {
// go h.run(h.bmt.leaves[i/2], h.pool.hasher(), i%2 == 0, s) Reset() // standard init to be called before reuse
// } Write(index int, data []byte) // write into section of index
Sum(b []byte, length int, span []byte) []byte // returns the hash of the buffer
SectionSize() int // size of the async section unit to use
}
// AsyncHasher extends BMT Hasher with an asynchronous segment/section writer interface
// AsyncHasher is unsafe and does not check indexes and section data lengths
// it must be used with the right indexes and length and the right number of sections
//
// behaviour is undefined if
// * non-final sections are shorter or longer than secsize
// * if final section does not match length
// * write a section with index that is higher than length/secsize
// * set length in Sum call when length/secsize < maxsec
//
// * if Sum() is not called on a Hasher that is fully written
// a process will block, can be terminated with Reset
// * it will not leak processes if not all sections are written but it blocks
// and keeps the resource which can be released calling Reset()
type AsyncHasher struct {
*Hasher // extends the Hasher
mtx sync.Mutex // to lock the cursor access
double bool // whether to use double segments (call Hasher.writeSection)
secsize int // size of base section (size of hash or double)
write func(i int, section []byte, final bool)
}
// methods needed to implement AsyncWriter
// SectionSize returns the size of async section unit to use
func (sw *AsyncHasher) SectionSize() int {
return sw.secsize
}
// Write writes the i-th section of the BMT base
// this function can and is meant to be called concurrently
// it sets max segment threadsafely
func (sw *AsyncHasher) Write(i int, section []byte) {
sw.mtx.Lock()
defer sw.mtx.Unlock()
t := sw.getTree()
// cursor keeps track of the rightmost section written so far
// if index is lower than cursor then just write non-final section as is
if i < t.cursor {
// if index is not the rightmost, safe to write section
go sw.write(i, section, false)
return
}
// if there is a previous rightmost section safe to write section
if t.offset > 0 {
if i == t.cursor {
// i==cursor implies cursor was set by Hash call so we can write section as final one
// since it can be shorter, first we copy it to the padded buffer
t.section = make([]byte, sw.secsize)
copy(t.section, section)
go sw.write(i, t.section, true)
return
}
// the rightmost section just changed, so we write the previous one as non-final
go sw.write(t.cursor, t.section, false)
}
// set i as the index of the righmost section written so far
// set t.offset to cursor*secsize+1
t.cursor = i
t.offset = i*sw.secsize + 1
t.section = make([]byte, sw.secsize)
copy(t.section, section)
}
// Sum can be called any time once the length and the span is known
// potentially even before all segments have been written
// in such cases Sum will block until all segments are present and
// the hash for the length can be calculated.
//
// b: digest is appended to b
// length: known length of the input (unsafe; undefined if out of range)
// meta: metadata to hash together with BMT root for the final digest
// e.g., span for protection against existential forgery
func (sw *AsyncHasher) Sum(b []byte, length int, meta []byte) (s []byte) {
sw.mtx.Lock()
t := sw.getTree()
if length == 0 {
sw.mtx.Unlock()
s = sw.pool.zerohashes[sw.pool.Depth]
} else {
// for non-zero input the rightmost section is written to the tree asynchronously
// if the actual last section has been written (t.cursor == length/t.secsize)
maxsec := (length - 1) / sw.secsize
if t.offset > 0 {
go sw.write(t.cursor, t.section, maxsec == t.cursor)
}
// set cursor to maxsec so final section is written when it arrives
t.cursor = maxsec
t.offset = length
result := t.result
sw.mtx.Unlock()
// wait for the result or reset
s = <-result
}
// relesase the tree back to the pool
sw.releaseTree()
// if no meta is given just append digest to b
if len(meta) == 0 {
return append(b, s...)
}
// hash together meta and BMT root hash using the pools
return doSum(sw.pool.hasher(), b, meta, s)
}
// writeSection writes the hash of i-th section into level 1 node of the BMT tree // writeSection writes the hash of i-th section into level 1 node of the BMT tree
func (h *Hasher) writeSection(i int, section []byte, final bool) { func (h *Hasher) writeSection(i int, section []byte, double bool, final bool) {
// select the leaf node for the section // select the leaf node for the section
n := h.bmt.leaves[i] var n *node
isLeft := n.isLeft var isLeft bool
n = n.parent var hasher hash.Hash
bh := h.pool.hasher() var level int
// hash the section t := h.getTree()
s := doHash(bh, nil, section) if double {
level++
n = t.leaves[i]
hasher = n.hasher
isLeft = n.isLeft
n = n.parent
// hash the section
section = doSum(hasher, nil, section)
} else {
n = t.leaves[i/2]
hasher = n.hasher
isLeft = i%2 == 0
}
// write hash into parent node // write hash into parent node
if final { if final {
// for the last segment use writeFinalNode // for the last segment use writeFinalNode
h.writeFinalNode(1, n, bh, isLeft, s) h.writeFinalNode(level, n, hasher, isLeft, section)
} else { } else {
h.writeNode(n, bh, isLeft, s) h.writeNode(n, hasher, isLeft, section)
} }
} }
// writeNode pushes the data to the node // writeNode pushes the data to the node
// if it is the first of 2 sisters written the routine returns // if it is the first of 2 sisters written, the routine terminates
// if it is the second, it calculates the hash and writes it // if it is the second, it calculates the hash and writes it
// to the parent node recursively // to the parent node recursively
// since hashing the parent is synchronous the same hasher can be used
func (h *Hasher) writeNode(n *node, bh hash.Hash, isLeft bool, s []byte) { func (h *Hasher) writeNode(n *node, bh hash.Hash, isLeft bool, s []byte) {
level := 1 level := 1
for { for {
// at the root of the bmt just write the result to the result channel // at the root of the bmt just write the result to the result channel
if n == nil { if n == nil {
h.bmt.result <- s h.getTree().result <- s
return return
} }
// otherwise assign child hash to branc // otherwise assign child hash to left or right segment
if isLeft { if isLeft {
n.left = s n.left = s
} else { } else {
n.right = s n.right = s
} }
// the child-thread first arriving will quit // the child-thread first arriving will terminate
if n.toggle() { if n.toggle() {
return return
} }
// the thread coming later now can be sure both left and right children are written // the thread coming second now can be sure both left and right children are written
// it calculates the hash of left|right and pushes it to the parent // so it calculates the hash of left|right and pushes it to the parent
s = doHash(bh, nil, n.left, n.right) s = doSum(bh, nil, n.left, n.right)
isLeft = n.isLeft isLeft = n.isLeft
n = n.parent n = n.parent
level++ level++
@ -476,7 +599,7 @@ func (h *Hasher) writeFinalNode(level int, n *node, bh hash.Hash, isLeft bool, s
// at the root of the bmt just write the result to the result channel // at the root of the bmt just write the result to the result channel
if n == nil { if n == nil {
if s != nil { if s != nil {
h.bmt.result <- s h.getTree().result <- s
} }
return return
} }
@ -485,25 +608,28 @@ func (h *Hasher) writeFinalNode(level int, n *node, bh hash.Hash, isLeft bool, s
// coming from left sister branch // coming from left sister branch
// when the final section's path is going via left child node // when the final section's path is going via left child node
// we include an all-zero subtree hash for the right level and toggle the node. // we include an all-zero subtree hash for the right level and toggle the node.
// when the path is going through right child node, nothing to do
n.right = h.pool.zerohashes[level] n.right = h.pool.zerohashes[level]
if s != nil { if s != nil {
n.left = s n.left = s
// if a left final node carries a hash, it must be the first (and only thread) // if a left final node carries a hash, it must be the first (and only thread)
// so the toggle is already in passive state no need no call // so the toggle is already in passive state no need no call
// yet thread needs to carry on pushing hash to parent // yet thread needs to carry on pushing hash to parent
noHash = false
} else { } else {
// if again first thread then propagate nil and calculate no hash // if again first thread then propagate nil and calculate no hash
noHash = n.toggle() noHash = n.toggle()
} }
} else { } else {
// right sister branch // right sister branch
// if s is nil, then thread arrived first at previous node and here there will be two,
// so no need to do anything
if s != nil { if s != nil {
// if hash was pushed from right child node, write right segment change state
n.right = s n.right = s
// if toggle is true, we arrived first so no hashing just push nil to parent
noHash = n.toggle() noHash = n.toggle()
} else { } else {
// if s is nil, then thread arrived first at previous node and here there will be two,
// so no need to do anything and keep s = nil for parent
noHash = true noHash = true
} }
} }
@ -513,15 +639,16 @@ func (h *Hasher) writeFinalNode(level int, n *node, bh hash.Hash, isLeft bool, s
if noHash { if noHash {
s = nil s = nil
} else { } else {
s = doHash(bh, nil, n.left, n.right) s = doSum(bh, nil, n.left, n.right)
} }
// iterate to parent
isLeft = n.isLeft isLeft = n.isLeft
n = n.parent n = n.parent
level++ level++
} }
} }
// getTree obtains a BMT resource by reserving one from the pool // getTree obtains a BMT resource by reserving one from the pool and assigns it to the bmt field
func (h *Hasher) getTree() *tree { func (h *Hasher) getTree() *tree {
if h.bmt != nil { if h.bmt != nil {
return h.bmt return h.bmt
@ -539,7 +666,7 @@ func (n *node) toggle() bool {
} }
// calculates the hash of the data using hash.Hash // calculates the hash of the data using hash.Hash
func doHash(h hash.Hash, b []byte, data ...[]byte) []byte { func doSum(h hash.Hash, b []byte, data ...[]byte) []byte {
h.Reset() h.Reset()
for _, v := range data { for _, v := range data {
h.Write(v) h.Write(v)
@ -547,6 +674,7 @@ func doHash(h hash.Hash, b []byte, data ...[]byte) []byte {
return h.Sum(b) return h.Sum(b)
} }
// hashstr is a pretty printer for bytes used in tree.draw
func hashstr(b []byte) string { func hashstr(b []byte) string {
end := len(b) end := len(b)
if end > 4 { if end > 4 {

281
swarm/bmt/bmt_test.go
View File

@ -39,13 +39,12 @@ var counts = []int{1, 2, 3, 4, 5, 8, 9, 15, 16, 17, 32, 37, 42, 53, 63, 64, 65,
// calculates the Keccak256 SHA3 hash of the data // calculates the Keccak256 SHA3 hash of the data
func sha3hash(data ...[]byte) []byte { func sha3hash(data ...[]byte) []byte {
h := sha3.NewKeccak256() h := sha3.NewKeccak256()
return doHash(h, nil, data...) return doSum(h, nil, data...)
} }
// TestRefHasher tests that the RefHasher computes the expected BMT hash for // TestRefHasher tests that the RefHasher computes the expected BMT hash for
// all data lengths between 0 and 256 bytes // some small data lengths
func TestRefHasher(t *testing.T) { func TestRefHasher(t *testing.T) {
// the test struct is used to specify the expected BMT hash for // the test struct is used to specify the expected BMT hash for
// segment counts between from and to and lengths from 1 to datalength // segment counts between from and to and lengths from 1 to datalength
type test struct { type test struct {
@ -129,7 +128,7 @@ func TestRefHasher(t *testing.T) {
} }
} }
// tests if hasher responds with correct hash // tests if hasher responds with correct hash comparing the reference implementation return value
func TestHasherEmptyData(t *testing.T) { func TestHasherEmptyData(t *testing.T) {
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
var data []byte var data []byte
@ -140,7 +139,7 @@ func TestHasherEmptyData(t *testing.T) {
bmt := New(pool) bmt := New(pool)
rbmt := NewRefHasher(hasher, count) rbmt := NewRefHasher(hasher, count)
refHash := rbmt.Hash(data) refHash := rbmt.Hash(data)
expHash := Hash(bmt, nil, data) expHash := syncHash(bmt, nil, data)
if !bytes.Equal(expHash, refHash) { if !bytes.Equal(expHash, refHash) {
t.Fatalf("hash mismatch with reference. expected %x, got %x", refHash, expHash) t.Fatalf("hash mismatch with reference. expected %x, got %x", refHash, expHash)
} }
@ -148,7 +147,8 @@ func TestHasherEmptyData(t *testing.T) {
} }
} }
func TestHasherCorrectness(t *testing.T) { // tests sequential write with entire max size written in one go
func TestSyncHasherCorrectness(t *testing.T) {
data := newData(BufferSize) data := newData(BufferSize)
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
size := hasher().Size() size := hasher().Size()
@ -157,7 +157,7 @@ func TestHasherCorrectness(t *testing.T) {
for _, count := range counts { for _, count := range counts {
t.Run(fmt.Sprintf("segments_%v", count), func(t *testing.T) { t.Run(fmt.Sprintf("segments_%v", count), func(t *testing.T) {
max := count * size max := count * size
incr := 1 var incr int
capacity := 1 capacity := 1
pool := NewTreePool(hasher, count, capacity) pool := NewTreePool(hasher, count, capacity)
defer pool.Drain(0) defer pool.Drain(0)
@ -173,6 +173,44 @@ func TestHasherCorrectness(t *testing.T) {
} }
} }
// tests order-neutral concurrent writes with entire max size written in one go
func TestAsyncCorrectness(t *testing.T) {
data := newData(BufferSize)
hasher := sha3.NewKeccak256
size := hasher().Size()
whs := []whenHash{first, last, random}
for _, double := range []bool{false, true} {
for _, wh := range whs {
for _, count := range counts {
t.Run(fmt.Sprintf("double_%v_hash_when_%v_segments_%v", double, wh, count), func(t *testing.T) {
max := count * size
var incr int
capacity := 1
pool := NewTreePool(hasher, count, capacity)
defer pool.Drain(0)
for n := 1; n <= max; n += incr {
incr = 1 + rand.Intn(5)
bmt := New(pool)
d := data[:n]
rbmt := NewRefHasher(hasher, count)
exp := rbmt.Hash(d)
got := syncHash(bmt, nil, d)
if !bytes.Equal(got, exp) {
t.Fatalf("wrong sync hash for datalength %v: expected %x (ref), got %x", n, exp, got)
}
sw := bmt.NewAsyncWriter(double)
got = asyncHashRandom(sw, nil, d, wh)
if !bytes.Equal(got, exp) {
t.Fatalf("wrong async hash for datalength %v: expected %x, got %x", n, exp, got)
}
}
})
}
}
}
}
// Tests that the BMT hasher can be synchronously reused with poolsizes 1 and PoolSize // Tests that the BMT hasher can be synchronously reused with poolsizes 1 and PoolSize
func TestHasherReuse(t *testing.T) { func TestHasherReuse(t *testing.T) {
t.Run(fmt.Sprintf("poolsize_%d", 1), func(t *testing.T) { t.Run(fmt.Sprintf("poolsize_%d", 1), func(t *testing.T) {
@ -183,6 +221,7 @@ func TestHasherReuse(t *testing.T) {
}) })
} }
// tests if bmt reuse is not corrupting result
func testHasherReuse(poolsize int, t *testing.T) { func testHasherReuse(poolsize int, t *testing.T) {
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
pool := NewTreePool(hasher, SegmentCount, poolsize) pool := NewTreePool(hasher, SegmentCount, poolsize)
@ -191,7 +230,7 @@ func testHasherReuse(poolsize int, t *testing.T) {
for i := 0; i < 100; i++ { for i := 0; i < 100; i++ {
data := newData(BufferSize) data := newData(BufferSize)
n := rand.Intn(bmt.DataLength()) n := rand.Intn(bmt.Size())
err := testHasherCorrectness(bmt, hasher, data, n, SegmentCount) err := testHasherCorrectness(bmt, hasher, data, n, SegmentCount)
if err != nil { if err != nil {
t.Fatal(err) t.Fatal(err)
@ -199,8 +238,8 @@ func testHasherReuse(poolsize int, t *testing.T) {
} }
} }
// Tests if pool can be cleanly reused even in concurrent use // Tests if pool can be cleanly reused even in concurrent use by several hasher
func TestBMTHasherConcurrentUse(t *testing.T) { func TestBMTConcurrentUse(t *testing.T) {
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
pool := NewTreePool(hasher, SegmentCount, PoolSize) pool := NewTreePool(hasher, SegmentCount, PoolSize)
defer pool.Drain(0) defer pool.Drain(0)
@ -211,7 +250,7 @@ func TestBMTHasherConcurrentUse(t *testing.T) {
go func() { go func() {
bmt := New(pool) bmt := New(pool)
data := newData(BufferSize) data := newData(BufferSize)
n := rand.Intn(bmt.DataLength()) n := rand.Intn(bmt.Size())
errc <- testHasherCorrectness(bmt, hasher, data, n, 128) errc <- testHasherCorrectness(bmt, hasher, data, n, 128)
}() }()
} }
@ -234,7 +273,7 @@ LOOP:
// Tests BMT Hasher io.Writer interface is working correctly // Tests BMT Hasher io.Writer interface is working correctly
// even multiple short random write buffers // even multiple short random write buffers
func TestBMTHasherWriterBuffers(t *testing.T) { func TestBMTWriterBuffers(t *testing.T) {
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
for _, count := range counts { for _, count := range counts {
@ -247,7 +286,7 @@ func TestBMTHasherWriterBuffers(t *testing.T) {
data := newData(n) data := newData(n)
rbmt := NewRefHasher(hasher, count) rbmt := NewRefHasher(hasher, count)
refHash := rbmt.Hash(data) refHash := rbmt.Hash(data)
expHash := Hash(bmt, nil, data) expHash := syncHash(bmt, nil, data)
if !bytes.Equal(expHash, refHash) { if !bytes.Equal(expHash, refHash) {
t.Fatalf("hash mismatch with reference. expected %x, got %x", refHash, expHash) t.Fatalf("hash mismatch with reference. expected %x, got %x", refHash, expHash)
} }
@ -308,57 +347,65 @@ func testHasherCorrectness(bmt *Hasher, hasher BaseHasherFunc, d []byte, n, coun
data := d[:n] data := d[:n]
rbmt := NewRefHasher(hasher, count) rbmt := NewRefHasher(hasher, count)
exp := sha3hash(span, rbmt.Hash(data)) exp := sha3hash(span, rbmt.Hash(data))
got := Hash(bmt, span, data) got := syncHash(bmt, span, data)
if !bytes.Equal(got, exp) { if !bytes.Equal(got, exp) {
return fmt.Errorf("wrong hash: expected %x, got %x", exp, got) return fmt.Errorf("wrong hash: expected %x, got %x", exp, got)
} }
return err return err
} }
func BenchmarkSHA3_4k(t *testing.B) { benchmarkSHA3(4096, t) } //
func BenchmarkSHA3_2k(t *testing.B) { benchmarkSHA3(4096/2, t) } func BenchmarkBMT(t *testing.B) {
func BenchmarkSHA3_1k(t *testing.B) { benchmarkSHA3(4096/4, t) } for size := 4096; size >= 128; size /= 2 {
func BenchmarkSHA3_512b(t *testing.B) { benchmarkSHA3(4096/8, t) } t.Run(fmt.Sprintf("%v_size_%v", "SHA3", size), func(t *testing.B) {
func BenchmarkSHA3_256b(t *testing.B) { benchmarkSHA3(4096/16, t) } benchmarkSHA3(t, size)
func BenchmarkSHA3_128b(t *testing.B) { benchmarkSHA3(4096/32, t) } })
t.Run(fmt.Sprintf("%v_size_%v", "Baseline", size), func(t *testing.B) {
benchmarkBMTBaseline(t, size)
})
t.Run(fmt.Sprintf("%v_size_%v", "REF", size), func(t *testing.B) {
benchmarkRefHasher(t, size)
})
t.Run(fmt.Sprintf("%v_size_%v", "BMT", size), func(t *testing.B) {
benchmarkBMT(t, size)
})
}
}
func BenchmarkBMTBaseline_4k(t *testing.B) { benchmarkBMTBaseline(4096, t) } type whenHash = int
func BenchmarkBMTBaseline_2k(t *testing.B) { benchmarkBMTBaseline(4096/2, t) }
func BenchmarkBMTBaseline_1k(t *testing.B) { benchmarkBMTBaseline(4096/4, t) }
func BenchmarkBMTBaseline_512b(t *testing.B) { benchmarkBMTBaseline(4096/8, t) }
func BenchmarkBMTBaseline_256b(t *testing.B) { benchmarkBMTBaseline(4096/16, t) }
func BenchmarkBMTBaseline_128b(t *testing.B) { benchmarkBMTBaseline(4096/32, t) }
func BenchmarkRefHasher_4k(t *testing.B) { benchmarkRefHasher(4096, t) } const (
func BenchmarkRefHasher_2k(t *testing.B) { benchmarkRefHasher(4096/2, t) } first whenHash = iota
func BenchmarkRefHasher_1k(t *testing.B) { benchmarkRefHasher(4096/4, t) } last
func BenchmarkRefHasher_512b(t *testing.B) { benchmarkRefHasher(4096/8, t) } random
func BenchmarkRefHasher_256b(t *testing.B) { benchmarkRefHasher(4096/16, t) } )
func BenchmarkRefHasher_128b(t *testing.B) { benchmarkRefHasher(4096/32, t) }
func BenchmarkBMTHasher_4k(t *testing.B) { benchmarkBMTHasher(4096, t) } func BenchmarkBMTAsync(t *testing.B) {
func BenchmarkBMTHasher_2k(t *testing.B) { benchmarkBMTHasher(4096/2, t) } whs := []whenHash{first, last, random}
func BenchmarkBMTHasher_1k(t *testing.B) { benchmarkBMTHasher(4096/4, t) } for size := 4096; size >= 128; size /= 2 {
func BenchmarkBMTHasher_512b(t *testing.B) { benchmarkBMTHasher(4096/8, t) } for _, wh := range whs {
func BenchmarkBMTHasher_256b(t *testing.B) { benchmarkBMTHasher(4096/16, t) } for _, double := range []bool{false, true} {
func BenchmarkBMTHasher_128b(t *testing.B) { benchmarkBMTHasher(4096/32, t) } t.Run(fmt.Sprintf("double_%v_hash_when_%v_size_%v", double, wh, size), func(t *testing.B) {
benchmarkBMTAsync(t, size, wh, double)
})
}
}
}
}
func BenchmarkBMTHasherNoPool_4k(t *testing.B) { benchmarkBMTHasherPool(1, 4096, t) } func BenchmarkPool(t *testing.B) {
func BenchmarkBMTHasherNoPool_2k(t *testing.B) { benchmarkBMTHasherPool(1, 4096/2, t) } caps := []int{1, PoolSize}
func BenchmarkBMTHasherNoPool_1k(t *testing.B) { benchmarkBMTHasherPool(1, 4096/4, t) } for size := 4096; size >= 128; size /= 2 {
func BenchmarkBMTHasherNoPool_512b(t *testing.B) { benchmarkBMTHasherPool(1, 4096/8, t) } for _, c := range caps {
func BenchmarkBMTHasherNoPool_256b(t *testing.B) { benchmarkBMTHasherPool(1, 4096/16, t) } t.Run(fmt.Sprintf("poolsize_%v_size_%v", c, size), func(t *testing.B) {
func BenchmarkBMTHasherNoPool_128b(t *testing.B) { benchmarkBMTHasherPool(1, 4096/32, t) } benchmarkPool(t, c, size)
})
func BenchmarkBMTHasherPool_4k(t *testing.B) { benchmarkBMTHasherPool(PoolSize, 4096, t) } }
func BenchmarkBMTHasherPool_2k(t *testing.B) { benchmarkBMTHasherPool(PoolSize, 4096/2, t) } }
func BenchmarkBMTHasherPool_1k(t *testing.B) { benchmarkBMTHasherPool(PoolSize, 4096/4, t) } }
func BenchmarkBMTHasherPool_512b(t *testing.B) { benchmarkBMTHasherPool(PoolSize, 4096/8, t) }
func BenchmarkBMTHasherPool_256b(t *testing.B) { benchmarkBMTHasherPool(PoolSize, 4096/16, t) }
func BenchmarkBMTHasherPool_128b(t *testing.B) { benchmarkBMTHasherPool(PoolSize, 4096/32, t) }
// benchmarks simple sha3 hash on chunks // benchmarks simple sha3 hash on chunks
func benchmarkSHA3(n int, t *testing.B) { func benchmarkSHA3(t *testing.B, n int) {
data := newData(n) data := newData(n)
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
h := hasher() h := hasher()
@ -366,9 +413,7 @@ func benchmarkSHA3(n int, t *testing.B) {
t.ReportAllocs() t.ReportAllocs()
t.ResetTimer() t.ResetTimer()
for i := 0; i < t.N; i++ { for i := 0; i < t.N; i++ {
h.Reset() doSum(h, nil, data)
h.Write(data)
h.Sum(nil)
} }
} }
@ -377,7 +422,7 @@ func benchmarkSHA3(n int, t *testing.B) {
// doing it on n PoolSize each reusing the base hasher // doing it on n PoolSize each reusing the base hasher
// the premise is that this is the minimum computation needed for a BMT // the premise is that this is the minimum computation needed for a BMT
// therefore this serves as a theoretical optimum for concurrent implementations // therefore this serves as a theoretical optimum for concurrent implementations
func benchmarkBMTBaseline(n int, t *testing.B) { func benchmarkBMTBaseline(t *testing.B, n int) {
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
hashSize := hasher().Size() hashSize := hasher().Size()
data := newData(hashSize) data := newData(hashSize)
@ -394,9 +439,7 @@ func benchmarkBMTBaseline(n int, t *testing.B) {
defer wg.Done() defer wg.Done()
h := hasher() h := hasher()
for atomic.AddInt32(&i, 1) < count { for atomic.AddInt32(&i, 1) < count {
h.Reset() doSum(h, nil, data)
h.Write(data)
h.Sum(nil)
} }
}() }()
} }
@ -405,21 +448,39 @@ func benchmarkBMTBaseline(n int, t *testing.B) {
} }
// benchmarks BMT Hasher // benchmarks BMT Hasher
func benchmarkBMTHasher(n int, t *testing.B) { func benchmarkBMT(t *testing.B, n int) {
data := newData(n) data := newData(n)
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
pool := NewTreePool(hasher, SegmentCount, PoolSize) pool := NewTreePool(hasher, SegmentCount, PoolSize)
bmt := New(pool)
t.ReportAllocs() t.ReportAllocs()
t.ResetTimer() t.ResetTimer()
for i := 0; i < t.N; i++ { for i := 0; i < t.N; i++ {
bmt := New(pool) syncHash(bmt, nil, data)
Hash(bmt, nil, data) }
}
// benchmarks BMT hasher with asynchronous concurrent segment/section writes
func benchmarkBMTAsync(t *testing.B, n int, wh whenHash, double bool) {
data := newData(n)
hasher := sha3.NewKeccak256
pool := NewTreePool(hasher, SegmentCount, PoolSize)
bmt := New(pool).NewAsyncWriter(double)
idxs, segments := splitAndShuffle(bmt.SectionSize(), data)
shuffle(len(idxs), func(i int, j int) {
idxs[i], idxs[j] = idxs[j], idxs[i]
})
t.ReportAllocs()
t.ResetTimer()
for i := 0; i < t.N; i++ {
asyncHash(bmt, nil, n, wh, idxs, segments)
} }
} }
// benchmarks 100 concurrent bmt hashes with pool capacity // benchmarks 100 concurrent bmt hashes with pool capacity
func benchmarkBMTHasherPool(poolsize, n int, t *testing.B) { func benchmarkPool(t *testing.B, poolsize, n int) {
data := newData(n) data := newData(n)
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
pool := NewTreePool(hasher, SegmentCount, poolsize) pool := NewTreePool(hasher, SegmentCount, poolsize)
@ -434,7 +495,7 @@ func benchmarkBMTHasherPool(poolsize, n int, t *testing.B) {
go func() { go func() {
defer wg.Done() defer wg.Done()
bmt := New(pool) bmt := New(pool)
Hash(bmt, nil, data) syncHash(bmt, nil, data)
}() }()
} }
wg.Wait() wg.Wait()
@ -442,7 +503,7 @@ func benchmarkBMTHasherPool(poolsize, n int, t *testing.B) {
} }
// benchmarks the reference hasher // benchmarks the reference hasher
func benchmarkRefHasher(n int, t *testing.B) { func benchmarkRefHasher(t *testing.B, n int) {
data := newData(n) data := newData(n)
hasher := sha3.NewKeccak256 hasher := sha3.NewKeccak256
rbmt := NewRefHasher(hasher, 128) rbmt := NewRefHasher(hasher, 128)
@ -462,3 +523,93 @@ func newData(bufferSize int) []byte {
} }
return data return data
} }
// Hash hashes the data and the span using the bmt hasher
func syncHash(h *Hasher, span, data []byte) []byte {
h.ResetWithLength(span)
h.Write(data)
return h.Sum(nil)
}
func splitAndShuffle(secsize int, data []byte) (idxs []int, segments [][]byte) {
l := len(data)
n := l / secsize
if l%secsize > 0 {
n++
}
for i := 0; i < n; i++ {
idxs = append(idxs, i)
end := (i + 1) * secsize
if end > l {
end = l
}
section := data[i*secsize : end]
segments = append(segments, section)
}
shuffle(n, func(i int, j int) {
idxs[i], idxs[j] = idxs[j], idxs[i]
})
return idxs, segments
}
// splits the input data performs a random shuffle to mock async section writes
func asyncHashRandom(bmt SectionWriter, span []byte, data []byte, wh whenHash) (s []byte) {
idxs, segments := splitAndShuffle(bmt.SectionSize(), data)
return asyncHash(bmt, span, len(data), wh, idxs, segments)
}
// mock for async section writes for BMT SectionWriter
// requires a permutation (a random shuffle) of list of all indexes of segments
// and writes them in order to the appropriate section
// the Sum function is called according to the wh parameter (first, last, random [relative to segment writes])
func asyncHash(bmt SectionWriter, span []byte, l int, wh whenHash, idxs []int, segments [][]byte) (s []byte) {
bmt.Reset()
if l == 0 {
return bmt.Sum(nil, l, span)
}
c := make(chan []byte, 1)
hashf := func() {
c <- bmt.Sum(nil, l, span)
}
maxsize := len(idxs)
var r int
if wh == random {
r = rand.Intn(maxsize)
}
for i, idx := range idxs {
bmt.Write(idx, segments[idx])
if (wh == first || wh == random) && i == r {
go hashf()
}
}
if wh == last {
return bmt.Sum(nil, l, span)
}
return <-c
}
// this is also in swarm/network_test.go
// shuffle pseudo-randomizes the order of elements.
// n is the number of elements. Shuffle panics if n < 0.
// swap swaps the elements with indexes i and j.
func shuffle(n int, swap func(i, j int)) {
if n < 0 {
panic("invalid argument to Shuffle")
}
// Fisher-Yates shuffle: https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle
// Shuffle really ought not be called with n that doesn't fit in 32 bits.
// Not only will it take a very long time, but with 2³¹! possible permutations,
// there's no way that any PRNG can have a big enough internal state to
// generate even a minuscule percentage of the possible permutations.
// Nevertheless, the right API signature accepts an int n, so handle it as best we can.
i := n - 1
for ; i > 1<<31-1-1; i-- {
j := int(rand.Int63n(int64(i + 1)))
swap(i, j)
}
for ; i > 0; i-- {
j := int(rand.Int31n(int32(i + 1)))
swap(i, j)
}
}