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package arbo
import ( "crypto/rand" "encoding/hex" "fmt" "math/big" "runtime" "testing" "time"
qt "github.com/frankban/quicktest" "github.com/iden3/go-merkletree/db/leveldb" "github.com/iden3/go-merkletree/db/memory" )
var debug = true
func debugTime(descr string, time1, time2 time.Duration) { if debug { fmt.Printf("%s was %f times faster than without AddBatch\n", descr, float64(time1)/float64(time2)) } }
func testInit(c *qt.C, n int) (*Tree, *Tree) { tree1, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree1.db.Close()
tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree2.db.Close()
// add the initial leafs to fill a bit the trees before calling the
// AddBatch method
for i := 0; i < n; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree1.Add(k, v); err != nil { c.Fatal(err) } if err := tree2.Add(k, v); err != nil { c.Fatal(err) } } return tree1, tree2 }
func TestAddBatchCaseA(t *testing.T) { c := qt.New(t)
nLeafs := 1024
tree, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree.db.Close()
start := time.Now() for i := 0; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree.Add(k, v); err != nil { t.Fatal(err) } } time1 := time.Since(start)
tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree2.db.Close()
var keys, values [][]byte for i := 0; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keys = append(keys, k) values = append(values, v) } start = time.Now() indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) time2 := time.Since(start) debugTime("CASE A, AddBatch", time1, time2) c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree.Root()) }
func TestAddBatchCaseANotPowerOf2(t *testing.T) { c := qt.New(t)
nLeafs := 1027
tree, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree.db.Close()
for i := 0; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree.Add(k, v); err != nil { t.Fatal(err) } }
tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree2.db.Close()
var keys, values [][]byte for i := 0; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keys = append(keys, k) values = append(values, v) } indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree.Root()) }
func randomBytes(n int) []byte { b := make([]byte, n) _, err := rand.Read(b) if err != nil { panic(err) } return b }
func TestBuildTreeBottomUpSingleThread(t *testing.T) { c := qt.New(t) tree1, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionBlake2b) c.Assert(err, qt.IsNil) defer tree1.db.Close()
tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionBlake2b) c.Assert(err, qt.IsNil) defer tree2.db.Close()
testvectorKeys := []string{ "1c7c2265e368314ca58ed2e1f33a326f1220e234a566d55c3605439dbe411642", "2c9f0a578afff5bfa4e0992a43066460faaab9e8e500db0b16647c701cdb16bf", "1c45cb31f2fa39ec7b9ebf0fad40e0b8296016b5ce8844ae06ff77226379d9a5", "d8af98bbbb585129798ae54d5eabbc9d0561d583faf1663b3a3724d15bda4ec7", } var keys, values [][]byte for i := 0; i < len(testvectorKeys); i++ { key, err := hex.DecodeString(testvectorKeys[i]) c.Assert(err, qt.IsNil) keys = append(keys, key) values = append(values, []byte{0}) }
for i := 0; i < len(keys); i++ { if err := tree1.Add(keys[i], values[i]); err != nil { t.Fatal(err) } }
kvs, err := tree2.keysValuesToKvs(keys, values) c.Assert(err, qt.IsNil) sortKvs(kvs)
tree2.tx, err = tree2.db.NewTx() c.Assert(err, qt.IsNil) // indexes, err := tree2.buildTreeBottomUpSingleThread(kvs)
indexes, err := tree2.buildTreeBottomUp(4, kvs) c.Assert(err, qt.IsNil) // tree1.PrintGraphviz(nil)
// tree2.PrintGraphviz(nil)
c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) // 15b6a23945ae6c81342b7eb14e70fff50812dc8791cb15ec791eb08f91784139
}
func TestAddBatchCaseATestVector(t *testing.T) { c := qt.New(t) tree1, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionBlake2b) c.Assert(err, qt.IsNil) defer tree1.db.Close()
tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionBlake2b) c.Assert(err, qt.IsNil) defer tree2.db.Close()
// leafs in 2nd level subtrees: [ 6, 0, 1, 1]
testvectorKeys := []string{ "1c7c2265e368314ca58ed2e1f33a326f1220e234a566d55c3605439dbe411642", "2c9f0a578afff5bfa4e0992a43066460faaab9e8e500db0b16647c701cdb16bf", "1c45cb31f2fa39ec7b9ebf0fad40e0b8296016b5ce8844ae06ff77226379d9a5", "d8af98bbbb585129798ae54d5eabbc9d0561d583faf1663b3a3724d15bda4ec7", } var keys, values [][]byte for i := 0; i < len(testvectorKeys); i++ { key, err := hex.DecodeString(testvectorKeys[i]) c.Assert(err, qt.IsNil) keys = append(keys, key) values = append(values, []byte{0}) }
for i := 0; i < len(keys); i++ { if err := tree1.Add(keys[i], values[i]); err != nil { t.Fatal(err) } }
indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) // tree1.PrintGraphviz(nil)
// tree2.PrintGraphviz(nil)
c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
// fmt.Println(hex.EncodeToString(tree1.Root()))
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) }
func TestAddBatchCaseARandomKeys(t *testing.T) { c := qt.New(t)
nLeafs := 8
tree1, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionBlake2b) c.Assert(err, qt.IsNil) defer tree1.db.Close()
tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionBlake2b) c.Assert(err, qt.IsNil) defer tree2.db.Close()
var keys, values [][]byte for i := 0; i < nLeafs; i++ { keys = append(keys, randomBytes(32)) // values = append(values, randomBytes(32))
values = append(values, []byte{0}) // fmt.Println("K", hex.EncodeToString(keys[i]))
}
// TMP:
keys[0], _ = hex.DecodeString("1c7c2265e368314ca58ed2e1f33a326f1220e234a566d55c3605439dbe411642") keys[1], _ = hex.DecodeString("2c9f0a578afff5bfa4e0992a43066460faaab9e8e500db0b16647c701cdb16bf") keys[2], _ = hex.DecodeString("9cb87ec67e875c61390edcd1ab517f443591047709a4d4e45b0f9ed980857b8e") keys[3], _ = hex.DecodeString("9b4e9e92e974a589f426ceeb4cb291dc24893513fecf8e8460992dcf52621d4d") keys[4], _ = hex.DecodeString("1c45cb31f2fa39ec7b9ebf0fad40e0b8296016b5ce8844ae06ff77226379d9a5") keys[5], _ = hex.DecodeString("d8af98bbbb585129798ae54d5eabbc9d0561d583faf1663b3a3724d15bda4ec7") keys[6], _ = hex.DecodeString("3cd55dbfb8f975f20a0925dfbdabe79fa2d51dd0268afbb8ba6b01de9dfcdd3c") keys[7], _ = hex.DecodeString("5d0a9d6d9f197c091bf054fac9cb60e11ec723d6610ed8578e617b4d46cb43d5")
for i := 0; i < len(keys); i++ { if err := tree1.Add(keys[i], values[i]); err != nil { t.Fatal(err) } }
indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) // tree1.PrintGraphviz(nil)
// tree2.PrintGraphviz(nil)
c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) }
func TestAddBatchCaseB(t *testing.T) { c := qt.New(t)
nLeafs := 1024 initialNLeafs := 99 // TMP TODO use const minLeafsThreshold-1 once ready
tree1, tree2 := testInit(c, initialNLeafs)
start := time.Now() for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree1.Add(k, v); err != nil { t.Fatal(err) } } time1 := time.Since(start)
// prepare the key-values to be added
var keys, values [][]byte for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keys = append(keys, k) values = append(values, v) } start = time.Now() indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) time2 := time.Since(start) debugTime("CASE B, AddBatch", time1, time2) c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) }
func TestAddBatchCaseBRepeatedLeafs(t *testing.T) { c := qt.New(t)
nLeafs := 1024 initialNLeafs := 99 // TMP TODO use const minLeafsThreshold-1 once ready
tree1, tree2 := testInit(c, initialNLeafs)
for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree1.Add(k, v); err != nil { t.Fatal(err) } }
// prepare the key-values to be added, including already existing keys
var keys, values [][]byte for i := 0; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keys = append(keys, k) values = append(values, v) } indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) c.Check(len(indexes), qt.Equals, initialNLeafs)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) }
func TestCombineInKVSet(t *testing.T) { c := qt.New(t)
var a, b, expected []kv for i := 0; i < 10; i++ { k := BigIntToBytes(big.NewInt(int64(i))) kv := kv{k: k} if i < 7 { a = append(a, kv) } if i >= 4 { b = append(b, kv) } expected = append(expected, kv) }
r, invalids := combineInKVSet(a, b) for i := 0; i < len(r); i++ { c.Assert(r[i].k, qt.DeepEquals, expected[i].k) } c.Assert(len(invalids), qt.Equals, 7-4) }
func TestGetKeysAtLevel(t *testing.T) { c := qt.New(t)
tree, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree.db.Close()
for i := 0; i < 32; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree.Add(k, v); err != nil { t.Fatal(err) } }
keys, err := tree.getKeysAtLevel(2) c.Assert(err, qt.IsNil) expected := []string{ "a5d5f14fce7348e40751496cf25d107d91b0bd043435b9577d778a01f8aa6111", "e9e8dd9b28a7f81d1ff34cb5cefc0146dd848b31031a427b79bdadb62e7f6910", } for i := 0; i < len(keys); i++ { c.Assert(hex.EncodeToString(keys[i]), qt.Equals, expected[i]) }
keys, err = tree.getKeysAtLevel(3) c.Assert(err, qt.IsNil) expected = []string{ "9f12c13e52bca96ad4882a26558e48ab67ddd63e062b839207e893d961390f01", "16d246dd6826ec7346c7328f11c4261facf82d4689f33263ff6e207956a77f21", "4a22cc901c6337daa17a431fa20170684b710e5f551509511492ec24e81a8f2f", "470d61abcbd154977bffc9a9ec5a8daff0caabcf2a25e8441f604c79daa0f82d", } for i := 0; i < len(keys); i++ { c.Assert(hex.EncodeToString(keys[i]), qt.Equals, expected[i]) }
keys, err = tree.getKeysAtLevel(4) c.Assert(err, qt.IsNil) expected = []string{ "7a5d1c81f7b96318012de3417e53d4f13df5b1337718651cd29d0cb0a66edd20", "3408213e4e844bdf3355eb8781c74e31626812898c2dbe141ed6d2c92256fc1c", "dfd8a4d0b6954a3e9f3892e655b58d456eeedf9367f27dfdd9bc2dd6a5577312", "9e99fbec06fb2a6725997c12c4995f62725eb4cce4808523a5a5e80cca64b007", "0befa1e070231dbf4e8ff841c05878cdec823e0c09594c24910a248b3ff5a628", "b7131b0a15c772a57005a4dc5d0d6dd4b3414f5d9ee7408ce5e86c5ab3520e04", "6d1abe0364077846a56bab1deb1a04883eb796b74fe531a7676a9a370f83ab21", "4270116394bede69cf9cd72069eca018238080380bef5de75be8dcbbe968e105", } for i := 0; i < len(keys); i++ { c.Assert(hex.EncodeToString(keys[i]), qt.Equals, expected[i]) } }
func TestSplitInBuckets(t *testing.T) { c := qt.New(t)
nLeafs := 16 kvs := make([]kv, nLeafs) for i := 0; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keyPath := make([]byte, 32) copy(keyPath[:], k) kvs[i].pos = i kvs[i].keyPath = k kvs[i].k = k kvs[i].v = v }
// check keyToBucket results for 4 buckets & 8 keys
c.Assert(keyToBucket(kvs[0].k, 4), qt.Equals, 0) c.Assert(keyToBucket(kvs[1].k, 4), qt.Equals, 2) c.Assert(keyToBucket(kvs[2].k, 4), qt.Equals, 1) c.Assert(keyToBucket(kvs[3].k, 4), qt.Equals, 3) c.Assert(keyToBucket(kvs[4].k, 4), qt.Equals, 0) c.Assert(keyToBucket(kvs[5].k, 4), qt.Equals, 2) c.Assert(keyToBucket(kvs[6].k, 4), qt.Equals, 1) c.Assert(keyToBucket(kvs[7].k, 4), qt.Equals, 3)
// check keyToBucket results for 8 buckets & 8 keys
c.Assert(keyToBucket(kvs[0].k, 8), qt.Equals, 0) c.Assert(keyToBucket(kvs[1].k, 8), qt.Equals, 4) c.Assert(keyToBucket(kvs[2].k, 8), qt.Equals, 2) c.Assert(keyToBucket(kvs[3].k, 8), qt.Equals, 6) c.Assert(keyToBucket(kvs[4].k, 8), qt.Equals, 1) c.Assert(keyToBucket(kvs[5].k, 8), qt.Equals, 5) c.Assert(keyToBucket(kvs[6].k, 8), qt.Equals, 3) c.Assert(keyToBucket(kvs[7].k, 8), qt.Equals, 7)
buckets := splitInBuckets(kvs, 4)
expected := [][]string{ { "00000000", // bucket 0
"08000000", "04000000", "0c000000", }, { "02000000", // bucket 1
"0a000000", "06000000", "0e000000", }, { "01000000", // bucket 2
"09000000", "05000000", "0d000000", }, { "03000000", // bucket 3
"0b000000", "07000000", "0f000000", }, }
for i := 0; i < len(buckets); i++ { sortKvs(buckets[i]) c.Assert(len(buckets[i]), qt.Equals, len(expected[i])) for j := 0; j < len(buckets[i]); j++ { c.Check(hex.EncodeToString(buckets[i][j].k[:4]), qt.Equals, expected[i][j]) } } }
func TestAddBatchCaseC(t *testing.T) { c := qt.New(t)
nLeafs := 1024 initialNLeafs := 101 // TMP TODO use const minLeafsThreshold+1 once ready
tree1, tree2 := testInit(c, initialNLeafs)
start := time.Now() for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree1.Add(k, v); err != nil { t.Fatal(err) } } time1 := time.Since(start)
// prepare the key-values to be added
var keys, values [][]byte for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keys = append(keys, k) values = append(values, v) } start = time.Now() indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) time2 := time.Since(start) debugTime("CASE C, AddBatch", time1, time2) c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) }
func TestAddBatchCaseD(t *testing.T) { c := qt.New(t)
nLeafs := 4096 initialNLeafs := 900
tree1, tree2 := testInit(c, initialNLeafs)
start := time.Now() for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree1.Add(k, v); err != nil { t.Fatal(err) } } time1 := time.Since(start)
// prepare the key-values to be added
var keys, values [][]byte for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keys = append(keys, k) values = append(values, v) } start = time.Now() indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) time2 := time.Since(start) debugTime("CASE D, AddBatch", time1, time2) c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) }
func TestAddBatchCaseE(t *testing.T) { c := qt.New(t)
nLeafs := 4096 initialNLeafs := 900
tree1, _ := testInit(c, initialNLeafs)
start := time.Now() for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) if err := tree1.Add(k, v); err != nil { t.Fatal(err) } } time1 := time.Since(start)
tree2, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon) c.Assert(err, qt.IsNil) defer tree2.db.Close()
var keys, values [][]byte // add the initial leafs to fill a bit the tree before calling the
// AddBatch method
for i := 0; i < initialNLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) // use only the keys of one bucket, store the not used ones for
// later
if i%4 != 0 { keys = append(keys, k) values = append(values, v) continue } if err := tree2.Add(k, v); err != nil { t.Fatal(err) } }
for i := initialNLeafs; i < nLeafs; i++ { k := BigIntToBytes(big.NewInt(int64(i))) v := BigIntToBytes(big.NewInt(int64(i * 2))) keys = append(keys, k) values = append(values, v) } start = time.Now() indexes, err := tree2.AddBatch(keys, values) c.Assert(err, qt.IsNil) time2 := time.Since(start) debugTime("CASE E, AddBatch", time1, time2) c.Check(len(indexes), qt.Equals, 0)
// check that both trees roots are equal
c.Check(tree2.Root(), qt.DeepEquals, tree1.Root()) }
func TestFlp2(t *testing.T) { c := qt.New(t) c.Assert(flp2(31), qt.Equals, 16) c.Assert(flp2(32), qt.Equals, 32) c.Assert(flp2(33), qt.Equals, 32) c.Assert(flp2(63), qt.Equals, 32) c.Assert(flp2(64), qt.Equals, 64) c.Assert(flp2(9000), qt.Equals, 8192) }
func TestAddBatchBench(t *testing.T) { nLeafs := 50_000 fmt.Printf("TestAddBatchBench\n nCPU: %d, nLeafs: %d, hash: Blake2b, db: leveldb\n", runtime.NumCPU(), nLeafs)
// prepare inputs
var ks, vs [][]byte for i := 0; i < nLeafs; i++ { k := randomBytes(32) v := randomBytes(32) ks = append(ks, k) vs = append(vs, v) }
benchAdd(t, ks, vs)
benchAddBatch(t, ks, vs) }
func benchAdd(t *testing.T, ks, vs [][]byte) { c := qt.New(t)
dbDir := t.TempDir() storage, err := leveldb.NewLevelDbStorage(dbDir, false) c.Assert(err, qt.IsNil) tree, err := NewTree(storage, 140, HashFunctionBlake2b) c.Assert(err, qt.IsNil)
start := time.Now() for i := 0; i < len(ks); i++ { err = tree.Add(ks[i], vs[i]) c.Assert(err, qt.IsNil) } printRes(" Add loop", time.Since(start)) }
func benchAddBatch(t *testing.T, ks, vs [][]byte) { c := qt.New(t)
dbDir := t.TempDir() storage, err := leveldb.NewLevelDbStorage(dbDir, false) c.Assert(err, qt.IsNil) tree, err := NewTree(storage, 140, HashFunctionBlake2b) c.Assert(err, qt.IsNil)
start := time.Now() invalids, err := tree.AddBatch(ks, vs) printRes(" AddBatch", time.Since(start)) c.Assert(err, qt.IsNil) c.Assert(len(invalids), qt.Equals, 0) }
func printRes(name string, duration time.Duration) { if debug { fmt.Printf(" %s: %s \n", name, duration) } }
// func printLeafs(name string, t *Tree) {
// w := bytes.NewBufferString("")
//
// err := t.Iterate(func(k, v []byte) {
// if v[0] != PrefixValueLeaf {
// return
// }
// leafK, _ := readLeafValue(v)
// fmt.Fprintf(w, hex.EncodeToString(leafK[:4])+"\n")
// })
// if err != nil {
// panic(err)
// }
// err = ioutil.WriteFile(name, w.Bytes(), 0644)
// if err != nil {
// panic(err)
// }
//
// }
// func TestComputeCosts(t *testing.T) {
// fmt.Println(computeSimpleAddCost(10))
// fmt.Println(computeBottomUpAddCost(10))
//
// fmt.Println(computeSimpleAddCost(1024))
// fmt.Println(computeBottomUpAddCost(1024))
// }
// TODO test tree with nLeafs > minLeafsThreshold, but that at level L, there is
// less keys than nBuckets (so CASE C could be applied if first few leafs are
// added to balance the tree)
// TODO test adding batch with repeated keys in the batch
// TODO test adding batch with multiple invalid keys
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