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

swarm/bmt/bmt.go

@@ -14,7 +14,7 @@
 // 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/>.
 
-// Package bmt provides a binary merkle tree implementation
+// Package bmt provides a binary merkle tree implementation used for swarm chunk hash
 package bmt
 
 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
-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
+of the underlying chunk using any base hash function (e.g., keccak 256 SHA3).
+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
 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
-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
 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.
@@ -46,11 +46,12 @@ Two implementations are provided:
   that is simple to understand
 * Hasher is optimized for speed taking advantage of concurrency with minimalistic
   control structure to coordinate the concurrent routines
-  It implements the following interfaces
-	* standard golang hash.Hash
-	* SwarmHash
-	* io.Writer
-	* TODO: SegmentWriter
+
+  BMT Hasher implements the following interfaces
+	* standard golang hash.Hash - synchronous, reusable
+	* SwarmHash - SumWithSpan provided
+	* io.Writer - synchronous left-to-right datawriter
+	* AsyncWriter - concurrent section writes and asynchronous Sum call
 */
 
 const (
@@ -69,7 +70,7 @@ type BaseHasherFunc func() hash.Hash
 // Hasher a reusable hasher for fixed maximum size chunks representing a BMT
 // - implements the hash.Hash interface
 // - 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
 // - the same hasher instance must not be called concurrently on more than one chunk
 // - the same hasher instance is synchronously reuseable
@@ -81,8 +82,7 @@ type Hasher struct {
 	bmt  *tree     // prebuilt BMT resource for flowcontrol and proofs
 }
 
-// New creates a reusable Hasher
-// implements the hash.Hash interface
+// New creates a reusable BMT Hasher that
 // pulls a new tree from a resource pool for hashing each chunk
 func New(p *TreePool) *Hasher {
 	return &Hasher{
@@ -90,9 +90,9 @@ func New(p *TreePool) *Hasher {
 	}
 }
 
-// TreePool provides a pool of trees used as resources by Hasher
-// a tree popped from the pool is guaranteed to have clean state
-// for hashing a new chunk
+// TreePool provides a pool of trees used as resources by the BMT Hasher.
+// A tree popped from the pool is guaranteed to have a clean state ready
+// for hashing a new chunk.
 type TreePool struct {
 	lock         sync.Mutex
 	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
 	Capacity     int            // pool capacity, controls concurrency
 	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
 	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
 	depth := calculateDepthFor(segmentCount)
 	segmentSize := hasher().Size()
-	zerohashes := make([][]byte, depth)
+	zerohashes := make([][]byte, depth+1)
 	zeros := make([]byte, segmentSize)
 	zerohashes[0] = zeros
 	h := hasher()
-	for i := 1; i < depth; i++ {
-		zeros = doHash(h, nil, zeros, zeros)
+	for i := 1; i < depth+1; i++ {
+		zeros = doSum(h, nil, zeros, zeros)
 		zerohashes[i] = zeros
 	}
 	return &TreePool{
@@ -126,7 +126,7 @@ func NewTreePool(hasher BaseHasherFunc, segmentCount, capacity int) *TreePool {
 		SegmentSize:  segmentSize,
 		SegmentCount: segmentCount,
 		Capacity:     capacity,
-		Datalength:   segmentCount * segmentSize,
+		Size:         segmentCount * segmentSize,
 		Depth:        depth,
 		zerohashes:   zerohashes,
 	}
@@ -155,7 +155,7 @@ func (p *TreePool) reserve() *tree {
 	select {
 	case t = <-p.c:
 	default:
-		t = newTree(p.SegmentSize, p.Depth)
+		t = newTree(p.SegmentSize, p.Depth, p.hasher)
 		p.count++
 	}
 	return t
@@ -173,29 +173,28 @@ func (p *TreePool) release(t *tree) {
 // the tree is 'locked' while not in the pool
 type tree struct {
 	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
-	segment []byte      // the rightmost open segment (not complete)
 	section []byte      // the rightmost open section (double segment)
-	depth   int         // number of levels
 	result  chan []byte // result channel
-	hash    []byte      // to record the result
 	span    []byte      // The span of the data subsumed under the chunk
 }
 
 // node is a reuseable segment hasher representing a node in a BMT
 type node struct {
-	isLeft      bool   // whether it is left side of the parent double segment
-	parent      *node  // pointer to parent node in the BMT
-	state       int32  // atomic increment impl concurrent boolean toggle
-	left, right []byte // this is where the content segment is set
+	isLeft      bool      // whether it is left side of the parent double segment
+	parent      *node     // pointer to parent node in the BMT
+	state       int32     // atomic increment impl concurrent boolean toggle
+	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)
-func newNode(index int, parent *node) *node {
+func newNode(index int, parent *node, hasher hash.Hash) *node {
 	return &node{
 		parent: parent,
 		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
 // - segment size is stipulated to be the size of the hash
-func newTree(segmentSize, depth int) *tree {
-	n := newNode(0, nil)
+func newTree(segmentSize, depth int, hashfunc func() hash.Hash) *tree {
+	n := newNode(0, nil, hashfunc())
 	prevlevel := []*node{n}
 	// 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
 	for level := depth - 2; level >= 0; level-- {
 		nodes := make([]*node, count)
 		for i := 0; i < count; i++ {
 			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
 		count *= 2
@@ -270,13 +274,12 @@ func newTree(segmentSize, depth int) *tree {
 	// the datanode level is the nodes on the last level
 	return &tree{
 		leaves:  prevlevel,
-		result:  make(chan []byte, 1),
-		segment: make([]byte, segmentSize),
+		result:  make(chan []byte),
 		section: make([]byte, 2*segmentSize),
 	}
 }
 
-// methods needed by hash.Hash
+// methods needed to implement hash.Hash
 
 // Size returns the size
 func (h *Hasher) Size() int {
@@ -285,63 +288,40 @@ func (h *Hasher) Size() int {
 
 // BlockSize returns the block size
 func (h *Hasher) BlockSize() int {
-	return h.pool.SegmentSize
-}
-
-// Hash hashes the data and the span using the bmt hasher
-func Hash(h *Hasher, span, data []byte) []byte {
-	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
+	return 2 * h.pool.SegmentSize
 }
 
-// Sum returns the hash of the buffer
+// Sum returns the BMT root hash of the buffer
+// using Sum presupposes sequential synchronous writes (io.Writer interface)
 // hash.Hash interface Sum method appends the byte slice to the underlying
 // data before it calculates and returns the hash of the chunk
 // caller must make sure Sum is not called concurrently with Write, writeSection
-// and WriteSegment (TODO:)
-func (h *Hasher) Sum(b []byte) (r []byte) {
-	return h.sum(b, true, true)
-}
-
-// sum implements Sum taking parameters
-// * 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
+func (h *Hasher) Sum(b []byte) (s []byte) {
+	t := h.getTree()
+	// write the last section with final flag set to true
+	go h.writeSection(t.cursor, t.section, true, true)
+	// wait for the result
+	s = <-t.result
 	span := t.span
-	// fmt.Println(t.draw(bmtHash))
-	if release {
-		h.releaseTree()
-	}
+	// release the tree resource back to the pool
+	h.releaseTree()
 	// b + sha3(span + BMT(pure_chunk))
-	if span == nil {
-		return append(b, bmtHash...)
+	if len(span) == 0 {
+		return append(b, s...)
 	}
-	return doHash(bh, b, span, bmtHash)
+	return doSum(h.pool.hasher(), b, span, s)
 }
 
-// Hasher implements the SwarmHash interface
-
-// Hasher implements the io.Writer interface
+// methods needed to implement the SwarmHash and the io.Writer interfaces
 
-// Write fills the buffer to hash,
-// with every full segment calls writeSection
+// Write calls sequentially add to the buffer to be hashed,
+// with every full segment calls writeSection in a go routine
 func (h *Hasher) Write(b []byte) (int, error) {
 	l := len(b)
-	if l <= 0 {
+	if l == 0 {
 		return 0, nil
 	}
-	t := h.bmt
+	t := h.getTree()
 	secsize := 2 * h.pool.SegmentSize
 	// calculate length of missing bit to complete current open section
 	smax := secsize - t.offset
@@ -359,20 +339,21 @@ func (h *Hasher) Write(b []byte) (int, error) {
 			return l, nil
 		}
 	} else {
-		if t.cur == h.pool.SegmentCount*2 {
+		// if end of a section
+		if t.cursor == h.pool.SegmentCount*2 {
 			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 {
 		// 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
 		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:])
 		// advance cursor
-		t.cur++
+		t.cursor++
 		// smax here represents successive offsets in the input buffer
 		smax += secsize
 	}
@@ -382,83 +363,225 @@ func (h *Hasher) Write(b []byte) (int, error) {
 
 // Reset needs to be called before writing to the hasher
 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
 // the argument is supposed to be the byte slice binary representation of
 // the length of the data subsumed under the hash, i.e., span
 func (h *Hasher) ResetWithLength(span []byte) {
 	h.Reset()
-	h.bmt.span = span
+	h.getTree().span = span
 }
 
 // releaseTree gives back the Tree to the pool whereby it unlocks
 // it resets tree, segment and index
 func (h *Hasher) releaseTree() {
 	t := h.bmt
-	if t != nil {
-		t.cur = 0
+	if t == nil {
+		return
+	}
+	h.bmt = nil
+	go func() {
+		t.cursor = 0
 		t.offset = 0
 		t.span = nil
-		t.hash = nil
-		h.bmt = nil
 		t.section = make([]byte, h.pool.SegmentSize*2)
-		t.segment = make([]byte, h.pool.SegmentSize)
+		select {
+		case <-t.result:
+		default:
+		}
 		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,
+	}
+}
+
+// SectionWriter is an asynchronous segment/section writer interface
+type SectionWriter interface {
+	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
 }
 
-// TODO: writeSegment writes the ith segment into the BMT tree
-// func (h *Hasher) writeSegment(i int, s []byte) {
-// 	go h.run(h.bmt.leaves[i/2], h.pool.hasher(), i%2 == 0, s)
-// }
+// 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
-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
-	n := h.bmt.leaves[i]
-	isLeft := n.isLeft
-	n = n.parent
-	bh := h.pool.hasher()
-	// hash the section
-	s := doHash(bh, nil, section)
+	var n *node
+	var isLeft bool
+	var hasher hash.Hash
+	var level int
+	t := h.getTree()
+	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
 	if final {
 		// for the last segment use writeFinalNode
-		h.writeFinalNode(1, n, bh, isLeft, s)
+		h.writeFinalNode(level, n, hasher, isLeft, section)
 	} else {
-		h.writeNode(n, bh, isLeft, s)
+		h.writeNode(n, hasher, isLeft, section)
 	}
 }
 
 // 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
 // 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) {
 	level := 1
 	for {
 		// at the root of the bmt just write the result to the result channel
 		if n == nil {
-			h.bmt.result <- s
+			h.getTree().result <- s
 			return
 		}
-		// otherwise assign child hash to branc
+		// otherwise assign child hash to left or right segment
 		if isLeft {
 			n.left = s
 		} else {
 			n.right = s
 		}
-		// the child-thread first arriving will quit
+		// the child-thread first arriving will terminate
 		if n.toggle() {
 			return
 		}
-		// the thread coming later now can be sure both left and right children are written
-		// it calculates the hash of left|right and pushes it to the parent
-		s = doHash(bh, nil, n.left, n.right)
+		// the thread coming second now can be sure both left and right children are written
+		// so it calculates the hash of left|right and pushes it to the parent
+		s = doSum(bh, nil, n.left, n.right)
 		isLeft = n.isLeft
 		n = n.parent
 		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
 		if n == nil {
 			if s != nil {
-				h.bmt.result <- s
+				h.getTree().result <- s
 			}
 			return
 		}
@@ -485,25 +608,28 @@ func (h *Hasher) writeFinalNode(level int, n *node, bh hash.Hash, isLeft bool, s
 			// coming from left sister branch
 			// 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.
-			// when the path is going through right child node, nothing to do
 			n.right = h.pool.zerohashes[level]
 			if s != nil {
 				n.left = s
 				// 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
 				// yet thread needs to carry on pushing hash to parent
+				noHash = false
 			} else {
 				// if again first thread then propagate nil and calculate no hash
 				noHash = n.toggle()
 			}
 		} else {
 			// 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 hash was pushed from right child node, write right segment change state
 				n.right = s
+				// if toggle is true, we arrived first so no hashing just push nil to parent
 				noHash = n.toggle()
+
 			} 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
 			}
 		}
@@ -513,15 +639,16 @@ func (h *Hasher) writeFinalNode(level int, n *node, bh hash.Hash, isLeft bool, s
 		if noHash {
 			s = nil
 		} else {
-			s = doHash(bh, nil, n.left, n.right)
+			s = doSum(bh, nil, n.left, n.right)
 		}
+		// iterate to parent
 		isLeft = n.isLeft
 		n = n.parent
 		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 {
 	if h.bmt != nil {
 		return h.bmt
@@ -539,7 +666,7 @@ func (n *node) toggle() bool {
 }
 
 // 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()
 	for _, v := range data {
 		h.Write(v)
@@ -547,6 +674,7 @@ func doHash(h hash.Hash, b []byte, data ...[]byte) []byte {
 	return h.Sum(b)
 }
 
+// hashstr is a pretty printer for bytes used in tree.draw
 func hashstr(b []byte) string {
 	end := len(b)
 	if end > 4 {

swarm/bmt/bmt_test.go

@@ -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
 func sha3hash(data ...[]byte) []byte {
 	h := sha3.NewKeccak256()
-	return doHash(h, nil, data...)
+	return doSum(h, nil, data...)
 }
 
 // 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) {
-
 	// the test struct is used to specify the expected BMT hash for
 	// segment counts between from and to and lengths from 1 to datalength
 	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) {
 	hasher := sha3.NewKeccak256
 	var data []byte
@@ -140,7 +139,7 @@ func TestHasherEmptyData(t *testing.T) {
 			bmt := New(pool)
 			rbmt := NewRefHasher(hasher, count)
 			refHash := rbmt.Hash(data)
-			expHash := Hash(bmt, nil, data)
+			expHash := syncHash(bmt, nil, data)
 			if !bytes.Equal(expHash, refHash) {
 				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)
 	hasher := sha3.NewKeccak256
 	size := hasher().Size()
@@ -157,7 +157,7 @@ func TestHasherCorrectness(t *testing.T) {
 	for _, count := range counts {
 		t.Run(fmt.Sprintf("segments_%v", count), func(t *testing.T) {
 			max := count * size
-			incr := 1
+			var incr int
 			capacity := 1
 			pool := NewTreePool(hasher, count, capacity)
 			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
 func TestHasherReuse(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) {
 	hasher := sha3.NewKeccak256
 	pool := NewTreePool(hasher, SegmentCount, poolsize)
@@ -191,7 +230,7 @@ func testHasherReuse(poolsize int, t *testing.T) {
 
 	for i := 0; i < 100; i++ {
 		data := newData(BufferSize)
-		n := rand.Intn(bmt.DataLength())
+		n := rand.Intn(bmt.Size())
 		err := testHasherCorrectness(bmt, hasher, data, n, SegmentCount)
 		if err != nil {
 			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
-func TestBMTHasherConcurrentUse(t *testing.T) {
+// Tests if pool can be cleanly reused even in concurrent use by several hasher
+func TestBMTConcurrentUse(t *testing.T) {
 	hasher := sha3.NewKeccak256
 	pool := NewTreePool(hasher, SegmentCount, PoolSize)
 	defer pool.Drain(0)
@@ -211,7 +250,7 @@ func TestBMTHasherConcurrentUse(t *testing.T) {
 		go func() {
 			bmt := New(pool)
 			data := newData(BufferSize)
-			n := rand.Intn(bmt.DataLength())
+			n := rand.Intn(bmt.Size())
 			errc <- testHasherCorrectness(bmt, hasher, data, n, 128)
 		}()
 	}
@@ -234,7 +273,7 @@ LOOP:
 
 // Tests BMT Hasher io.Writer interface is working correctly
 // even multiple short random write buffers
-func TestBMTHasherWriterBuffers(t *testing.T) {
+func TestBMTWriterBuffers(t *testing.T) {
 	hasher := sha3.NewKeccak256
 
 	for _, count := range counts {
@@ -247,7 +286,7 @@ func TestBMTHasherWriterBuffers(t *testing.T) {
 			data := newData(n)
 			rbmt := NewRefHasher(hasher, count)
 			refHash := rbmt.Hash(data)
-			expHash := Hash(bmt, nil, data)
+			expHash := syncHash(bmt, nil, data)
 			if !bytes.Equal(expHash, refHash) {
 				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]
 	rbmt := NewRefHasher(hasher, count)
 	exp := sha3hash(span, rbmt.Hash(data))
-	got := Hash(bmt, span, data)
+	got := syncHash(bmt, span, data)
 	if !bytes.Equal(got, exp) {
 		return fmt.Errorf("wrong hash: expected %x, got %x", exp, got)
 	}
 	return err
 }
 
-func BenchmarkSHA3_4k(t *testing.B)   { benchmarkSHA3(4096, t) }
-func BenchmarkSHA3_2k(t *testing.B)   { benchmarkSHA3(4096/2, t) }
-func BenchmarkSHA3_1k(t *testing.B)   { benchmarkSHA3(4096/4, t) }
-func BenchmarkSHA3_512b(t *testing.B) { benchmarkSHA3(4096/8, t) }
-func BenchmarkSHA3_256b(t *testing.B) { benchmarkSHA3(4096/16, t) }
-func BenchmarkSHA3_128b(t *testing.B) { benchmarkSHA3(4096/32, t) }
-
-func BenchmarkBMTBaseline_4k(t *testing.B)   { benchmarkBMTBaseline(4096, t) }
-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) }
-func BenchmarkRefHasher_2k(t *testing.B)   { benchmarkRefHasher(4096/2, t) }
-func BenchmarkRefHasher_1k(t *testing.B)   { benchmarkRefHasher(4096/4, t) }
-func BenchmarkRefHasher_512b(t *testing.B) { benchmarkRefHasher(4096/8, t) }
-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 BenchmarkBMTHasher_2k(t *testing.B)   { benchmarkBMTHasher(4096/2, t) }
-func BenchmarkBMTHasher_1k(t *testing.B)   { benchmarkBMTHasher(4096/4, t) }
-func BenchmarkBMTHasher_512b(t *testing.B) { benchmarkBMTHasher(4096/8, t) }
-func BenchmarkBMTHasher_256b(t *testing.B) { benchmarkBMTHasher(4096/16, t) }
-func BenchmarkBMTHasher_128b(t *testing.B) { benchmarkBMTHasher(4096/32, t) }
-
-func BenchmarkBMTHasherNoPool_4k(t *testing.B)   { benchmarkBMTHasherPool(1, 4096, t) }
-func BenchmarkBMTHasherNoPool_2k(t *testing.B)   { benchmarkBMTHasherPool(1, 4096/2, t) }
-func BenchmarkBMTHasherNoPool_1k(t *testing.B)   { benchmarkBMTHasherPool(1, 4096/4, t) }
-func BenchmarkBMTHasherNoPool_512b(t *testing.B) { benchmarkBMTHasherPool(1, 4096/8, t) }
-func BenchmarkBMTHasherNoPool_256b(t *testing.B) { benchmarkBMTHasherPool(1, 4096/16, t) }
-func BenchmarkBMTHasherNoPool_128b(t *testing.B) { benchmarkBMTHasherPool(1, 4096/32, t) }
-
-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) }
+//
+func BenchmarkBMT(t *testing.B) {
+	for size := 4096; size >= 128; size /= 2 {
+		t.Run(fmt.Sprintf("%v_size_%v", "SHA3", size), func(t *testing.B) {
+			benchmarkSHA3(t, size)
+		})
+		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)
+		})
+	}
+}
+
+type whenHash = int
+
+const (
+	first whenHash = iota
+	last
+	random
+)
+
+func BenchmarkBMTAsync(t *testing.B) {
+	whs := []whenHash{first, last, random}
+	for size := 4096; size >= 128; size /= 2 {
+		for _, wh := range whs {
+			for _, double := range []bool{false, true} {
+				t.Run(fmt.Sprintf("double_%v_hash_when_%v_size_%v", double, wh, size), func(t *testing.B) {
+					benchmarkBMTAsync(t, size, wh, double)
+				})
+			}
+		}
+	}
+}
+
+func BenchmarkPool(t *testing.B) {
+	caps := []int{1, PoolSize}
+	for size := 4096; size >= 128; size /= 2 {
+		for _, c := range caps {
+			t.Run(fmt.Sprintf("poolsize_%v_size_%v", c, size), func(t *testing.B) {
+				benchmarkPool(t, c, size)
+			})
+		}
+	}
+}
 
 // benchmarks simple sha3 hash on chunks
-func benchmarkSHA3(n int, t *testing.B) {
+func benchmarkSHA3(t *testing.B, n int) {
 	data := newData(n)
 	hasher := sha3.NewKeccak256
 	h := hasher()
@@ -366,9 +413,7 @@ func benchmarkSHA3(n int, t *testing.B) {
 	t.ReportAllocs()
 	t.ResetTimer()
 	for i := 0; i < t.N; i++ {
-		h.Reset()
-		h.Write(data)
-		h.Sum(nil)
+		doSum(h, nil, data)
 	}
 }
 
@@ -377,7 +422,7 @@ func benchmarkSHA3(n int, t *testing.B) {
 // doing it on n PoolSize each reusing the base hasher
 // the premise is that this is the minimum computation needed for a BMT
 // 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
 	hashSize := hasher().Size()
 	data := newData(hashSize)
@@ -394,9 +439,7 @@ func benchmarkBMTBaseline(n int, t *testing.B) {
 				defer wg.Done()
 				h := hasher()
 				for atomic.AddInt32(&i, 1) < count {
-					h.Reset()
-					h.Write(data)
-					h.Sum(nil)
+					doSum(h, nil, data)
 				}
 			}()
 		}
@@ -405,21 +448,39 @@ func benchmarkBMTBaseline(n int, t *testing.B) {
 }
 
 // benchmarks BMT Hasher
-func benchmarkBMTHasher(n int, t *testing.B) {
+func benchmarkBMT(t *testing.B, n int) {
 	data := newData(n)
 	hasher := sha3.NewKeccak256
 	pool := NewTreePool(hasher, SegmentCount, PoolSize)
+	bmt := New(pool)
 
 	t.ReportAllocs()
 	t.ResetTimer()
 	for i := 0; i < t.N; i++ {
-		bmt := New(pool)
-		Hash(bmt, nil, data)
+		syncHash(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
-func benchmarkBMTHasherPool(poolsize, n int, t *testing.B) {
+func benchmarkPool(t *testing.B, poolsize, n int) {
 	data := newData(n)
 	hasher := sha3.NewKeccak256
 	pool := NewTreePool(hasher, SegmentCount, poolsize)
@@ -434,7 +495,7 @@ func benchmarkBMTHasherPool(poolsize, n int, t *testing.B) {
 			go func() {
 				defer wg.Done()
 				bmt := New(pool)
-				Hash(bmt, nil, data)
+				syncHash(bmt, nil, data)
 			}()
 		}
 		wg.Wait()
@@ -442,7 +503,7 @@ func benchmarkBMTHasherPool(poolsize, n int, t *testing.B) {
 }
 
 // benchmarks the reference hasher
-func benchmarkRefHasher(n int, t *testing.B) {
+func benchmarkRefHasher(t *testing.B, n int) {
 	data := newData(n)
 	hasher := sha3.NewKeccak256
 	rbmt := NewRefHasher(hasher, 128)
@@ -462,3 +523,93 @@ func newData(bufferSize int) []byte {
 	}
 	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)
+	}
+}