arbo/addbatch.go

package arbo

import (
	"bytes"
	"fmt"
	"math"
	"sort"
)

/*

AddBatch design
===============


CASE A: Empty Tree --> if tree is empty (root==0)
=================================================
- Build the full tree from bottom to top (from all the leaf to the root)


CASE B: ALMOST CASE A, Almost empty Tree --> if Tree has numLeafs < minLeafsThreshold
==============================================================================
- Get the Leafs (key & value) (iterate the tree from the current root getting
the leafs)
- Create a new empty Tree
- Do CASE A for the new Tree, giving the already existing key&values (leafs)
from the original Tree + the new key&values to be added from the AddBatch call


       R                 R
      / \               /  \
     A   *             /    \
        / \           /      \
       B   C         *        *
                    / |      / \
                   /  |     /   \
                  /   |    /     \
           L:    A    B   G       D
                         / \
                        /   \
                       /     \
                      C      *
                            / \
                           /   \
                          /     \
                         ...     ... (nLeafs < minLeafsThreshold)


CASE C: ALMOST CASE B --> if Tree has few Leafs (but numLeafs>=minLeafsThreshold)
==============================================================================
- Use A, B, G, F as Roots of subtrees
- Do CASE B for each subtree
- Then go from L to the Root

              R
             /  \
            /    \
           /      \
          *        *
         / |      / \
        /  |     /   \
       /   |    /     \
L:    A    B   G       D
              / \
             /   \
            /     \
           C      *
                 / \
                /   \
               /     \
              ...    ... (nLeafs >= minLeafsThreshold)



CASE D: Already populated Tree
==============================
- Use A, B, C, D as subtree
- Sort the Keys in Buckets that share the initial part of the path
- For each subtree add there the new leafs

              R
             /  \
            /    \
           /      \
          *        *
         / |      / \
        /  |     /   \
       /   |    /     \
L:    A    B   C       D
     /\   /\  / \     / \
    ...  ... ... ... ... ...


CASE E: Already populated Tree Unbalanced
=========================================
- Need to fill M1 and M2, and then will be able to use CASE D
	- Search for M1 & M2 in the inputed Keys
	- Add M1 & M2 to the Tree
	- From here can use CASE D

              R
             /  \
            /    \
           /      \
          *        *
           |        \
           |         \
           |          \
L:    M1   *   M2      *        (where M1 and M2 are empty)
          / |         /
         /  |        /
        /   |       /
       A    *      *
           / \     | \
          /   \    |  \
         /     \   |   \
        B      *   *   C
              / \  |\
           ... ... | \
                   |  \
                   D  E



Algorithm decision
==================
- if nLeafs==0 (root==0): CASE A
- if nLeafs<minLeafsThreshold: CASE B
- if nLeafs>=minLeafsThreshold && (nLeafs/nBuckets) < minLeafsThreshold: CASE C
- else: CASE D & CASE E


- Multiple tree.Add calls: O(n log n)
	- Used in: cases A, B, C
- Tree from bottom to top: O(log n)
	- Used in: cases D, E

*/

const (
	minLeafsThreshold = uint64(100) // nolint:gomnd // TMP WIP this will be autocalculated
	nBuckets          = uint64(4)   // TMP WIP this will be autocalculated from
)

// AddBatchOpt is the WIP implementation of the AddBatch method in a more
// optimized approach.
func (t *Tree) AddBatchOpt(keys, values [][]byte) ([]int, error) {
	t.updateAccessTime()
	t.Lock()
	defer t.Unlock()

	// TODO if len(keys) is not a power of 2, add padding of empty
	// keys&values. Maybe when len(keyvalues) is not a power of 2, cut at
	// the biggest power of 2 under the len(keys), add those 2**n key-values
	// using the AddBatch approach, and then add the remaining key-values
	// using tree.Add.

	kvs, err := t.keysValuesToKvs(keys, values)
	if err != nil {
		return nil, err
	}

	t.tx, err = t.db.NewTx() // TODO add t.tx.Commit()
	if err != nil {
		return nil, err
	}

	// CASE A: if nLeafs==0 (root==0)
	if bytes.Equal(t.root, t.emptyHash) {
		// sort keys & values by path
		sortKvs(kvs)
		return t.buildTreeBottomUp(kvs)
	}

	// CASE B: if nLeafs<nBuckets
	nLeafs, err := t.GetNLeafs()
	if err != nil {
		return nil, err
	}
	if nLeafs < minLeafsThreshold { // CASE B
		invalids, excedents, err := t.caseB(0, kvs)
		if err != nil {
			return nil, err
		}
		// add the excedents
		for i := 0; i < len(excedents); i++ {
			err = t.add(0, excedents[i].k, excedents[i].v)
			if err != nil {
				invalids = append(invalids, excedents[i].pos)
			}
		}
		return invalids, nil
	}

	// CASE C: if nLeafs>=minLeafsThreshold && (nLeafs/nBuckets) < minLeafsThreshold
	// available parallelization, will need to be a power of 2 (2**n)
	var excedents []kv
	l := int(math.Log2(float64(nBuckets)))
	if nLeafs >= minLeafsThreshold && (nLeafs/nBuckets) < minLeafsThreshold {
		// TODO move to own function
		// 1. go down until level L (L=log2(nBuckets))
		keysAtL, err := t.getKeysAtLevel(l + 1)
		if err != nil {
			return nil, err
		}

		buckets := splitInBuckets(kvs, nBuckets)

		// 2. use keys at level L as roots of the subtrees under each one
		var subRoots [][]byte
		// TODO parallelize
		for i := 0; i < len(keysAtL); i++ {
			bucketTree := Tree{tx: t.tx, db: t.db, maxLevels: t.maxLevels,
				hashFunction: t.hashFunction, root: keysAtL[i]}

			// 3. and do CASE B for each
			_, bucketExcedents, err := bucketTree.caseB(l, buckets[i])
			if err != nil {
				return nil, err
			}
			excedents = append(excedents, bucketExcedents...)
			subRoots = append(subRoots, bucketTree.root)
		}
		// 4. go upFromKeys from the new roots of the subtrees
		newRoot, err := t.upFromKeys(subRoots)
		if err != nil {
			return nil, err
		}
		t.root = newRoot

		var invalids []int
		for i := 0; i < len(excedents); i++ {
			// Add until the level L
			err = t.add(0, excedents[i].k, excedents[i].v)
			if err != nil {
				invalids = append(invalids, excedents[i].pos) // TODO WIP
			}
		}

		return invalids, nil
	}

	// TODO store t.root into DB
	// TODO update NLeafs from DB

	return nil, fmt.Errorf("UNIMPLEMENTED")
}

func (t *Tree) caseB(l int, kvs []kv) ([]int, []kv, error) {
	// get already existing keys
	aKs, aVs, err := t.getLeafs(t.root)
	if err != nil {
		return nil, nil, err
	}
	aKvs, err := t.keysValuesToKvs(aKs, aVs)
	if err != nil {
		return nil, nil, err
	}
	// add already existing key-values to the inputted key-values
	kvs = append(kvs, aKvs...)

	// proceed with CASE A
	sortKvs(kvs)

	// cutPowerOfTwo, the excedent add it as normal Tree.Add
	kvsP2, kvsNonP2 := cutPowerOfTwo(kvs)
	invalids, err := t.buildTreeBottomUp(kvsP2)
	if err != nil {
		return nil, nil, err
	}
	// return the excedents which will be added at the full tree at the end
	return invalids, kvsNonP2, nil
}

func splitInBuckets(kvs []kv, nBuckets uint64) [][]kv {
	buckets := make([][]kv, nBuckets)
	// 1. classify the keyvalues into buckets
	for i := 0; i < len(kvs); i++ {
		pair := kvs[i]

		bucketnum := keyToBucket(pair.k, int(nBuckets))
		buckets[bucketnum] = append(buckets[bucketnum], pair)
	}
	return buckets
}

// TODO rename in a more 'real' name (calculate bucket from/for key)
func keyToBucket(k []byte, nBuckets int) int {
	nLevels := int(math.Log2(float64(nBuckets)))
	b := make([]int, nBuckets)
	for i := 0; i < nBuckets; i++ {
		b[i] = i
	}
	r := b
	mid := len(r) / 2 //nolint:gomnd
	for i := 0; i < nLevels; i++ {
		if int(k[i/8]&(1<<(i%8))) != 0 {
			r = r[mid:]
			mid = len(r) / 2 //nolint:gomnd
		} else {
			r = r[:mid]
			mid = len(r) / 2 //nolint:gomnd
		}
	}
	return r[0]
}

type kv struct {
	pos     int // original position in the array
	keyPath []byte
	k       []byte
	v       []byte
}

// compareBytes compares byte slices where the bytes are compared from left to
// right and each byte is compared by bit from right to left
func compareBytes(a, b []byte) bool {
	// WIP
	for i := 0; i < len(a); i++ {
		for j := 0; j < 8; j++ {
			aBit := a[i] & (1 << j)
			bBit := b[i] & (1 << j)
			if aBit > bBit {
				return false
			} else if aBit < bBit {
				return true
			}
		}
	}
	return false
}

// sortKvs sorts the kv by path
func sortKvs(kvs []kv) {
	sort.Slice(kvs, func(i, j int) bool {
		return compareBytes(kvs[i].keyPath, kvs[j].keyPath)
	})
}

func (t *Tree) keysValuesToKvs(ks, vs [][]byte) ([]kv, error) {
	if len(ks) != len(vs) {
		return nil, fmt.Errorf("len(keys)!=len(values) (%d!=%d)",
			len(ks), len(vs))
	}
	kvs := make([]kv, len(ks))
	for i := 0; i < len(ks); i++ {
		keyPath := make([]byte, t.hashFunction.Len())
		copy(keyPath[:], ks[i])
		kvs[i].pos = i
		kvs[i].keyPath = ks[i]
		kvs[i].k = ks[i]
		kvs[i].v = vs[i]
	}

	return kvs, nil
}

/*
func (t *Tree) kvsToKeysValues(kvs []kv) ([][]byte, [][]byte) {
	ks := make([][]byte, len(kvs))
	vs := make([][]byte, len(kvs))
	for i := 0; i < len(kvs); i++ {
		ks[i] = kvs[i].k
		vs[i] = kvs[i].v
	}
	return ks, vs
}
*/

// keys & values must be sorted by path, and the array ks must be length
// multiple of 2
// TODO return index of failed keyvaules
func (t *Tree) buildTreeBottomUp(kvs []kv) ([]int, error) {
	// build the leafs
	leafKeys := make([][]byte, len(kvs))
	for i := 0; i < len(kvs); i++ {
		// TODO handle the case where Key&Value == 0
		leafKey, leafValue, err := newLeafValue(t.hashFunction, kvs[i].k, kvs[i].v)
		if err != nil {
			return nil, err
		}
		// store leafKey & leafValue to db
		if err := t.tx.Put(leafKey, leafValue); err != nil {
			return nil, err
		}
		leafKeys[i] = leafKey
	}
	// TODO parallelize t.upFromKeys until level log2(nBuckets) is reached
	r, err := t.upFromKeys(leafKeys)
	if err != nil {
		return nil, err
	}
	t.root = r
	return nil, nil
}

// keys & values must be sorted by path, and the array ks must be length
// multiple of 2
func (t *Tree) upFromKeys(ks [][]byte) ([]byte, error) {
	if len(ks) == 1 {
		return ks[0], nil
	}

	var rKs [][]byte
	for i := 0; i < len(ks); i += 2 {
		// TODO handle the case where Key&Value == 0
		k, v, err := newIntermediate(t.hashFunction, ks[i], ks[i+1])
		if err != nil {
			return nil, err
		}
		// store k-v to db
		if err = t.tx.Put(k, v); err != nil {
			return nil, err
		}
		rKs = append(rKs, k)
	}
	return t.upFromKeys(rKs)
}

func (t *Tree) getLeafs(root []byte) ([][]byte, [][]byte, error) {
	var ks, vs [][]byte
	err := t.iter(root, func(k, v []byte) {
		if v[0] != PrefixValueLeaf {
			return
		}
		leafK, leafV := readLeafValue(v)
		ks = append(ks, leafK)
		vs = append(vs, leafV)
	})
	return ks, vs, err
}

func (t *Tree) getKeysAtLevel(l int) ([][]byte, error) {
	var keys [][]byte
	err := t.iterWithStop(t.root, 0, func(currLvl int, k, v []byte) bool {
		if currLvl == l {
			keys = append(keys, k)
		}
		if currLvl >= l {
			return true // to stop the iter from going down
		}
		return false
	})

	return keys, err
}

// cutPowerOfTwo returns []kv of length that is a power of 2, and a second []kv
// with the extra elements that don't fit in a power of 2 length
func cutPowerOfTwo(kvs []kv) ([]kv, []kv) {
	x := len(kvs)
	if (x & (x - 1)) != 0 {
		p2 := highestPowerOfTwo(x)
		return kvs[:p2], kvs[p2:]
	}
	return kvs, nil
}

func highestPowerOfTwo(n int) int {
	res := 0
	for i := n; i >= 1; i-- {
		if (i & (i - 1)) == 0 {
			res = i
			break
		}
	}
	return res
}

// func computeSimpleAddCost(nLeafs int) int {
//         // nLvls 2^nLvls
//         nLvls := int(math.Log2(float64(nLeafs)))
//         return nLvls * int(math.Pow(2, float64(nLvls)))
// }
//
// func computeBottomUpAddCost(nLeafs int) int {
//         // 2^nLvls * 2 - 1
//         nLvls := int(math.Log2(float64(nLeafs)))
//         return (int(math.Pow(2, float64(nLvls))) * 2) - 1
// }