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5 Commits

Author SHA1 Message Date
Elichai Turkel
e3463b7268 Replace Keccak256 in oPoW with CSHAKE256 with domain seperation (#1842)
* Replace keccak with CSHAKE256 in oPoW

* Add benchmarks to hash writers to compare blake2b to the CSHAKE

* Update genesis blocks

* Update tests

* Define genesis's block level to be the maximal one

* Add message to genesis coinbase

* Add comments to genesis coinbase

* Fix tests

Co-authored-by: Ori Newman <orinewman1@gmail.com>
2021-11-07 18:36:30 +02:00
Ori Newman
a2173ef80a Switch PoW to a keccak heavyhash variant (#1841)
* Add another hash domain for HeavyHash

* Add a xoShiRo256PlusPlus implementation

* Add a HeavyHash implementation

* Replace our current PoW algorithm with oPoW

* Change to pow hash to keccak256

* Fix genesis

* Fix tests

Co-authored-by: Elichai Turkel <elichai.turkel@gmail.com>
2021-11-07 11:17:15 +02:00
stasatdaglabs
aeb4500b61 Add the daglabs-dev mainnet dnsseeder. (#1840) 2021-11-07 10:39:54 +02:00
Ori Newman
0a1daae319 Allow mainnet flag and raise wallet fee (#1838)
Co-authored-by: stasatdaglabs <39559713+stasatdaglabs@users.noreply.github.com>
2021-11-07 10:04:27 +02:00
stasatdaglabs
131cd3357e Rename FixedSubsidySwitchHashRateDifference to FixedSubsidySwitchHashRateThreshold and set its value to 150GH/s. (#1837) 2021-11-07 09:33:39 +02:00
21 changed files with 566 additions and 206 deletions

View File

@@ -28,7 +28,7 @@ func (s *server) CreateUnsignedTransaction(_ context.Context, request *pb.Create
}
// TODO: Implement a better fee estimation mechanism
const feePerInput = 1000
const feePerInput = 10000
selectedUTXOs, changeSompi, err := s.selectUTXOs(request.Amount, feePerInput)
if err != nil {
return nil, err

View File

@@ -206,7 +206,7 @@ func (f *factory) NewConsensus(config *Config, db infrastructuredatabase.Databas
config.CoinbasePayloadScriptPublicKeyMaxLength,
config.GenesisHash,
config.FixedSubsidySwitchPruningPointInterval,
config.FixedSubsidySwitchHashRateDifference,
config.FixedSubsidySwitchHashRateThreshold,
dagTraversalManager,
ghostdagDataStore,
acceptanceDataStore,

View File

@@ -49,7 +49,7 @@ func (c *coinbaseManager) isBlockRewardFixed(stagingArea *model.StagingArea, blo
blueWorkDifference := new(big.Int).Sub(highPruningPointHeader.BlueWork(), lowPruningPointHeader.BlueWork())
blueScoreDifference := new(big.Int).SetUint64(highPruningPointHeader.BlueScore() - lowPruningPointHeader.BlueScore())
estimatedAverageHashRate := new(big.Int).Div(blueWorkDifference, blueScoreDifference)
if estimatedAverageHashRate.Cmp(c.fixedSubsidySwitchHashRateDifference) >= 0 {
if estimatedAverageHashRate.Cmp(c.fixedSubsidySwitchHashRateThreshold) >= 0 {
return true, nil
}

View File

@@ -32,7 +32,7 @@ func TestBlockRewardSwitch(t *testing.T) {
// Set the hash rate difference such that the switch would trigger exactly
// on the `FixedSubsidySwitchPruningPointInterval + 1`th pruning point
workToAcceptGenesis := difficulty.CalcWork(consensusConfig.GenesisBlock.Header.Bits())
consensusConfig.FixedSubsidySwitchHashRateDifference = workToAcceptGenesis
consensusConfig.FixedSubsidySwitchHashRateThreshold = workToAcceptGenesis
// Set the min, max, and post-switch subsidies to values that would make it
// easy to tell whether the switch happened

View File

@@ -22,7 +22,7 @@ type coinbaseManager struct {
coinbasePayloadScriptPublicKeyMaxLength uint8
genesisHash *externalapi.DomainHash
fixedSubsidySwitchPruningPointInterval uint64
fixedSubsidySwitchHashRateDifference *big.Int
fixedSubsidySwitchHashRateThreshold *big.Int
databaseContext model.DBReader
dagTraversalManager model.DAGTraversalManager
@@ -364,7 +364,7 @@ func New(
coinbasePayloadScriptPublicKeyMaxLength uint8,
genesisHash *externalapi.DomainHash,
fixedSubsidySwitchPruningPointInterval uint64,
fixedSubsidySwitchHashRateDifference *big.Int,
fixedSubsidySwitchHashRateThreshold *big.Int,
dagTraversalManager model.DAGTraversalManager,
ghostdagDataStore model.GHOSTDAGDataStore,
@@ -385,7 +385,7 @@ func New(
coinbasePayloadScriptPublicKeyMaxLength: coinbasePayloadScriptPublicKeyMaxLength,
genesisHash: genesisHash,
fixedSubsidySwitchPruningPointInterval: fixedSubsidySwitchPruningPointInterval,
fixedSubsidySwitchHashRateDifference: fixedSubsidySwitchHashRateDifference,
fixedSubsidySwitchHashRateThreshold: fixedSubsidySwitchHashRateThreshold,
dagTraversalManager: dagTraversalManager,
ghostdagDataStore: ghostdagDataStore,

View File

@@ -22,6 +22,150 @@ func TestBlockWindow(t *testing.T) {
expectedWindow []string
}{
dagconfig.MainnetParams.Name: {
{
parents: []string{"A"},
id: "B",
expectedWindow: []string{},
},
{
parents: []string{"B"},
id: "C",
expectedWindow: []string{"B"},
},
{
parents: []string{"B"},
id: "D",
expectedWindow: []string{"B"},
},
{
parents: []string{"C", "D"},
id: "E",
expectedWindow: []string{"C", "D", "B"},
},
{
parents: []string{"C", "D"},
id: "F",
expectedWindow: []string{"C", "D", "B"},
},
{
parents: []string{"A"},
id: "G",
expectedWindow: []string{},
},
{
parents: []string{"G"},
id: "H",
expectedWindow: []string{"G"},
},
{
parents: []string{"H", "F"},
id: "I",
expectedWindow: []string{"F", "H", "C", "D", "B", "G"},
},
{
parents: []string{"I"},
id: "J",
expectedWindow: []string{"I", "F", "H", "C", "D", "B", "G"},
},
{
parents: []string{"J"},
id: "K",
expectedWindow: []string{"J", "I", "F", "H", "C", "D", "B", "G"},
},
{
parents: []string{"K"},
id: "L",
expectedWindow: []string{"K", "J", "I", "F", "H", "C", "D", "B", "G"},
},
{
parents: []string{"L"},
id: "M",
expectedWindow: []string{"L", "K", "J", "I", "F", "H", "C", "D", "B", "G"},
},
{
parents: []string{"M"},
id: "N",
expectedWindow: []string{"M", "L", "K", "J", "I", "F", "H", "C", "D", "B"},
},
{
parents: []string{"N"},
id: "O",
expectedWindow: []string{"N", "M", "L", "K", "J", "I", "F", "H", "C", "D"},
},
},
dagconfig.TestnetParams.Name: {
{
parents: []string{"A"},
id: "B",
expectedWindow: []string{},
},
{
parents: []string{"B"},
id: "C",
expectedWindow: []string{"B"},
},
{
parents: []string{"B"},
id: "D",
expectedWindow: []string{"B"},
},
{
parents: []string{"C", "D"},
id: "E",
expectedWindow: []string{"C", "D", "B"},
},
{
parents: []string{"C", "D"},
id: "F",
expectedWindow: []string{"C", "D", "B"},
},
{
parents: []string{"A"},
id: "G",
expectedWindow: []string{},
},
{
parents: []string{"G"},
id: "H",
expectedWindow: []string{"G"},
},
{
parents: []string{"H", "F"},
id: "I",
expectedWindow: []string{"F", "H", "C", "D", "G", "B"},
},
{
parents: []string{"I"},
id: "J",
expectedWindow: []string{"I", "F", "H", "C", "D", "G", "B"},
},
{
parents: []string{"J"},
id: "K",
expectedWindow: []string{"J", "I", "F", "H", "C", "D", "G", "B"},
},
{
parents: []string{"K"},
id: "L",
expectedWindow: []string{"K", "J", "I", "F", "H", "C", "D", "G", "B"},
},
{
parents: []string{"L"},
id: "M",
expectedWindow: []string{"L", "K", "J", "I", "F", "H", "C", "D", "G", "B"},
},
{
parents: []string{"M"},
id: "N",
expectedWindow: []string{"M", "L", "K", "J", "I", "F", "H", "C", "D", "G"},
},
{
parents: []string{"N"},
id: "O",
expectedWindow: []string{"N", "M", "L", "K", "J", "I", "F", "H", "C", "D"},
},
},
dagconfig.DevnetParams.Name: {
{
parents: []string{"A"},
id: "B",
@@ -93,7 +237,7 @@ func TestBlockWindow(t *testing.T) {
expectedWindow: []string{"N", "M", "L", "K", "J", "I", "F", "D", "C", "H"},
},
},
dagconfig.TestnetParams.Name: {
dagconfig.SimnetParams.Name: {
{
parents: []string{"A"},
id: "B",
@@ -110,12 +254,12 @@ func TestBlockWindow(t *testing.T) {
expectedWindow: []string{"B"},
},
{
parents: []string{"C", "D"},
parents: []string{"D", "C"},
id: "E",
expectedWindow: []string{"D", "C", "B"},
},
{
parents: []string{"C", "D"},
parents: []string{"D", "C"},
id: "F",
expectedWindow: []string{"D", "C", "B"},
},
@@ -165,150 +309,6 @@ func TestBlockWindow(t *testing.T) {
expectedWindow: []string{"N", "M", "L", "K", "J", "I", "F", "D", "H", "C"},
},
},
dagconfig.DevnetParams.Name: {
{
parents: []string{"A"},
id: "B",
expectedWindow: []string{},
},
{
parents: []string{"B"},
id: "C",
expectedWindow: []string{"B"},
},
{
parents: []string{"B"},
id: "D",
expectedWindow: []string{"B"},
},
{
parents: []string{"D", "C"},
id: "E",
expectedWindow: []string{"D", "C", "B"},
},
{
parents: []string{"D", "C"},
id: "F",
expectedWindow: []string{"D", "C", "B"},
},
{
parents: []string{"A"},
id: "G",
expectedWindow: []string{},
},
{
parents: []string{"G"},
id: "H",
expectedWindow: []string{"G"},
},
{
parents: []string{"H", "F"},
id: "I",
expectedWindow: []string{"F", "D", "C", "H", "G", "B"},
},
{
parents: []string{"I"},
id: "J",
expectedWindow: []string{"I", "F", "D", "C", "H", "G", "B"},
},
{
parents: []string{"J"},
id: "K",
expectedWindow: []string{"J", "I", "F", "D", "C", "H", "G", "B"},
},
{
parents: []string{"K"},
id: "L",
expectedWindow: []string{"K", "J", "I", "F", "D", "C", "H", "G", "B"},
},
{
parents: []string{"L"},
id: "M",
expectedWindow: []string{"L", "K", "J", "I", "F", "D", "C", "H", "G", "B"},
},
{
parents: []string{"M"},
id: "N",
expectedWindow: []string{"M", "L", "K", "J", "I", "F", "D", "C", "H", "G"},
},
{
parents: []string{"N"},
id: "O",
expectedWindow: []string{"N", "M", "L", "K", "J", "I", "F", "D", "C", "H"},
},
},
dagconfig.SimnetParams.Name: {
{
parents: []string{"A"},
id: "B",
expectedWindow: []string{},
},
{
parents: []string{"B"},
id: "C",
expectedWindow: []string{"B"},
},
{
parents: []string{"B"},
id: "D",
expectedWindow: []string{"B"},
},
{
parents: []string{"D", "C"},
id: "E",
expectedWindow: []string{"C", "D", "B"},
},
{
parents: []string{"D", "C"},
id: "F",
expectedWindow: []string{"C", "D", "B"},
},
{
parents: []string{"A"},
id: "G",
expectedWindow: []string{},
},
{
parents: []string{"G"},
id: "H",
expectedWindow: []string{"G"},
},
{
parents: []string{"H", "F"},
id: "I",
expectedWindow: []string{"F", "C", "D", "H", "G", "B"},
},
{
parents: []string{"I"},
id: "J",
expectedWindow: []string{"I", "F", "C", "D", "H", "G", "B"},
},
{
parents: []string{"J"},
id: "K",
expectedWindow: []string{"J", "I", "F", "C", "D", "H", "G", "B"},
},
{
parents: []string{"K"},
id: "L",
expectedWindow: []string{"K", "J", "I", "F", "C", "D", "H", "G", "B"},
},
{
parents: []string{"L"},
id: "M",
expectedWindow: []string{"L", "K", "J", "I", "F", "C", "D", "H", "G", "B"},
},
{
parents: []string{"M"},
id: "N",
expectedWindow: []string{"M", "L", "K", "J", "I", "F", "C", "D", "H", "G"},
},
{
parents: []string{"N"},
id: "O",
expectedWindow: []string{"N", "M", "L", "K", "J", "I", "F", "C", "D", "H"},
},
},
}
testutils.ForAllNets(t, true, func(t *testing.T, consensusConfig *consensus.Config) {
consensusConfig.K = 1

View File

@@ -19,6 +19,12 @@ import (
func TestDifficulty(t *testing.T) {
testutils.ForAllNets(t, true, func(t *testing.T, consensusConfig *consensus.Config) {
// Mainnet's genesis is too new, so if we'll build on it we'll get to the future very quickly.
// TODO: Once it gets older, we should unskip this test.
if consensusConfig.Name == "kaspa-mainnet" {
return
}
if consensusConfig.DisableDifficultyAdjustment {
return
}
@@ -132,7 +138,7 @@ func TestDifficulty(t *testing.T) {
case dagconfig.TestnetParams.Name, dagconfig.DevnetParams.Name:
expectedBits = uint32(0x1e7f83df)
case dagconfig.MainnetParams.Name:
expectedBits = uint32(0x207f83df)
expectedBits = uint32(0x1e7f83df)
}
if tip.Header.Bits() != expectedBits {

View File

@@ -37,10 +37,10 @@ func TestPruning(t *testing.T) {
dagconfig.SimnetParams.Name: "1582",
},
"dag-for-test-pruning.json": {
dagconfig.MainnetParams.Name: "503",
dagconfig.MainnetParams.Name: "502",
dagconfig.TestnetParams.Name: "502",
dagconfig.DevnetParams.Name: "503",
dagconfig.SimnetParams.Name: "503",
dagconfig.DevnetParams.Name: "502",
dagconfig.SimnetParams.Name: "502",
},
}

View File

@@ -4,6 +4,7 @@ import (
"crypto/sha256"
"github.com/pkg/errors"
"golang.org/x/crypto/blake2b"
"golang.org/x/crypto/sha3"
)
const (
@@ -13,6 +14,7 @@ const (
transcationSigningECDSADomain = "TransactionSigningHashECDSA"
blockDomain = "BlockHash"
proofOfWorkDomain = "ProofOfWorkHash"
heavyHashDomain = "HeavyHash"
merkleBranchDomain = "MerkleBranchHash"
)
@@ -65,12 +67,15 @@ func NewBlockHashWriter() HashWriter {
}
// NewPoWHashWriter Returns a new HashWriter used for the PoW function
func NewPoWHashWriter() HashWriter {
blake, err := blake2b.New256([]byte(proofOfWorkDomain))
if err != nil {
panic(errors.Wrapf(err, "this should never happen. %s is less than 64 bytes", proofOfWorkDomain))
}
return HashWriter{blake}
func NewPoWHashWriter() ShakeHashWriter {
shake256 := sha3.NewCShake256(nil, []byte(proofOfWorkDomain))
return ShakeHashWriter{shake256}
}
// NewHeavyHashWriter Returns a new HashWriter used for the HeavyHash function
func NewHeavyHashWriter() ShakeHashWriter {
shake256 := sha3.NewCShake256(nil, []byte(heavyHashDomain))
return ShakeHashWriter{shake256}
}
// NewMerkleBranchHashWriter Returns a new HashWriter used for a merkle tree branch

View File

@@ -3,6 +3,7 @@ package hashes
import (
"github.com/kaspanet/kaspad/domain/consensus/model/externalapi"
"github.com/pkg/errors"
"golang.org/x/crypto/sha3"
"hash"
)
@@ -30,3 +31,29 @@ func (h HashWriter) Finalize() *externalapi.DomainHash {
copy(sum[:], h.Sum(sum[:0]))
return externalapi.NewDomainHashFromByteArray(&sum)
}
// ShakeHashWriter is exactly the same as HashWriter but for CShake256
type ShakeHashWriter struct {
sha3.ShakeHash
}
// InfallibleWrite is just like write but doesn't return anything
func (h *ShakeHashWriter) InfallibleWrite(p []byte) {
// This write can never return an error, this is part of the hash.Hash interface contract.
_, err := h.Write(p)
if err != nil {
panic(errors.Wrap(err, "this should never happen. sha3.ShakeHash interface promises to not return errors."))
}
}
// Finalize returns the resulting hash
func (h *ShakeHashWriter) Finalize() *externalapi.DomainHash {
var sum [externalapi.DomainHashSize]byte
// This should prevent `Sum` for allocating an output buffer, by using the DomainHash buffer. we still copy because we don't want to rely on that.
_, err := h.Read(sum[:])
if err != nil {
panic(errors.Wrap(err, "this should never happen. sha3.ShakeHash interface promises to not return errors."))
}
h.ShakeHash = nil // prevent double reading as it will return a different hash
return externalapi.NewDomainHashFromByteArray(&sum)
}

View File

@@ -0,0 +1,50 @@
package hashes
import (
"math/rand"
"testing"
)
func BenchmarkNewBlockHashWriterSmall(b *testing.B) {
r := rand.New(rand.NewSource(0))
var someBytes [32]byte
r.Read(someBytes[:])
for i := 0; i < b.N; i++ {
hasher := NewBlockHashWriter()
hasher.InfallibleWrite(someBytes[:])
hasher.Finalize()
}
}
func BenchmarkNewBlockHashWriterBig(b *testing.B) {
r := rand.New(rand.NewSource(0))
var someBytes [1024]byte
r.Read(someBytes[:])
for i := 0; i < b.N; i++ {
hasher := NewBlockHashWriter()
hasher.InfallibleWrite(someBytes[:])
hasher.Finalize()
}
}
func BenchmarkNewHeavyHashWriterSmall(b *testing.B) {
r := rand.New(rand.NewSource(0))
var someBytes [32]byte
r.Read(someBytes[:])
for i := 0; i < b.N; i++ {
hasher := NewHeavyHashWriter()
hasher.InfallibleWrite(someBytes[:])
hasher.Finalize()
}
}
func BenchmarkNewHeavyHashWriterBig(b *testing.B) {
r := rand.New(rand.NewSource(0))
var someBytes [1024]byte
r.Read(someBytes[:])
for i := 0; i < b.N; i++ {
hasher := NewHeavyHashWriter()
hasher.InfallibleWrite(someBytes[:])
hasher.Finalize()
}
}

View File

@@ -0,0 +1,91 @@
package pow
import (
"github.com/kaspanet/kaspad/domain/consensus/model/externalapi"
"github.com/kaspanet/kaspad/domain/consensus/utils/hashes"
"math"
)
const eps float64 = 1e-9
type matrix [64][64]uint16
func generateMatrix(hash *externalapi.DomainHash) *matrix {
var mat matrix
generator := newxoShiRo256PlusPlus(hash)
for {
for i := range mat {
for j := 0; j < 64; j += 16 {
val := generator.Uint64()
for shift := 0; shift < 16; shift++ {
mat[i][j+shift] = uint16(val >> (4 * shift) & 0x0F)
}
}
}
if mat.computeRank() == 64 {
return &mat
}
}
}
func (mat *matrix) computeRank() int {
var B [64][64]float64
for i := range B {
for j := range B[0] {
B[i][j] = float64(mat[i][j])
}
}
var rank int
var rowSelected [64]bool
for i := 0; i < 64; i++ {
var j int
for j := 0; j < 64; j++ {
if !rowSelected[j] && math.Abs(B[j][i]) > eps {
break
}
}
if j != 64 {
rank++
rowSelected[j] = true
for p := i + 1; p < 64; p++ {
B[j][p] /= B[j][i]
}
for k := 0; k < 64; k++ {
if k != j && math.Abs(B[k][i]) > eps {
for p := i + 1; p < 64; p++ {
B[k][p] -= B[j][p] * B[k][i]
}
}
}
}
}
return rank
}
func (mat *matrix) HeavyHash(hash *externalapi.DomainHash) *externalapi.DomainHash {
hashBytes := hash.ByteArray()
var vector [64]uint16
var product [64]uint16
for i := 0; i < 32; i++ {
vector[2*i] = uint16(hashBytes[i] >> 4)
vector[2*i+1] = uint16(hashBytes[i] & 0x0F)
}
// Matrix-vector multiplication, and convert to 4 bits.
for i := 0; i < 64; i++ {
var sum uint16
for j := 0; j < 64; j++ {
sum += mat[i][j] * vector[j]
}
product[i] = sum >> 10
}
// Concatenate 4 LSBs back to 8 bit xor with sum1
var res [32]byte
for i := range res {
res[i] = hashBytes[i] ^ (byte(product[2*i]<<4) | byte(product[2*i+1]))
}
// Hash again
writer := hashes.NewHeavyHashWriter()
writer.InfallibleWrite(res[:])
return writer.Finalize()
}

View File

@@ -0,0 +1,102 @@
package pow
import (
"bytes"
"encoding/hex"
"github.com/kaspanet/kaspad/domain/consensus/utils/hashes"
"testing"
)
func BenchmarkMatrix_HeavyHash(b *testing.B) {
input := []byte("BenchmarkMatrix_HeavyHash")
writer := hashes.NewPoWHashWriter()
writer.InfallibleWrite(input)
hash := writer.Finalize()
matrix := generateMatrix(hash)
for i := 0; i < b.N; i++ {
hash = matrix.HeavyHash(hash)
}
}
func TestMatrix_HeavyHash(t *testing.T) {
expected, err := hex.DecodeString("87689f379943eaf9b7475ca95325687772bfcc68fc7899caeb4409ec4590c325")
if err != nil {
t.Fatal(err)
}
input := []byte{0xC1, 0xEC, 0xFD, 0xFC}
writer := hashes.NewPoWHashWriter()
writer.InfallibleWrite(input)
hashed := testMatrix.HeavyHash(writer.Finalize())
if !bytes.Equal(expected, hashed.ByteSlice()) {
t.Fatalf("expected: %x == %s", expected, hashed)
}
}
var testMatrix = matrix{
{13, 2, 14, 13, 2, 15, 14, 3, 10, 4, 1, 8, 4, 3, 8, 15, 15, 15, 15, 15, 2, 11, 15, 15, 15, 1, 7, 12, 12, 4, 2, 0, 6, 1, 14, 10, 12, 14, 15, 8, 10, 12, 0, 5, 13, 3, 14, 10, 10, 6, 12, 11, 11, 7, 6, 6, 10, 2, 2, 4, 11, 12, 0, 5},
{4, 13, 0, 2, 1, 15, 13, 13, 11, 2, 5, 12, 15, 7, 0, 10, 7, 2, 6, 3, 12, 0, 12, 0, 2, 6, 7, 7, 7, 7, 10, 12, 11, 14, 12, 12, 4, 11, 10, 0, 10, 11, 2, 10, 1, 7, 7, 12, 15, 9, 5, 14, 9, 12, 3, 0, 12, 13, 4, 13, 8, 15, 11, 6},
{14, 6, 15, 9, 8, 2, 2, 12, 2, 3, 4, 12, 13, 15, 4, 5, 13, 4, 3, 0, 14, 3, 5, 14, 3, 13, 4, 15, 9, 12, 7, 15, 5, 1, 13, 12, 9, 9, 8, 11, 14, 11, 4, 10, 12, 6, 12, 8, 6, 3, 9, 8, 1, 6, 0, 5, 8, 9, 12, 5, 14, 15, 2, 2},
{9, 6, 7, 6, 0, 11, 5, 6, 2, 14, 12, 6, 4, 13, 8, 9, 2, 1, 9, 7, 4, 5, 10, 8, 11, 11, 11, 15, 7, 11, 1, 14, 3, 8, 14, 8, 2, 8, 13, 7, 8, 8, 15, 7, 1, 13, 7, 9, 1, 7, 15, 15, 0, 0, 12, 15, 13, 5, 13, 10, 1, 5, 6, 13},
{4, 0, 12, 10, 6, 11, 14, 2, 2, 15, 4, 1, 2, 4, 2, 12, 13, 1, 9, 10, 8, 0, 2, 10, 13, 8, 9, 7, 5, 3, 8, 2, 6, 6, 1, 12, 3, 0, 1, 4, 2, 8, 3, 13, 6, 15, 0, 13, 14, 4, 15, 0, 7, 3, 7, 8, 5, 14, 14, 5, 5, 0, 1, 2},
{12, 14, 6, 3, 3, 4, 6, 7, 1, 3, 2, 7, 15, 15, 15, 10, 9, 12, 0, 6, 3, 8, 5, 0, 13, 5, 0, 6, 0, 14, 2, 12, 10, 4, 11, 2, 10, 7, 7, 6, 8, 11, 4, 4, 11, 9, 3, 12, 10, 5, 2, 6, 5, 5, 10, 13, 12, 10, 1, 6, 14, 7, 12, 4},
{7, 14, 6, 7, 7, 12, 4, 1, 8, 6, 8, 13, 13, 5, 12, 14, 10, 8, 6, 2, 12, 3, 8, 15, 5, 15, 15, 3, 14, 0, 8, 6, 9, 12, 9, 7, 3, 8, 4, 0, 7, 14, 3, 3, 13, 14, 3, 7, 3, 2, 2, 3, 3, 12, 6, 7, 4, 1, 14, 10, 6, 10, 2, 9},
{14, 11, 15, 5, 7, 10, 1, 11, 4, 2, 6, 2, 9, 7, 4, 0, 9, 12, 11, 2, 3, 13, 1, 5, 4, 10, 5, 6, 6, 12, 8, 1, 1, 15, 4, 2, 12, 12, 0, 4, 14, 3, 11, 1, 7, 5, 9, 4, 3, 15, 7, 3, 15, 9, 8, 3, 8, 3, 3, 6, 7, 6, 9, 2},
{10, 4, 6, 10, 5, 2, 15, 12, 0, 14, 14, 15, 14, 0, 12, 9, 1, 12, 4, 5, 5, 2, 10, 4, 2, 13, 11, 3, 1, 8, 10, 0, 7, 0, 12, 4, 11, 1, 14, 6, 14, 5, 5, 11, 11, 1, 3, 8, 0, 6, 11, 11, 8, 4, 7, 6, 14, 4, 9, 14, 9, 7, 13, 9},
{12, 7, 9, 8, 2, 3, 3, 5, 14, 8, 0, 9, 7, 4, 2, 15, 15, 3, 11, 11, 8, 5, 7, 5, 0, 15, 10, 8, 0, 13, 1, 14, 8, 10, 1, 4, 13, 1, 13, 3, 11, 11, 2, 3, 10, 6, 8, 14, 15, 2, 10, 10, 12, 7, 7, 6, 6, 3, 13, 8, 1, 14, 2, 1},
{2, 11, 6, 9, 13, 3, 12, 6, 0, 4, 6, 13, 8, 14, 6, 9, 10, 2, 10, 8, 4, 13, 6, 5, 0, 13, 15, 4, 2, 2, 1, 7, 5, 3, 3, 13, 7, 3, 5, 9, 15, 14, 14, 6, 0, 15, 11, 2, 4, 15, 6, 9, 8, 9, 15, 2, 6, 9, 15, 8, 4, 4, 11, 1},
{10, 11, 8, 3, 11, 13, 10, 2, 2, 5, 2, 14, 15, 10, 2, 11, 0, 1, 8, 2, 14, 1, 10, 0, 3, 7, 5, 10, 7, 8, 15, 7, 2, 5, 13, 4, 10, 3, 6, 2, 3, 9, 6, 11, 7, 14, 1, 11, 9, 3, 3, 7, 6, 0, 9, 11, 4, 10, 4, 1, 9, 7, 4, 15},
{13, 8, 15, 14, 11, 12, 5, 3, 9, 14, 1, 5, 14, 13, 14, 5, 13, 5, 4, 10, 9, 9, 0, 0, 6, 12, 5, 7, 2, 7, 2, 6, 6, 6, 1, 12, 9, 15, 7, 11, 11, 10, 11, 1, 10, 10, 0, 8, 1, 4, 5, 5, 8, 10, 10, 15, 6, 8, 13, 11, 11, 3, 15, 5},
{8, 11, 5, 10, 1, 10, 9, 1, 12, 7, 6, 11, 1, 1, 4, 1, 2, 8, 4, 4, 7, 7, 8, 2, 7, 1, 14, 1, 8, 15, 15, 12, 10, 4, 15, 11, 3, 6, 10, 7, 4, 0, 10, 9, 11, 7, 1, 14, 4, 14, 3, 14, 10, 4, 13, 12, 5, 3, 12, 7, 10, 8, 0, 3},
{9, 11, 6, 15, 14, 10, 0, 4, 7, 7, 6, 0, 7, 7, 12, 15, 5, 4, 12, 3, 7, 3, 0, 12, 2, 7, 11, 6, 7, 3, 2, 8, 5, 11, 9, 4, 3, 8, 11, 12, 3, 5, 14, 12, 4, 13, 12, 0, 3, 14, 4, 9, 1, 1, 9, 14, 10, 14, 8, 15, 6, 14, 10, 15},
{10, 14, 10, 0, 10, 12, 15, 0, 3, 9, 11, 10, 3, 5, 1, 1, 9, 1, 7, 15, 7, 8, 10, 10, 12, 11, 5, 1, 10, 3, 6, 6, 13, 0, 13, 1, 4, 5, 9, 4, 9, 15, 8, 4, 13, 13, 4, 5, 5, 11, 1, 13, 15, 3, 10, 15, 7, 11, 10, 15, 8, 12, 10, 3},
{8, 5, 11, 3, 8, 13, 15, 15, 3, 12, 1, 13, 1, 7, 1, 5, 6, 13, 7, 8, 5, 1, 12, 3, 10, 7, 12, 6, 14, 12, 15, 5, 3, 12, 2, 15, 11, 13, 1, 13, 8, 5, 8, 0, 13, 15, 7, 13, 6, 13, 10, 1, 11, 0, 8, 9, 5, 11, 2, 9, 9, 10, 4, 15},
{0, 4, 12, 14, 3, 1, 7, 5, 11, 13, 5, 3, 11, 12, 6, 8, 10, 15, 11, 8, 7, 10, 0, 2, 5, 15, 6, 10, 4, 2, 3, 1, 13, 7, 6, 12, 14, 7, 6, 14, 12, 10, 6, 14, 12, 0, 12, 11, 6, 9, 3, 1, 12, 15, 15, 3, 5, 5, 10, 11, 7, 15, 13, 3},
{12, 14, 2, 14, 13, 6, 15, 7, 8, 8, 14, 13, 9, 2, 2, 10, 3, 15, 6, 10, 11, 7, 13, 0, 12, 1, 5, 8, 8, 12, 1, 11, 1, 3, 2, 4, 10, 7, 7, 7, 3, 10, 7, 2, 2, 3, 0, 1, 13, 5, 8, 2, 14, 0, 11, 13, 9, 3, 13, 2, 14, 2, 15, 4},
{0, 0, 13, 6, 9, 12, 15, 7, 8, 0, 7, 4, 12, 15, 3, 2, 7, 1, 14, 4, 9, 3, 13, 12, 11, 12, 9, 9, 3, 7, 10, 9, 1, 9, 10, 2, 10, 14, 11, 0, 14, 4, 15, 12, 12, 9, 9, 8, 14, 1, 9, 14, 0, 6, 1, 0, 13, 9, 7, 6, 13, 2, 3, 9},
{8, 0, 10, 13, 0, 7, 9, 7, 5, 1, 0, 3, 7, 10, 3, 15, 1, 15, 3, 11, 2, 6, 3, 10, 0, 10, 10, 3, 4, 15, 8, 6, 11, 11, 7, 5, 8, 5, 7, 15, 1, 11, 7, 13, 13, 6, 13, 13, 4, 2, 3, 15, 9, 5, 10, 6, 6, 6, 3, 11, 15, 13, 1, 15},
{1, 1, 2, 10, 2, 2, 9, 5, 9, 2, 0, 1, 14, 2, 11, 6, 11, 6, 1, 0, 13, 7, 14, 1, 15, 14, 13, 7, 12, 11, 8, 11, 2, 11, 6, 10, 2, 3, 0, 0, 15, 0, 4, 6, 4, 12, 5, 5, 7, 14, 10, 6, 0, 3, 13, 0, 8, 1, 13, 10, 5, 1, 7, 5},
{0, 5, 2, 12, 10, 2, 5, 1, 14, 0, 1, 4, 15, 11, 8, 7, 11, 14, 15, 6, 4, 1, 6, 6, 7, 13, 12, 5, 13, 2, 1, 6, 2, 13, 5, 15, 0, 8, 8, 6, 5, 5, 2, 0, 3, 13, 14, 2, 10, 5, 7, 6, 14, 5, 1, 4, 11, 2, 11, 1, 8, 15, 2, 4},
{9, 9, 4, 5, 2, 5, 3, 12, 14, 5, 1, 3, 3, 0, 0, 6, 7, 14, 0, 15, 14, 11, 3, 10, 1, 9, 4, 14, 7, 14, 1, 0, 15, 11, 5, 9, 4, 0, 0, 10, 4, 4, 0, 7, 8, 15, 12, 8, 10, 8, 1, 2, 1, 11, 12, 14, 14, 14, 8, 10, 1, 5, 13, 10},
{5, 10, 4, 4, 11, 10, 0, 6, 0, 12, 10, 5, 9, 11, 8, 10, 11, 3, 11, 14, 12, 9, 4, 6, 11, 12, 8, 7, 6, 14, 0, 6, 12, 4, 5, 3, 9, 0, 11, 6, 1, 3, 2, 12, 8, 9, 7, 12, 14, 7, 12, 6, 11, 13, 0, 2, 1, 3, 1, 8, 12, 2, 15, 15},
{10, 11, 2, 3, 11, 10, 1, 7, 1, 10, 10, 14, 5, 13, 10, 3, 11, 15, 9, 14, 11, 11, 3, 15, 11, 6, 15, 13, 13, 1, 1, 10, 5, 1, 5, 11, 10, 3, 9, 12, 12, 1, 5, 6, 3, 3, 1, 1, 12, 8, 3, 15, 6, 2, 8, 14, 3, 4, 10, 9, 7, 13, 2, 6},
{12, 0, 1, 0, 4, 3, 3, 6, 8, 3, 1, 13, 6, 12, 1, 1, 1, 4, 12, 4, 4, 9, 9, 14, 15, 3, 6, 4, 11, 1, 12, 5, 6, 0, 10, 9, 1, 8, 14, 5, 2, 8, 4, 15, 12, 13, 7, 14, 12, 2, 6, 9, 4, 13, 0, 15, 10, 10, 6, 12, 7, 12, 9, 10},
{0, 8, 5, 11, 12, 12, 11, 7, 2, 9, 2, 15, 1, 1, 0, 0, 6, 5, 10, 1, 11, 12, 8, 7, 1, 7, 10, 4, 2, 8, 2, 5, 1, 1, 2, 9, 2, 0, 3, 7, 5, 1, 5, 5, 3, 1, 4, 3, 14, 8, 11, 7, 8, 0, 2, 13, 3, 15, 1, 13, 14, 15, 11, 13},
{8, 13, 5, 14, 2, 9, 9, 13, 15, 8, 2, 14, 4, 2, 6, 0, 1, 13, 10, 13, 6, 12, 15, 11, 6, 11, 9, 9, 2, 9, 6, 14, 2, 9, 12, 1, 13, 9, 5, 11, 10, 4, 4, 5, 8, 9, 13, 10, 9, 0, 5, 15, 4, 12, 7, 10, 6, 5, 5, 15, 8, 8, 11, 14},
{6, 9, 6, 7, 1, 15, 0, 1, 4, 15, 5, 3, 10, 9, 15, 9, 14, 12, 7, 6, 3, 0, 12, 8, 12, 2, 11, 8, 11, 8, 1, 10, 10, 7, 7, 5, 3, 5, 1, 2, 13, 11, 2, 5, 2, 10, 10, 1, 14, 14, 8, 1, 11, 1, 2, 6, 15, 10, 8, 7, 10, 7, 0, 3},
{12, 6, 11, 1, 1, 7, 8, 1, 5, 5, 8, 4, 6, 5, 6, 4, 2, 8, 4, 1, 0, 0, 14, 2, 10, 14, 14, 11, 2, 9, 14, 15, 12, 14, 9, 3, 7, 14, 4, 7, 12, 9, 3, 5, 1, 0, 12, 9, 10, 5, 11, 12, 10, 10, 6, 14, 6, 13, 13, 5, 5, 10, 13, 10},
{12, 6, 13, 0, 8, 0, 10, 6, 15, 15, 7, 3, 0, 10, 13, 14, 10, 13, 5, 13, 15, 14, 3, 4, 10, 10, 9, 6, 6, 15, 2, 7, 0, 10, 6, 14, 2, 9, 11, 7, 5, 5, 13, 14, 11, 15, 9, 4, 2, 0, 15, 5, 4, 14, 14, 1, 3, 4, 5, 8, 1, 1, 10, 12},
{2, 5, 0, 4, 11, 5, 5, 6, 10, 4, 6, 7, 10, 3, 0, 14, 14, 0, 12, 15, 11, 12, 13, 7, 6, 3, 9, 1, 9, 8, 8, 8, 4, 10, 3, 1, 7, 10, 3, 2, 12, 6, 15, 14, 0, 6, 8, 10, 1, 9, 12, 12, 15, 7, 1, 11, 15, 13, 0, 4, 10, 0, 12, 11},
{8, 12, 14, 15, 14, 15, 10, 0, 2, 14, 3, 1, 2, 6, 0, 2, 1, 7, 9, 0, 15, 13, 5, 14, 6, 8, 15, 4, 15, 6, 10, 6, 15, 3, 12, 8, 5, 4, 10, 5, 3, 0, 4, 13, 10, 9, 8, 4, 6, 3, 9, 6, 12, 11, 9, 13, 8, 10, 9, 9, 8, 12, 1, 2},
{11, 10, 15, 15, 5, 14, 15, 7, 5, 9, 14, 14, 7, 11, 6, 6, 3, 8, 2, 3, 4, 14, 11, 1, 12, 15, 11, 6, 0, 0, 13, 7, 14, 3, 12, 14, 0, 15, 6, 1, 11, 2, 11, 8, 3, 13, 4, 12, 10, 13, 7, 14, 9, 13, 3, 10, 2, 14, 13, 4, 12, 13, 14, 10},
{1, 11, 2, 12, 1, 10, 7, 12, 3, 3, 14, 9, 1, 10, 0, 11, 8, 10, 12, 12, 4, 12, 2, 11, 5, 0, 3, 15, 8, 2, 14, 3, 10, 2, 1, 13, 6, 14, 0, 0, 8, 11, 6, 13, 15, 10, 12, 7, 7, 11, 14, 9, 2, 7, 6, 8, 14, 9, 14, 10, 11, 9, 9, 12},
{5, 10, 14, 2, 1, 4, 11, 5, 10, 2, 13, 9, 6, 12, 11, 5, 13, 4, 5, 14, 8, 7, 15, 9, 8, 4, 5, 2, 9, 11, 5, 3, 12, 2, 6, 1, 7, 4, 11, 4, 15, 0, 5, 2, 13, 11, 11, 2, 15, 10, 0, 12, 5, 8, 10, 1, 4, 11, 3, 13, 11, 7, 9, 14},
{9, 8, 10, 5, 0, 2, 5, 8, 7, 3, 3, 6, 11, 1, 13, 15, 4, 4, 11, 6, 2, 6, 13, 11, 2, 6, 9, 4, 5, 13, 12, 2, 8, 7, 7, 12, 14, 15, 5, 12, 7, 0, 15, 15, 0, 5, 15, 0, 3, 9, 10, 15, 9, 11, 10, 10, 5, 3, 9, 3, 12, 13, 0, 13},
{1, 11, 15, 0, 10, 5, 3, 5, 6, 7, 1, 11, 4, 11, 4, 2, 5, 12, 2, 5, 5, 6, 1, 5, 14, 9, 1, 5, 14, 12, 6, 10, 0, 8, 5, 11, 11, 11, 12, 10, 8, 10, 10, 1, 14, 1, 0, 8, 4, 7, 0, 11, 3, 1, 11, 12, 11, 8, 14, 15, 9, 3, 1, 14},
{14, 11, 12, 12, 4, 6, 8, 14, 15, 1, 11, 2, 13, 3, 6, 2, 7, 1, 8, 1, 4, 9, 11, 15, 8, 1, 10, 13, 4, 13, 2, 7, 7, 10, 5, 2, 12, 12, 12, 3, 10, 8, 2, 11, 0, 3, 8, 9, 4, 2, 15, 7, 15, 6, 4, 6, 12, 7, 14, 9, 9, 8, 14, 12},
{15, 4, 8, 12, 11, 11, 9, 5, 0, 0, 7, 6, 10, 5, 8, 2, 5, 6, 14, 11, 13, 0, 13, 15, 5, 4, 9, 15, 13, 12, 14, 15, 10, 2, 3, 6, 10, 14, 1, 8, 6, 7, 10, 1, 14, 9, 12, 13, 7, 2, 12, 10, 6, 11, 15, 1, 15, 11, 13, 0, 6, 13, 7, 15},
{3, 3, 12, 5, 14, 9, 14, 14, 8, 0, 9, 1, 2, 2, 14, 11, 7, 1, 3, 1, 14, 15, 12, 8, 14, 2, 4, 13, 10, 5, 10, 8, 1, 7, 6, 5, 4, 2, 11, 5, 4, 13, 14, 6, 13, 15, 6, 6, 7, 12, 11, 5, 13, 10, 9, 13, 9, 14, 5, 6, 7, 14, 11, 7},
{14, 12, 11, 5, 0, 5, 10, 5, 7, 1, 7, 11, 1, 0, 13, 6, 5, 14, 3, 0, 5, 14, 6, 7, 8, 5, 8, 6, 6, 3, 6, 1, 8, 3, 10, 7, 15, 6, 11, 6, 6, 7, 13, 2, 2, 0, 0, 11, 1, 15, 2, 14, 5, 1, 4, 8, 0, 1, 8, 0, 1, 1, 2, 2},
{10, 13, 13, 3, 15, 14, 9, 12, 15, 15, 8, 5, 8, 10, 5, 9, 6, 6, 7, 15, 1, 0, 14, 9, 1, 11, 6, 11, 13, 4, 6, 14, 9, 12, 13, 8, 14, 6, 14, 2, 3, 15, 4, 4, 14, 4, 9, 12, 8, 0, 9, 11, 13, 10, 8, 14, 3, 5, 7, 11, 6, 7, 15, 2},
{9, 9, 11, 6, 11, 0, 5, 4, 8, 10, 8, 11, 2, 12, 8, 7, 11, 13, 6, 1, 13, 13, 11, 4, 5, 7, 7, 9, 6, 4, 12, 0, 11, 8, 6, 12, 11, 4, 15, 11, 12, 8, 11, 11, 1, 3, 6, 14, 9, 6, 7, 5, 0, 10, 3, 15, 13, 7, 0, 1, 13, 15, 1, 14},
{10, 6, 8, 7, 3, 6, 9, 15, 1, 3, 10, 14, 9, 0, 0, 10, 0, 15, 2, 0, 0, 0, 6, 0, 13, 9, 9, 1, 8, 6, 13, 2, 1, 9, 14, 9, 1, 4, 8, 4, 2, 0, 8, 5, 0, 11, 12, 15, 13, 1, 14, 14, 15, 7, 8, 4, 4, 12, 1, 12, 8, 3, 9, 5},
{12, 11, 1, 4, 10, 14, 8, 12, 2, 4, 15, 2, 9, 7, 7, 11, 15, 12, 10, 11, 7, 4, 13, 0, 8, 6, 8, 8, 10, 5, 5, 13, 3, 7, 9, 13, 13, 14, 6, 8, 1, 5, 7, 12, 4, 4, 6, 9, 13, 1, 6, 1, 6, 14, 5, 8, 2, 10, 4, 10, 1, 9, 6, 15},
{4, 13, 4, 9, 6, 11, 1, 8, 7, 11, 11, 1, 3, 10, 12, 11, 1, 10, 6, 10, 0, 7, 3, 0, 0, 6, 3, 9, 2, 1, 4, 8, 2, 10, 2, 15, 9, 15, 14, 14, 15, 14, 3, 2, 7, 6, 6, 10, 8, 8, 4, 11, 1, 13, 6, 0, 2, 10, 0, 11, 15, 14, 6, 9},
{15, 0, 12, 13, 0, 9, 10, 4, 11, 5, 10, 0, 8, 7, 3, 2, 12, 6, 3, 8, 5, 15, 14, 2, 13, 13, 6, 11, 5, 6, 9, 10, 14, 5, 14, 4, 9, 7, 5, 11, 13, 2, 7, 1, 14, 9, 0, 7, 8, 12, 11, 15, 2, 1, 5, 11, 3, 7, 5, 1, 6, 3, 8, 6},
{0, 3, 8, 1, 4, 6, 3, 1, 3, 8, 2, 0, 15, 15, 14, 15, 13, 10, 11, 9, 2, 11, 5, 12, 3, 3, 0, 1, 5, 3, 11, 6, 10, 11, 8, 5, 7, 15, 4, 12, 8, 8, 12, 12, 12, 1, 9, 4, 11, 6, 10, 11, 1, 12, 8, 12, 5, 6, 1, 14, 2, 10, 3, 0},
{10, 13, 6, 9, 11, 1, 4, 10, 0, 13, 8, 7, 4, 12, 15, 5, 14, 12, 6, 9, 0, 0, 10, 5, 13, 10, 15, 3, 0, 8, 7, 0, 9, 8, 10, 6, 11, 8, 10, 13, 11, 7, 5, 5, 9, 13, 1, 15, 0, 5, 15, 5, 4, 7, 9, 9, 15, 8, 2, 6, 3, 8, 5, 8},
{14, 0, 6, 2, 4, 12, 2, 13, 6, 10, 5, 2, 2, 1, 6, 11, 1, 6, 9, 13, 0, 13, 9, 3, 12, 4, 3, 8, 7, 0, 9, 12, 0, 1, 7, 10, 10, 7, 3, 9, 13, 5, 15, 4, 13, 0, 8, 5, 4, 14, 11, 3, 3, 13, 15, 9, 9, 12, 9, 5, 2, 0, 1, 14},
{4, 14, 13, 0, 14, 15, 11, 10, 11, 1, 3, 3, 9, 1, 12, 8, 6, 5, 15, 11, 1, 7, 5, 3, 8, 13, 0, 13, 11, 5, 8, 1, 8, 6, 13, 4, 13, 7, 12, 6, 5, 5, 7, 0, 12, 1, 1, 8, 1, 6, 4, 2, 8, 8, 15, 11, 11, 11, 4, 4, 4, 7, 13, 12},
{14, 15, 10, 0, 4, 3, 1, 9, 13, 7, 9, 9, 15, 5, 0, 3, 9, 6, 4, 7, 13, 11, 3, 2, 7, 1, 6, 8, 13, 7, 10, 4, 3, 9, 5, 9, 2, 6, 10, 7, 9, 13, 2, 14, 2, 14, 7, 2, 14, 2, 8, 8, 0, 9, 0, 9, 12, 6, 7, 7, 6, 8, 12, 13},
{5, 15, 8, 12, 11, 3, 13, 4, 5, 14, 10, 4, 15, 15, 1, 10, 9, 14, 6, 6, 4, 12, 4, 9, 12, 2, 15, 13, 2, 5, 12, 2, 3, 2, 15, 11, 12, 2, 6, 2, 11, 6, 7, 9, 12, 10, 5, 1, 1, 5, 9, 6, 14, 11, 3, 11, 6, 10, 11, 11, 0, 12, 15, 1},
{12, 6, 8, 10, 2, 5, 7, 9, 8, 14, 15, 15, 13, 10, 15, 3, 10, 10, 6, 10, 14, 10, 7, 5, 3, 7, 6, 12, 11, 12, 8, 9, 12, 9, 15, 15, 15, 7, 8, 3, 15, 14, 1, 12, 0, 0, 4, 0, 9, 10, 8, 7, 14, 10, 8, 14, 6, 2, 8, 1, 11, 10, 0, 1},
{12, 1, 2, 12, 7, 10, 4, 11, 5, 14, 10, 2, 2, 9, 4, 13, 3, 14, 3, 15, 5, 0, 14, 7, 7, 15, 6, 5, 2, 8, 15, 9, 6, 6, 13, 10, 9, 8, 6, 3, 14, 7, 12, 9, 7, 8, 13, 12, 14, 13, 6, 0, 5, 1, 9, 12, 14, 0, 11, 11, 6, 3, 11, 7},
{15, 4, 8, 12, 8, 11, 4, 15, 1, 6, 2, 13, 1, 7, 7, 12, 0, 8, 14, 14, 10, 14, 0, 12, 0, 3, 3, 11, 7, 4, 2, 13, 0, 0, 11, 2, 5, 8, 12, 11, 6, 5, 6, 0, 0, 4, 0, 0, 1, 9, 9, 11, 3, 2, 13, 4, 13, 9, 15, 4, 7, 8, 3, 2},
{3, 13, 8, 8, 12, 10, 5, 4, 7, 13, 10, 13, 14, 3, 2, 12, 11, 0, 9, 5, 6, 4, 14, 4, 6, 9, 2, 5, 10, 3, 9, 10, 5, 0, 12, 5, 15, 5, 15, 15, 2, 12, 3, 11, 0, 15, 9, 14, 1, 5, 6, 6, 14, 5, 8, 0, 5, 9, 3, 7, 7, 12, 15, 1},
{1, 11, 7, 4, 13, 3, 0, 8, 11, 9, 15, 1, 4, 12, 2, 12, 10, 4, 14, 3, 9, 14, 14, 2, 3, 11, 12, 4, 5, 10, 6, 15, 2, 13, 13, 9, 9, 1, 11, 12, 12, 14, 1, 5, 15, 1, 7, 14, 12, 10, 11, 13, 13, 5, 2, 4, 7, 7, 9, 4, 14, 15, 13, 10},
{14, 15, 9, 14, 9, 5, 13, 2, 0, 0, 14, 8, 6, 2, 0, 7, 11, 10, 2, 13, 2, 14, 9, 6, 4, 11, 5, 14, 6, 1, 6, 14, 6, 3, 9, 5, 2, 9, 3, 11, 1, 14, 5, 4, 12, 5, 3, 5, 11, 3, 11, 6, 13, 7, 13, 7, 4, 9, 4, 13, 8, 3, 5, 11},
{13, 12, 12, 13, 8, 2, 4, 2, 10, 6, 3, 5, 7, 7, 6, 13, 8, 6, 15, 4, 12, 7, 15, 4, 3, 9, 8, 15, 0, 3, 12, 1, 9, 8, 13, 10, 15, 4, 14, 1, 6, 15, 0, 4, 8, 9, 3, 1, 3, 15, 5, 5, 1, 11, 11, 10, 11, 10, 8, 8, 5, 4, 13, 0},
{8, 4, 15, 9, 14, 9, 5, 8, 8, 10, 5, 15, 9, 8, 12, 5, 11, 10, 2, 12, 13, 1, 0, 2, 6, 13, 11, 9, 12, 0, 5, 0, 11, 5, 14, 12, 3, 4, 2, 10, 3, 12, 5, 15, 4, 8, 14, 1, 0, 13, 9, 5, 2, 4, 13, 8, 2, 5, 8, 9, 15, 3, 5, 5},
{0, 3, 3, 4, 6, 5, 5, 1, 3, 2, 14, 5, 10, 7, 15, 11, 7, 13, 15, 4, 0, 12, 9, 15, 12, 0, 3, 1, 14, 1, 12, 9, 13, 8, 9, 15, 12, 3, 5, 11, 3, 11, 4, 1, 9, 4, 13, 7, 4, 10, 6, 14, 13, 0, 9, 11, 15, 15, 3, 3, 13, 15, 10, 15},
}

View File

@@ -36,6 +36,7 @@ func CalculateProofOfWorkValue(header externalapi.MutableBlockHeader) *big.Int {
header.SetNonce(0)
prePowHash := consensushashing.HeaderHash(header)
matrix := generateMatrix(prePowHash)
header.SetTimeInMilliseconds(timestamp)
header.SetNonce(nonce)
@@ -52,7 +53,9 @@ func CalculateProofOfWorkValue(header externalapi.MutableBlockHeader) *big.Int {
if err != nil {
panic(errors.Wrap(err, "this should never happen. Hash digest should never return an error"))
}
return toBig(writer.Finalize())
powHash := writer.Finalize()
heavyHash := matrix.HeavyHash(powHash)
return toBig(heavyHash)
}
// ToBig converts a externalapi.DomainHash into a big.Int treated as a little endian string.
@@ -69,6 +72,12 @@ func toBig(hash *externalapi.DomainHash) *big.Int {
// BlockLevel returns the block level of the given header.
func BlockLevel(header externalapi.BlockHeader) int {
// Genesis is defined to be the root of all blocks at all levels, so we define it to be the maximal
// block level.
if len(header.DirectParents()) == 0 {
return constants.MaxBlockLevel
}
proofOfWorkValue := CalculateProofOfWorkValue(header.ToMutable())
for blockLevel := 0; ; blockLevel++ {
if blockLevel == constants.MaxBlockLevel || proofOfWorkValue.Bit(blockLevel+1) != 0 {

View File

@@ -0,0 +1,37 @@
package pow
import (
"encoding/binary"
"github.com/kaspanet/kaspad/domain/consensus/model/externalapi"
"math/bits"
)
type xoShiRo256PlusPlus struct {
s0 uint64
s1 uint64
s2 uint64
s3 uint64
}
func newxoShiRo256PlusPlus(hash *externalapi.DomainHash) *xoShiRo256PlusPlus {
hashArray := hash.ByteArray()
return &xoShiRo256PlusPlus{
s0: binary.LittleEndian.Uint64(hashArray[:8]),
s1: binary.LittleEndian.Uint64(hashArray[8:16]),
s2: binary.LittleEndian.Uint64(hashArray[16:24]),
s3: binary.LittleEndian.Uint64(hashArray[24:32]),
}
}
func (x *xoShiRo256PlusPlus) Uint64() uint64 {
res := bits.RotateLeft64(x.s0+x.s3, 23) + x.s0
t := x.s1 << 17
x.s2 ^= x.s0
x.s3 ^= x.s1
x.s1 ^= x.s2
x.s0 ^= x.s3
x.s2 ^= t
x.s3 = bits.RotateLeft64(x.s3, 45)
return res
}

View File

@@ -0,0 +1,17 @@
package pow
import "testing"
// Test vectors are from here: https://github.com/rust-random/rngs/blob/17aa826cc38d3e8408c9489ac859fa9397acd479/rand_xoshiro/src/xoshiro256plusplus.rs#L121
func TestXoShiRo256PlusPlus_Uint64(t *testing.T) {
state := xoShiRo256PlusPlus{1, 2, 3, 4}
expected := []uint64{41943041, 58720359, 3588806011781223, 3591011842654386,
9228616714210784205, 9973669472204895162, 14011001112246962877,
12406186145184390807, 15849039046786891736, 10450023813501588000}
for _, ex := range expected {
val := state.Uint64()
if val != ex {
t.Errorf("expected: %d, found: %d", ex, val)
}
}
}

View File

@@ -22,7 +22,7 @@ import (
//
const (
defaultMaxCoinbasePayloadLength = 150
defaultMaxCoinbasePayloadLength = 172
// defaultMaxBlockMass is a bound on the mass of a block, larger values increase the bound d
// on the round trip time of a block, which affects the other parameters as described below
defaultMaxBlockMass = 500_000

View File

@@ -19,8 +19,27 @@ var genesisTxPayload = []byte{
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // Blue score
0x00, 0xE1, 0xF5, 0x05, 0x00, 0x00, 0x00, 0x00, // Subsidy
0x00, 0x00, //script version
0x01, // Varint
0x00, // OP-FALSE
0x01, // Varint
0x00, // OP-FALSE
0xd7, 0x95, 0xd7, 0x9e, 0xd7, 0x94, 0x20, 0xd7, // ומה די עליך ועל אחיך ייטב בשאר כספא ודהבה למעבד כרעות אלהכם תעבדון
0x93, 0xd7, 0x99, 0x20, 0xd7, 0xa2, 0xd7, 0x9c,
0xd7, 0x99, 0xd7, 0x9a, 0x20, 0xd7, 0x95, 0xd7,
0xa2, 0xd7, 0x9c, 0x20, 0xd7, 0x90, 0xd7, 0x97,
0xd7, 0x99, 0xd7, 0x9a, 0x20, 0xd7, 0x99, 0xd7,
0x99, 0xd7, 0x98, 0xd7, 0x91, 0x20, 0xd7, 0x91,
0xd7, 0xa9, 0xd7, 0x90, 0xd7, 0xa8, 0x20, 0xd7,
0x9b, 0xd7, 0xa1, 0xd7, 0xa4, 0xd7, 0x90, 0x20,
0xd7, 0x95, 0xd7, 0x93, 0xd7, 0x94, 0xd7, 0x91,
0xd7, 0x94, 0x20, 0xd7, 0x9c, 0xd7, 0x9e, 0xd7,
0xa2, 0xd7, 0x91, 0xd7, 0x93, 0x20, 0xd7, 0x9b,
0xd7, 0xa8, 0xd7, 0xa2, 0xd7, 0x95, 0xd7, 0xaa,
0x20, 0xd7, 0x90, 0xd7, 0x9c, 0xd7, 0x94, 0xd7,
0x9b, 0xd7, 0x9d, 0x20, 0xd7, 0xaa, 0xd7, 0xa2,
0xd7, 0x91, 0xd7, 0x93, 0xd7, 0x95, 0xd7, 0x9f,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, // Bitcoin block hash 00000000000000000001733c62adb19f1b77fa0735d0e11f25af36fc9ca908a5
0x00, 0x01, 0x73, 0x3c, 0x62, 0xad, 0xb1, 0x9f,
0x1b, 0x77, 0xfa, 0x07, 0x35, 0xd0, 0xe1, 0x1f,
0x25, 0xaf, 0x36, 0xfc, 0x9c, 0xa9, 0x08, 0xa5,
}
// genesisCoinbaseTx is the coinbase transaction for the genesis blocks for
@@ -31,19 +50,19 @@ var genesisCoinbaseTx = transactionhelper.NewSubnetworkTransaction(0, []*externa
// genesisHash is the hash of the first block in the block DAG for the main
// network (genesis block).
var genesisHash = externalapi.NewDomainHashFromByteArray(&[externalapi.DomainHashSize]byte{
0x75, 0xd8, 0x51, 0xcc, 0x91, 0xba, 0x55, 0x32,
0xfd, 0xf9, 0x3e, 0xf2, 0xa5, 0x28, 0x92, 0x83,
0x35, 0xe0, 0x61, 0xa2, 0xe4, 0x77, 0x76, 0x5e,
0xd7, 0x10, 0x5d, 0x8e, 0x78, 0xc7, 0xb8, 0x0d,
0xca, 0xeb, 0x97, 0x96, 0x0a, 0x16, 0x0c, 0x21,
0x1a, 0x6b, 0x21, 0x96, 0xbd, 0x78, 0x39, 0x9f,
0xd4, 0xc4, 0xcc, 0x5b, 0x50, 0x9f, 0x55, 0xc1,
0x2c, 0x8a, 0x7d, 0x81, 0x5f, 0x75, 0x36, 0xea,
})
// genesisMerkleRoot is the hash of the first transaction in the genesis block
// for the main network.
var genesisMerkleRoot = externalapi.NewDomainHashFromByteArray(&[externalapi.DomainHashSize]byte{
0xea, 0xb2, 0xe3, 0xfa, 0xd6, 0x72, 0x95, 0x38,
0x04, 0xe0, 0x43, 0x1a, 0xf2, 0x2d, 0xc5, 0xeb,
0x27, 0xd8, 0x0a, 0xdd, 0x4c, 0xc5, 0xd9, 0x80,
0x90, 0xc7, 0x6c, 0x43, 0xce, 0x81, 0x23, 0x68,
0xca, 0xed, 0xaf, 0x7d, 0x4a, 0x08, 0xbb, 0xe8,
0x90, 0x11, 0x64, 0x0c, 0x48, 0x41, 0xb6, 0x6d,
0x5b, 0xba, 0x67, 0xd7, 0x28, 0x8c, 0xe6, 0xd6,
0x72, 0x28, 0xdb, 0x00, 0x09, 0x66, 0xe9, 0x74,
})
// genesisBlock defines the genesis block of the block DAG which serves as the
@@ -55,9 +74,9 @@ var genesisBlock = externalapi.DomainBlock{
genesisMerkleRoot,
&externalapi.DomainHash{},
externalapi.NewDomainHashFromByteArray(muhash.EmptyMuHashHash.AsArray()),
0x17c2df949fe,
0x207fffff,
0x0,
0x17cfb020c02,
0x1e7fffff,
0x3392c,
0,
0,
big.NewInt(0),
@@ -86,10 +105,10 @@ var devnetGenesisCoinbaseTx = transactionhelper.NewSubnetworkTransaction(0,
// devGenesisHash is the hash of the first block in the block DAG for the development
// network (genesis block).
var devnetGenesisHash = externalapi.NewDomainHashFromByteArray(&[externalapi.DomainHashSize]byte{
0xf1, 0xa4, 0x65, 0xfe, 0xd2, 0x08, 0x54, 0xc1,
0x72, 0x60, 0xdc, 0x8b, 0x29, 0x67, 0x90, 0x1f,
0xa9, 0x48, 0x47, 0x4e, 0x63, 0xa1, 0xfc, 0x09,
0x6d, 0x10, 0x7b, 0x08, 0x23, 0x37, 0xfd, 0x59,
0x34, 0x3b, 0x53, 0xb7, 0xad, 0x82, 0x8a, 0x33,
0x4b, 0x03, 0xb1, 0xbb, 0x13, 0x15, 0xb0, 0x75,
0xf3, 0xf0, 0x40, 0xfb, 0x64, 0x0c, 0xca, 0x19,
0xc9, 0x61, 0xe7, 0x69, 0xdb, 0x98, 0x98, 0x3e,
})
// devnetGenesisMerkleRoot is the hash of the first transaction in the genesis block
@@ -112,7 +131,7 @@ var devnetGenesisBlock = externalapi.DomainBlock{
externalapi.NewDomainHashFromByteArray(muhash.EmptyMuHashHash.AsArray()),
0x11e9db49828,
0x1e7fffff,
0x268db,
0x48e5e,
0,
0,
big.NewInt(0),
@@ -140,10 +159,10 @@ var simnetGenesisCoinbaseTx = transactionhelper.NewSubnetworkTransaction(0,
// simnetGenesisHash is the hash of the first block in the block DAG for
// the simnet (genesis block).
var simnetGenesisHash = externalapi.NewDomainHashFromByteArray(&[externalapi.DomainHashSize]byte{
0x9b, 0x66, 0xc8, 0x1a, 0xd5, 0xb8, 0xc2, 0xf7,
0x45, 0x45, 0x47, 0xd6, 0x83, 0x83, 0xf8, 0x27,
0x45, 0x46, 0xcf, 0x98, 0x1c, 0x74, 0x46, 0xcf,
0x25, 0x5e, 0xd3, 0xe7, 0xe4, 0x68, 0x47, 0x6f,
0x41, 0x1f, 0x8c, 0xd2, 0x6f, 0x3d, 0x41, 0xae,
0xa3, 0x9e, 0x78, 0x57, 0x39, 0x27, 0xda, 0x24,
0xd2, 0x39, 0x95, 0x70, 0x5b, 0x57, 0x9f, 0x30,
0x95, 0x9b, 0x91, 0x27, 0xe9, 0x6b, 0x79, 0xe3,
})
// simnetGenesisMerkleRoot is the hash of the first transaction in the genesis block
@@ -164,9 +183,9 @@ var simnetGenesisBlock = externalapi.DomainBlock{
simnetGenesisMerkleRoot,
&externalapi.DomainHash{},
externalapi.NewDomainHashFromByteArray(muhash.EmptyMuHashHash.AsArray()),
0x17c2df94abb,
0x17c5f62fbb6,
0x207fffff,
0x0,
0x2,
0,
0,
big.NewInt(0),
@@ -194,10 +213,10 @@ var testnetGenesisCoinbaseTx = transactionhelper.NewSubnetworkTransaction(0,
// testnetGenesisHash is the hash of the first block in the block DAG for the test
// network (genesis block).
var testnetGenesisHash = externalapi.NewDomainHashFromByteArray(&[externalapi.DomainHashSize]byte{
0x47, 0x4f, 0xfd, 0xd1, 0xf8, 0x3d, 0x1d, 0x00,
0xcb, 0x07, 0x17, 0x91, 0x56, 0x60, 0xd4, 0xa7,
0x27, 0x5e, 0x43, 0xc2, 0x74, 0xe6, 0x76, 0x6e,
0x34, 0xe4, 0x13, 0xbb, 0x24, 0x02, 0x30, 0x66,
0xf8, 0x96, 0xa3, 0x03, 0x48, 0x73, 0xbe, 0x17,
0x39, 0xfc, 0x43, 0x59, 0x23, 0x68, 0x99, 0xfd,
0x3d, 0x65, 0xd2, 0xbc, 0x94, 0xf9, 0x78, 0x0d,
0xf0, 0xd0, 0xda, 0x3e, 0xb1, 0xcc, 0x43, 0x70,
})
// testnetGenesisMerkleRoot is the hash of the first transaction in the genesis block
@@ -218,9 +237,9 @@ var testnetGenesisBlock = externalapi.DomainBlock{
testnetGenesisMerkleRoot,
&externalapi.DomainHash{},
externalapi.NewDomainHashFromByteArray(muhash.EmptyMuHashHash.AsArray()),
0x17c2df94abb,
0x17c5f62fbb6,
0x1e7fffff,
0x35f16,
0x14582,
0,
0,
big.NewInt(0),

View File

@@ -185,7 +185,7 @@ type Params struct {
FixedSubsidySwitchPruningPointInterval uint64
FixedSubsidySwitchHashRateDifference *big.Int
FixedSubsidySwitchHashRateThreshold *big.Int
}
// NormalizeRPCServerAddress returns addr with the current network default
@@ -211,6 +211,7 @@ var MainnetParams = Params{
Net: appmessage.Mainnet,
RPCPort: "16110",
DefaultPort: "16111",
DNSSeeds: []string{"mainnet-dnsseed.daglabs-dev.com"},
// DAG parameters
GenesisBlock: &genesisBlock,
@@ -262,7 +263,7 @@ var MainnetParams = Params{
CoinbasePayloadScriptPublicKeyMaxLength: defaultCoinbasePayloadScriptPublicKeyMaxLength,
PruningProofM: defaultPruningProofM,
FixedSubsidySwitchPruningPointInterval: defaultFixedSubsidySwitchPruningPointInterval,
FixedSubsidySwitchHashRateDifference: big.NewInt(1_000_000),
FixedSubsidySwitchHashRateThreshold: big.NewInt(150_000_000_000),
}
// TestnetParams defines the network parameters for the test Kaspa network.
@@ -324,7 +325,7 @@ var TestnetParams = Params{
CoinbasePayloadScriptPublicKeyMaxLength: defaultCoinbasePayloadScriptPublicKeyMaxLength,
PruningProofM: defaultPruningProofM,
FixedSubsidySwitchPruningPointInterval: defaultFixedSubsidySwitchPruningPointInterval,
FixedSubsidySwitchHashRateDifference: big.NewInt(1_000_000),
FixedSubsidySwitchHashRateThreshold: big.NewInt(150_000_000_000),
}
// SimnetParams defines the network parameters for the simulation test Kaspa
@@ -390,7 +391,7 @@ var SimnetParams = Params{
CoinbasePayloadScriptPublicKeyMaxLength: defaultCoinbasePayloadScriptPublicKeyMaxLength,
PruningProofM: defaultPruningProofM,
FixedSubsidySwitchPruningPointInterval: defaultFixedSubsidySwitchPruningPointInterval,
FixedSubsidySwitchHashRateDifference: big.NewInt(1_000_000),
FixedSubsidySwitchHashRateThreshold: big.NewInt(150_000_000_000),
}
// DevnetParams defines the network parameters for the development Kaspa network.
@@ -452,7 +453,7 @@ var DevnetParams = Params{
CoinbasePayloadScriptPublicKeyMaxLength: defaultCoinbasePayloadScriptPublicKeyMaxLength,
PruningProofM: defaultPruningProofM,
FixedSubsidySwitchPruningPointInterval: defaultFixedSubsidySwitchPruningPointInterval,
FixedSubsidySwitchHashRateDifference: big.NewInt(1_000_000),
FixedSubsidySwitchHashRateThreshold: big.NewInt(150_000_000_000),
}
var (

View File

@@ -81,10 +81,6 @@ func (networkFlags *NetworkFlags) ResolveNetwork(parser *flags.Parser) error {
return err
}
if numNets == 0 {
return errors.Errorf("Mainnet has not launched yet, use --testnet to run in testnet mode")
}
err := networkFlags.overrideDAGParams()
if err != nil {
return err

View File

@@ -14,7 +14,7 @@ import (
func TestGetHashrateString(t *testing.T) {
var results = map[string]string{
dagconfig.MainnetParams.Name: "2 H/s",
dagconfig.MainnetParams.Name: "131.07 KH/s",
dagconfig.TestnetParams.Name: "131.07 KH/s",
dagconfig.DevnetParams.Name: "131.07 KH/s",
dagconfig.SimnetParams.Name: "2.00 KH/s",