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Geth-Modification
Commit 3b00a77d authored by Péter Szilágyi's avatar Péter Szilágyi Committed by Felix Lange
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crypto, pow: add pure Go implementation of ethash

parent 288700c4
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Showing with 1929 additions and 2 deletions
crypto/crypto.go
View file @ 3b00a77d
......@@ -37,6 +37,11 @@ var (
secp256k1_halfN = new(big.Int).Div(secp256k1_N, big.NewInt(2))
)
// Hasher is a repetitive hasher allowing the same hash data structures to be
// reused between hash runs instead of requiring new ones to be created.
type Hasher func(data []byte) []byte
// Keccak256 calculates and returns the Keccak256 hash of the input data.
func Keccak256(data ...[]byte) []byte {
d := sha3.NewKeccak256()
for _, b := range data {
......@@ -45,6 +50,8 @@ func Keccak256(data ...[]byte) []byte {
return d.Sum(nil)
}
// Keccak256Hash calculates and returns the Keccak256 hash of the input data,
// converting it to an internal Hash data structure.
func Keccak256Hash(data ...[]byte) (h common.Hash) {
d := sha3.NewKeccak256()
for _, b := range data {
......@@ -54,6 +61,47 @@ func Keccak256Hash(data ...[]byte) (h common.Hash) {
return h
}
// Keccak256Hasher creates a repetitive Keccak256 hasher, allowing the same hash
// data structures to be reused between hash runs instead of requiring new ones
// to be created.
//
// The returned function is not thread safe!
func Keccak256Hasher() Hasher {
hasher := sha3.NewKeccak256()
return func(data []byte) []byte {
hasher.Write(data)
result := hasher.Sum(nil)
hasher.Reset()
return result
}
}
// Keccak512 calculates and returns the Keccak512 hash of the input data.
func Keccak512(data ...[]byte) []byte {
d := sha3.NewKeccak512()
for _, b := range data {
d.Write(b)
}
return d.Sum(nil)
}
// Keccak512Hasher creates a repetitive Keccak512 hasher, allowing the same hash
// data structures to be reused between hash runs instead of requiring new ones
// to be created.
//
// The returned function is not thread safe!
func Keccak512Hasher() Hasher {
hasher := sha3.NewKeccak512()
return func(data []byte) []byte {
hasher.Write(data)
result := hasher.Sum(nil)
hasher.Reset()
return result
}
}
// Deprecated: For backward compatibility as other packages depend on these
func Sha3Hash(data ...[]byte) common.Hash { return Keccak256Hash(data...) }
......
crypto/sha3/hashes.go
View file @ 3b00a77d
......@@ -15,6 +15,9 @@ import (
// NewKeccak256 creates a new Keccak-256 hash.
func NewKeccak256() hash.Hash { return &state{rate: 136, outputLen: 32, dsbyte: 0x01} }
// NewKeccak512 creates a new Keccak-512 hash.
func NewKeccak512() hash.Hash { return &state{rate: 72, outputLen: 64, dsbyte: 0x01} }
// New224 creates a new SHA3-224 hash.
// Its generic security strength is 224 bits against preimage attacks,
// and 112 bits against collision attacks.
......
crypto/sha3/keccakf_amd64.s
View file @ 3b00a77d
......@@ -322,7 +322,6 @@
// func keccakF1600(state *[25]uint64)
TEXT ·keccakF1600(SB), 0, $200-8
MOVQ state+0(FP), rpState
SUBQ $(8*25), SP
// Convert the user state into an internal state
NOTQ _be(rpState)
......@@ -388,5 +387,4 @@ TEXT ·keccakF1600(SB), 0, $200-8
NOTQ _mi(rpState)
NOTQ _sa(rpState)
ADDQ $(8*25), SP
RET
pow/ethash.go 0 → 100644
View file @ 3b00a77d
// Copyright 2017 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// 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 pow
import (
"encoding/binary"
"io"
"math/big"
"runtime"
"sync"
"sync/atomic"
"time"
"github.com/ethereum/go-ethereum/common"
"github.com/ethereum/go-ethereum/common/hexutil"
"github.com/ethereum/go-ethereum/crypto"
"github.com/ethereum/go-ethereum/log"
)
const (
datasetInitBytes = 1 << 30 // Bytes in dataset at genesis
datasetGrowthBytes = 1 << 23 // Dataset growth per epoch
cacheInitBytes = 1 << 24 // Bytes in cache at genesis
cacheGrowthBytes = 1 << 17 // Cache growth per epoch
epochLength = 30000 // Blocks per epoch
mixBytes = 128 // Width of mix
hashBytes = 64 // Hash length in bytes
hashWords = 16 // Number of 32 bit ints in a hash
datasetParents = 256 // Number of parents of each dataset element
cacheRounds = 3 // Number of rounds in cache production
loopAccesses = 64 // Number of accesses in hashimoto loop
)
var (
// Metadata fields to be compatible with the C++ ethash
ethashRevision = 23 // Data structure version
ethashMagic = hexutil.MustDecode("0xfee1deadbaddcafe") // Dataset dump magic number
)
// cacheSize calculates and returns the size of the ethash verification cache that
// belongs to a certain block number. The cache size grows linearly, however, we
// always take the highest prime below the linearly growing threshold in order to
// reduce the risk of accidental regularities leading to cyclic behavior.
func cacheSize(block uint64) uint64 {
// If we have a pre-generated value, use that
epoch := int(block / epochLength)
if epoch < len(cacheSizes) {
return cacheSizes[epoch]
}
// No known cache size, calculate manually (sanity branch only)
size := uint64(cacheInitBytes + cacheGrowthBytes*epoch - hashBytes)
for !new(big.Int).SetUint64(size / hashBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
size -= 2 * hashBytes
}
return size
}
// datasetSize calculates and returns the size of the ethash mining dataset that
// belongs to a certain block number. The dataset size grows linearly, however, we
// always take the highest prime below the linearly growing threshold in order to
// reduce the risk of accidental regularities leading to cyclic behavior.
func datasetSize(block uint64) uint64 {
// If we have a pre-generated value, use that
epoch := int(block / epochLength)
if epoch < len(datasetSizes) {
return datasetSizes[epoch]
}
// No known dataset size, calculate manually (sanity branch only)
size := uint64(datasetInitBytes + datasetGrowthBytes*epoch - mixBytes)
for !new(big.Int).SetUint64(size / mixBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
size -= 2 * mixBytes
}
return size
}
// seedHash is the seed to use for generating a vrification cache and the mining
// dataset.
func seedHash(block uint64) []byte {
seed := make([]byte, 32)
if block < epochLength {
return seed
}
keccak256 := crypto.Keccak256Hasher()
for i := 0; i < int(block/epochLength); i++ {
seed = keccak256(seed)
}
return seed
}
// generateCache creates a verification cache of a given size for an input seed.
// The cache production process involves first sequentially filling up 32 MB of
// memory, then performing two passes of Sergio Demian Lerner's RandMemoHash
// algorithm from Strict Memory Hard Hashing Functions (2014). The output is a
// set of 524288 64-byte values.
func generateCache(size uint64, seed []byte) []byte {
// Print some debug logs to allow analysis on low end devices
logger := log.New("size", size, "seed", hexutil.Bytes(seed))
logger.Debug("Generating ethash cache")
defer func(start time.Time) {
logger.Debug("Generated ethash cache", "elapsed", common.PrettyDuration(time.Since(start)))
}(time.Now())
// Calculate the number of thoretical rows (we'll store in one buffer nonetheless)
rows := int(size) / hashBytes
// Create a hasher to reuse between invocations
keccak512 := crypto.Keccak512Hasher()
// Sequentially produce the initial dataset
cache := make([]byte, size)
copy(cache, keccak512(seed))
for offset := uint64(hashBytes); offset < size; offset += hashBytes {
copy(cache[offset:], keccak512(cache[offset-hashBytes:offset]))
}
// Use a low-round version of randmemohash
temp := make([]byte, hashBytes)
for i := 0; i < cacheRounds; i++ {
for j := 0; j < rows; j++ {
var (
srcOff = ((j - 1 + rows) % rows) * hashBytes
dstOff = j * hashBytes
xorOff = (binary.LittleEndian.Uint32(cache[dstOff:]) % uint32(rows)) * hashBytes
)
xorBytes(temp, cache[srcOff:srcOff+hashBytes], cache[xorOff:xorOff+hashBytes])
copy(cache[dstOff:], keccak512(temp))
}
}
return cache
}
// prepare convers an ethash cache or dataset from a byte stream into the internal
// int representation. All ethash methods work with ints to avoid constant byte to
// int conversions as well as to handle both little and big endian systems.
func prepare(size uint64, r io.Reader) []uint32 {
ints := make([]uint32, size/4)
buffer := make([]byte, 4)
for i := 0; i < len(ints); i++ {
io.ReadFull(r, buffer)
ints[i] = binary.LittleEndian.Uint32(buffer)
}
return ints
}
// fnv is an algorithm inspired by the FNV hash, which in some cases is used as
// a non-associative substitute for XOR. Note that we multiply the prime with
// the full 32-bit input, in contrast with the FNV-1 spec which multiplies the
// prime with one byte (octet) in turn.
func fnv(a, b uint32) uint32 {
return a*0x01000193 ^ b
}
// fnvHash mixes in data into mix using the ethash fnv method.
func fnvHash(mix []uint32, data []uint32) {
for i := 0; i < len(mix); i++ {
mix[i] = mix[i]*0x01000193 ^ data[i]
}
}
// generateDatasetItem combines data from 256 pseudorandomly selected cache nodes,
// and hashes that to compute a single dataset node.
func generateDatasetItem(cache []uint32, index uint32, keccak512 crypto.Hasher) []byte {
// Calculate the number of thoretical rows (we use one buffer nonetheless)
rows := uint32(len(cache) / hashWords)
// Initialize the mix
mix := make([]byte, hashBytes)
binary.LittleEndian.PutUint32(mix, cache[(index%rows)*hashWords]^index)
for i := 1; i < hashWords; i++ {
binary.LittleEndian.PutUint32(mix[i*4:], cache[(index%rows)*hashWords+uint32(i)])
}
mix = keccak512(mix)
// Convert the mix to uint32s to avoid constant bit shifting
intMix := make([]uint32, hashWords)
for i := 0; i < len(intMix); i++ {
intMix[i] = binary.LittleEndian.Uint32(mix[i*4:])
}
// fnv it with a lot of random cache nodes based on index
for i := uint32(0); i < datasetParents; i++ {
parent := fnv(index^i, intMix[i%16]) % rows
fnvHash(intMix, cache[parent*hashWords:])
}
// Flatten the uint32 mix into a binary one and return
for i, val := range intMix {
binary.LittleEndian.PutUint32(mix[i*4:], val)
}
return keccak512(mix)
}
// generateDataset generates the entire ethash dataset for mining.
func generateDataset(size uint64, cache []uint32) []byte {
// Print some debug logs to allow analysis on low end devices
logger := log.New("size", size)
logger.Debug("Generating ethash dataset")
defer func(start time.Time) {
logger.Debug("Generated ethash dataset", "elapsed", common.PrettyDuration(time.Since(start)))
}(time.Now())
// Generate the dataset on many goroutines since it takes a while
dataset := make([]byte, size)
threads := runtime.NumCPU()
var pend sync.WaitGroup
pend.Add(threads)
var progress uint32
for i := 0; i < threads; i++ {
go func(id int) {
defer pend.Done()
// Create a hasher to reuse between invocations
keccak512 := crypto.Keccak512Hasher()
// Calculate the data segment this thread should generate
batch := uint32(size / hashBytes / uint64(threads))
start := uint32(id) * batch
limit := start + batch
if limit > uint32(size/hashBytes) {
limit = uint32(size / hashBytes)
}
// Calculate the dataset segment
percent := uint32(size / hashBytes / 100)
for index := start; index < limit; index++ {
copy(dataset[index*hashBytes:], generateDatasetItem(cache, index, keccak512))
if status := atomic.AddUint32(&progress, 1); status%percent == 0 {
logger.Info("Generating DAG in progress", "percentage", uint64(status*100)/(size/hashBytes))
}
}
}(i)
}
// Wait for all the generators to finish and return
pend.Wait()
return dataset
}
// hashimoto aggregates data from the full dataset in order to produce our final
// value for a particular header hash and nonce.
func hashimoto(hash []byte, nonce uint64, size uint64, lookup func(index uint32) []uint32) ([]byte, []byte) {
// Calculate the number of thoretical rows (we use one buffer nonetheless)
rows := uint32(size / mixBytes)
// Combine header+nonce into a 64 byte seed
seed := make([]byte, 40)
copy(seed, hash)
binary.LittleEndian.PutUint64(seed[32:], nonce)
seed = crypto.Keccak512(seed)
seedHead := binary.LittleEndian.Uint32(seed)
// Start the mix with replicated seed
mix := make([]uint32, mixBytes/4)
for i := 0; i < len(mix); i++ {
mix[i] = binary.LittleEndian.Uint32(seed[i%16*4:])
}
// Mix in random dataset nodes
temp := make([]uint32, len(mix))
for i := 0; i < loopAccesses; i++ {
parent := fnv(uint32(i)^seedHead, mix[i%len(mix)]) % rows
for j := uint32(0); j < mixBytes/hashBytes; j++ {
copy(temp[j*hashWords:], lookup(2*parent+j))
}
fnvHash(mix, temp)
}
// Compress mix
for i := 0; i < len(mix); i += 4 {
mix[i/4] = fnv(fnv(fnv(mix[i], mix[i+1]), mix[i+2]), mix[i+3])
}
mix = mix[:len(mix)/4]
digest := make([]byte, common.HashLength)
for i, val := range mix {
binary.LittleEndian.PutUint32(digest[i*4:], val)
}
return digest, crypto.Keccak256(append(seed, digest...))
}
// hashimotoLight aggregates data from the full dataset (using only a small
// in-memory cache) in order to produce our final value for a particular header
// hash and nonce.
func hashimotoLight(size uint64, cache []uint32, hash []byte, nonce uint64) ([]byte, []byte) {
keccak512 := crypto.Keccak512Hasher()
lookup := func(index uint32) []uint32 {
rawData := generateDatasetItem(cache, index, keccak512)
data := make([]uint32, len(rawData)/4)
for i := 0; i < len(data); i++ {
data[i] = binary.LittleEndian.Uint32(rawData[i*4:])
}
return data
}
return hashimoto(hash, nonce, size, lookup)
}
// hashimotoFull aggregates data from the full dataset (using the full in-memory
// dataset) in order to produce our final value for a particular header hash and
// nonce.
func hashimotoFull(size uint64, dataset []uint32, hash []byte, nonce uint64) ([]byte, []byte) {
lookup := func(index uint32) []uint32 {
offset := index * hashWords
return dataset[offset : offset+hashWords]
}
return hashimoto(hash, nonce, size, lookup)
}
// datasetSizes is a lookup table for the ethash dataset size for the first 2048
// epochs (i.e. 61440000 blocks).
var datasetSizes = []uint64{
1073739904, 1082130304, 1090514816, 1098906752, 1107293056,
1115684224, 1124070016, 1132461952, 1140849536, 1149232768,
1157627776, 1166013824, 1174404736, 1182786944, 1191180416,
1199568512, 1207958912, 1216345216, 1224732032, 1233124736,
1241513344, 1249902464, 1258290304, 1266673792, 1275067264,
1283453312, 1291844992, 1300234112, 1308619904, 1317010048,
1325397376, 1333787776, 1342176128, 1350561664, 1358954368,
1367339392, 1375731584, 1384118144, 1392507008, 1400897408,
1409284736, 1417673344, 1426062464, 1434451072, 1442839168,
1451229056, 1459615616, 1468006016, 1476394112, 1484782976,
1493171584, 1501559168, 1509948032, 1518337664, 1526726528,
1535114624, 1543503488, 1551892096, 1560278656, 1568669056,
1577056384, 1585446272, 1593831296, 1602219392, 1610610304,
1619000192, 1627386752, 1635773824, 1644164224, 1652555648,
1660943488, 1669332608, 1677721216, 1686109312, 1694497664,
1702886272, 1711274624, 1719661184, 1728047744, 1736434816,
1744829056, 1753218944, 1761606272, 1769995904, 1778382464,
1786772864, 1795157888, 1803550592, 1811937664, 1820327552,
1828711552, 1837102976, 1845488768, 1853879936, 1862269312,
1870656896, 1879048064, 1887431552, 1895825024, 1904212096,
1912601216, 1920988544, 1929379456, 1937765504, 1946156672,
1954543232, 1962932096, 1971321728, 1979707264, 1988093056,
1996487552, 2004874624, 2013262208, 2021653888, 2030039936,
2038430848, 2046819968, 2055208576, 2063596672, 2071981952,
2080373632, 2088762752, 2097149056, 2105539712, 2113928576,
2122315136, 2130700672, 2139092608, 2147483264, 2155872128,
2164257664, 2172642176, 2181035392, 2189426048, 2197814912,
2206203008, 2214587264, 2222979712, 2231367808, 2239758208,
2248145024, 2256527744, 2264922752, 2273312128, 2281701248,
2290086272, 2298476672, 2306867072, 2315251072, 2323639168,
2332032128, 2340420224, 2348808064, 2357196416, 2365580416,
2373966976, 2382363008, 2390748544, 2399139968, 2407530368,
2415918976, 2424307328, 2432695424, 2441084288, 2449472384,
2457861248, 2466247808, 2474637184, 2483026816, 2491414144,
2499803776, 2508191872, 2516582272, 2524970368, 2533359232,
2541743488, 2550134144, 2558525056, 2566913408, 2575301504,
2583686528, 2592073856, 2600467328, 2608856192, 2617240448,
2625631616, 2634022016, 2642407552, 2650796416, 2659188352,
2667574912, 2675965312, 2684352896, 2692738688, 2701130624,
2709518464, 2717907328, 2726293376, 2734685056, 2743073152,
2751462016, 2759851648, 2768232832, 2776625536, 2785017728,
2793401984, 2801794432, 2810182016, 2818571648, 2826959488,
2835349376, 2843734144, 2852121472, 2860514432, 2868900992,
2877286784, 2885676928, 2894069632, 2902451584, 2910843008,
2919234688, 2927622784, 2936011648, 2944400768, 2952789376,
2961177728, 2969565568, 2977951616, 2986338944, 2994731392,
3003120256, 3011508352, 3019895936, 3028287104, 3036675968,
3045063808, 3053452928, 3061837696, 3070228352, 3078615424,
3087003776, 3095394944, 3103782272, 3112173184, 3120562048,
3128944768, 3137339264, 3145725056, 3154109312, 3162505088,
3170893184, 3179280256, 3187669376, 3196056704, 3204445568,
3212836736, 3221224064, 3229612928, 3238002304, 3246391168,
3254778496, 3263165824, 3271556224, 3279944576, 3288332416,
3296719232, 3305110912, 3313500032, 3321887104, 3330273152,
3338658944, 3347053184, 3355440512, 3363827072, 3372220288,
3380608384, 3388997504, 3397384576, 3405774208, 3414163072,
3422551936, 3430937984, 3439328384, 3447714176, 3456104576,
3464493952, 3472883584, 3481268864, 3489655168, 3498048896,
3506434432, 3514826368, 3523213952, 3531603584, 3539987072,
3548380288, 3556763264, 3565157248, 3573545344, 3581934464,
3590324096, 3598712704, 3607098752, 3615488384, 3623877248,
3632265856, 3640646528, 3649043584, 3657430144, 3665821568,
3674207872, 3682597504, 3690984832, 3699367808, 3707764352,
3716152448, 3724541056, 3732925568, 3741318016, 3749706368,
3758091136, 3766481536, 3774872704, 3783260032, 3791650432,
3800036224, 3808427648, 3816815488, 3825204608, 3833592704,
3841981568, 3850370432, 3858755968, 3867147904, 3875536256,
3883920512, 3892313728, 3900702592, 3909087872, 3917478784,
3925868416, 3934256512, 3942645376, 3951032192, 3959422336,
3967809152, 3976200064, 3984588416, 3992974976, 4001363584,
4009751168, 4018141312, 4026530432, 4034911616, 4043308928,
4051695488, 4060084352, 4068472448, 4076862848, 4085249408,
4093640576, 4102028416, 4110413696, 4118805632, 4127194496,
4135583104, 4143971968, 4152360832, 4160746112, 4169135744,
4177525888, 4185912704, 4194303616, 4202691968, 4211076736,
4219463552, 4227855488, 4236246656, 4244633728, 4253022848,
4261412224, 4269799808, 4278184832, 4286578048, 4294962304,
4303349632, 4311743104, 4320130432, 4328521088, 4336909184,
4345295488, 4353687424, 4362073472, 4370458496, 4378852736,
4387238528, 4395630208, 4404019072, 4412407424, 4420790656,
4429182848, 4437571456, 4445962112, 4454344064, 4462738048,
4471119232, 4479516544, 4487904128, 4496289664, 4504682368,
4513068416, 4521459584, 4529846144, 4538232704, 4546619776,
4555010176, 4563402112, 4571790208, 4580174464, 4588567936,
4596957056, 4605344896, 4613734016, 4622119808, 4630511488,
4638898816, 4647287936, 4655675264, 4664065664, 4672451968,
4680842624, 4689231488, 4697620352, 4706007424, 4714397056,
4722786176, 4731173248, 4739562368, 4747951744, 4756340608,
4764727936, 4773114496, 4781504384, 4789894784, 4798283648,
4806667648, 4815059584, 4823449472, 4831835776, 4840226176,
4848612224, 4857003392, 4865391488, 4873780096, 4882169728,
4890557312, 4898946944, 4907333248, 4915722368, 4924110976,
4932499328, 4940889728, 4949276032, 4957666432, 4966054784,
4974438016, 4982831488, 4991221376, 4999607168, 5007998848,
5016386432, 5024763776, 5033164672, 5041544576, 5049941888,
5058329728, 5066717056, 5075107456, 5083494272, 5091883904,
5100273536, 5108662144, 5117048192, 5125436032, 5133827456,
5142215296, 5150605184, 5158993024, 5167382144, 5175769472,
5184157568, 5192543872, 5200936064, 5209324928, 5217711232,
5226102656, 5234490496, 5242877312, 5251263872, 5259654016,
5268040832, 5276434304, 5284819328, 5293209728, 5301598592,
5309986688, 5318374784, 5326764416, 5335151488, 5343542144,
5351929472, 5360319872, 5368706944, 5377096576, 5385484928,
5393871232, 5402263424, 5410650496, 5419040384, 5427426944,
5435816576, 5444205952, 5452594816, 5460981376, 5469367936,
5477760896, 5486148736, 5494536832, 5502925952, 5511315328,
5519703424, 5528089984, 5536481152, 5544869504, 5553256064,
5561645696, 5570032768, 5578423936, 5586811264, 5595193216,
5603585408, 5611972736, 5620366208, 5628750464, 5637143936,
5645528192, 5653921408, 5662310272, 5670694784, 5679082624,
5687474048, 5695864448, 5704251008, 5712641408, 5721030272,
5729416832, 5737806208, 5746194304, 5754583936, 5762969984,
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17137926016, 17146314368, 17154700928, 17163089792, 17171480192,
17179864192, 17188256896, 17196644992, 17205033856, 17213423488,
17221811072, 17230198912, 17238588032, 17246976896, 17255360384,
17263754624, 17272143232, 17280530048, 17288918912, 17297309312,
17305696384, 17314085504, 17322475136, 17330863744, 17339252096,
17347640192, 17356026496, 17364413824, 17372796544, 17381190016,
17389583488, 17397972608, 17406360704, 17414748544, 17423135872,
17431527296, 17439915904, 17448303232, 17456691584, 17465081728,
17473468288, 17481857408, 17490247552, 17498635904, 17507022464,
17515409024, 17523801728, 17532189824, 17540577664, 17548966016,
17557353344, 17565741184, 17574131584, 17582519168, 17590907008,
17599296128, 17607687808, 17616076672, 17624455808, 17632852352,
17641238656, 17649630848, 17658018944, 17666403968, 17674794112,
17683178368, 17691573376, 17699962496, 17708350592, 17716739968,
17725126528, 17733517184, 17741898112, 17750293888, 17758673024,
17767070336, 17775458432, 17783848832, 17792236928, 17800625536,
17809012352, 17817402752, 17825785984, 17834178944, 17842563968,
17850955648, 17859344512, 17867732864, 17876119424, 17884511872,
17892900224, 17901287296, 17909677696, 17918058112, 17926451072,
17934843776, 17943230848, 17951609216, 17960008576, 17968397696,
17976784256, 17985175424, 17993564032, 18001952128, 18010339712,
18018728576, 18027116672, 18035503232, 18043894144, 18052283264,
18060672128, 18069056384, 18077449856, 18085837184, 18094225792,
18102613376, 18111004544, 18119388544, 18127781248, 18136170368,
18144558976, 18152947328, 18161336192, 18169724288, 18178108544,
18186498944, 18194886784, 18203275648, 18211666048, 18220048768,
18228444544, 18236833408, 18245220736}
// cacheSizes is a lookup table for the ethash verification cache size for the
// first 2048 epochs (i.e. 61440000 blocks).
var cacheSizes = []uint64{
16776896, 16907456, 17039296, 17170112, 17301056, 17432512, 17563072,
17693888, 17824192, 17955904, 18087488, 18218176, 18349504, 18481088,
18611392, 18742336, 18874304, 19004224, 19135936, 19267264, 19398208,
19529408, 19660096, 19791424, 19922752, 20053952, 20184896, 20315968,
20446912, 20576576, 20709184, 20840384, 20971072, 21102272, 21233216,
21364544, 21494848, 21626816, 21757376, 21887552, 22019392, 22151104,
22281536, 22412224, 22543936, 22675264, 22806464, 22935872, 23068096,
23198272, 23330752, 23459008, 23592512, 23723968, 23854912, 23986112,
24116672, 24247616, 24378688, 24509504, 24640832, 24772544, 24903488,
25034432, 25165376, 25296704, 25427392, 25558592, 25690048, 25820096,
25951936, 26081728, 26214208, 26345024, 26476096, 26606656, 26737472,
26869184, 26998208, 27131584, 27262528, 27393728, 27523904, 27655744,
27786688, 27917888, 28049344, 28179904, 28311488, 28441792, 28573504,
28700864, 28835648, 28966208, 29096768, 29228608, 29359808, 29490752,
29621824, 29752256, 29882816, 30014912, 30144448, 30273728, 30406976,
30538432, 30670784, 30799936, 30932672, 31063744, 31195072, 31325248,
31456192, 31588288, 31719232, 31850432, 31981504, 32110784, 32243392,
32372672, 32505664, 32636608, 32767808, 32897344, 33029824, 33160768,
33289664, 33423296, 33554368, 33683648, 33816512, 33947456, 34076992,
34208704, 34340032, 34471744, 34600256, 34734016, 34864576, 34993984,
35127104, 35258176, 35386688, 35518528, 35650624, 35782336, 35910976,
36044608, 36175808, 36305728, 36436672, 36568384, 36699968, 36830656,
36961984, 37093312, 37223488, 37355072, 37486528, 37617472, 37747904,
37879232, 38009792, 38141888, 38272448, 38403392, 38535104, 38660672,
38795584, 38925632, 39059264, 39190336, 39320768, 39452096, 39581632,
39713984, 39844928, 39974848, 40107968, 40238144, 40367168, 40500032,
40631744, 40762816, 40894144, 41023552, 41155904, 41286208, 41418304,
41547712, 41680448, 41811904, 41942848, 42073792, 42204992, 42334912,
42467008, 42597824, 42729152, 42860096, 42991552, 43122368, 43253696,
43382848, 43515712, 43646912, 43777088, 43907648, 44039104, 44170432,
44302144, 44433344, 44564288, 44694976, 44825152, 44956864, 45088448,
45219008, 45350464, 45481024, 45612608, 45744064, 45874496, 46006208,
46136768, 46267712, 46399424, 46529344, 46660672, 46791488, 46923328,
47053504, 47185856, 47316928, 47447872, 47579072, 47710144, 47839936,
47971648, 48103232, 48234176, 48365248, 48496192, 48627136, 48757312,
48889664, 49020736, 49149248, 49283008, 49413824, 49545152, 49675712,
49807168, 49938368, 50069056, 50200256, 50331584, 50462656, 50593472,
50724032, 50853952, 50986048, 51117632, 51248576, 51379904, 51510848,
51641792, 51773248, 51903296, 52035136, 52164032, 52297664, 52427968,
52557376, 52690112, 52821952, 52952896, 53081536, 53213504, 53344576,
53475776, 53608384, 53738816, 53870528, 54000832, 54131776, 54263744,
54394688, 54525248, 54655936, 54787904, 54918592, 55049152, 55181248,
55312064, 55442752, 55574336, 55705024, 55836224, 55967168, 56097856,
56228672, 56358592, 56490176, 56621888, 56753728, 56884928, 57015488,
57146816, 57278272, 57409216, 57540416, 57671104, 57802432, 57933632,
58064576, 58195264, 58326976, 58457408, 58588864, 58720192, 58849984,
58981696, 59113024, 59243456, 59375552, 59506624, 59637568, 59768512,
59897792, 60030016, 60161984, 60293056, 60423872, 60554432, 60683968,
60817216, 60948032, 61079488, 61209664, 61341376, 61471936, 61602752,
61733696, 61865792, 61996736, 62127808, 62259136, 62389568, 62520512,
62651584, 62781632, 62910784, 63045056, 63176128, 63307072, 63438656,
63569216, 63700928, 63831616, 63960896, 64093888, 64225088, 64355392,
64486976, 64617664, 64748608, 64879424, 65009216, 65142464, 65273792,
65402816, 65535424, 65666752, 65797696, 65927744, 66060224, 66191296,
66321344, 66453056, 66584384, 66715328, 66846656, 66977728, 67108672,
67239104, 67370432, 67501888, 67631296, 67763776, 67895104, 68026304,
68157248, 68287936, 68419264, 68548288, 68681408, 68811968, 68942912,
69074624, 69205568, 69337024, 69467584, 69599168, 69729472, 69861184,
69989824, 70122944, 70253888, 70385344, 70515904, 70647232, 70778816,
70907968, 71040832, 71171648, 71303104, 71432512, 71564992, 71695168,
71826368, 71958464, 72089536, 72219712, 72350144, 72482624, 72613568,
72744512, 72875584, 73006144, 73138112, 73268672, 73400128, 73530944,
73662272, 73793344, 73924544, 74055104, 74185792, 74316992, 74448832,
74579392, 74710976, 74841664, 74972864, 75102784, 75233344, 75364544,
75497024, 75627584, 75759296, 75890624, 76021696, 76152256, 76283072,
76414144, 76545856, 76676672, 76806976, 76937792, 77070016, 77200832,
77331392, 77462464, 77593664, 77725376, 77856448, 77987776, 78118336,
78249664, 78380992, 78511424, 78642496, 78773056, 78905152, 79033664,
79166656, 79297472, 79429568, 79560512, 79690816, 79822784, 79953472,
80084672, 80214208, 80346944, 80477632, 80608576, 80740288, 80870848,
81002048, 81133504, 81264448, 81395648, 81525952, 81657536, 81786304,
81919808, 82050112, 82181312, 82311616, 82443968, 82573376, 82705984,
82835776, 82967744, 83096768, 83230528, 83359552, 83491264, 83622464,
83753536, 83886016, 84015296, 84147776, 84277184, 84409792, 84540608,
84672064, 84803008, 84934336, 85065152, 85193792, 85326784, 85458496,
85589312, 85721024, 85851968, 85982656, 86112448, 86244416, 86370112,
86506688, 86637632, 86769344, 86900672, 87031744, 87162304, 87293632,
87424576, 87555392, 87687104, 87816896, 87947968, 88079168, 88211264,
88341824, 88473152, 88603712, 88735424, 88862912, 88996672, 89128384,
89259712, 89390272, 89521984, 89652544, 89783872, 89914816, 90045376,
90177088, 90307904, 90438848, 90569152, 90700096, 90832832, 90963776,
91093696, 91223744, 91356992, 91486784, 91618496, 91749824, 91880384,
92012224, 92143552, 92273344, 92405696, 92536768, 92666432, 92798912,
92926016, 93060544, 93192128, 93322816, 93453632, 93583936, 93715136,
93845056, 93977792, 94109504, 94240448, 94371776, 94501184, 94632896,
94764224, 94895552, 95023424, 95158208, 95287744, 95420224, 95550016,
95681216, 95811904, 95943872, 96075328, 96203584, 96337856, 96468544,
96599744, 96731072, 96860992, 96992576, 97124288, 97254848, 97385536,
97517248, 97647808, 97779392, 97910464, 98041408, 98172608, 98303168,
98434496, 98565568, 98696768, 98827328, 98958784, 99089728, 99220928,
99352384, 99482816, 99614272, 99745472, 99876416, 100007104,
100138048, 100267072, 100401088, 100529984, 100662592, 100791872,
100925248, 101056064, 101187392, 101317952, 101449408, 101580608,
101711296, 101841728, 101973824, 102104896, 102235712, 102366016,
102498112, 102628672, 102760384, 102890432, 103021888, 103153472,
103284032, 103415744, 103545152, 103677248, 103808576, 103939648,
104070976, 104201792, 104332736, 104462528, 104594752, 104725952,
104854592, 104988608, 105118912, 105247808, 105381184, 105511232,
105643072, 105774784, 105903296, 106037056, 106167872, 106298944,
106429504, 106561472, 106691392, 106822592, 106954304, 107085376,
107216576, 107346368, 107478464, 107609792, 107739712, 107872192,
108003136, 108131392, 108265408, 108396224, 108527168, 108657344,
108789568, 108920384, 109049792, 109182272, 109312576, 109444928,
109572928, 109706944, 109837888, 109969088, 110099648, 110230976,
110362432, 110492992, 110624704, 110755264, 110886208, 111017408,
111148864, 111279296, 111410752, 111541952, 111673024, 111803456,
111933632, 112066496, 112196416, 112328512, 112457792, 112590784,
112715968, 112852672, 112983616, 113114944, 113244224, 113376448,
113505472, 113639104, 113770304, 113901376, 114031552, 114163264,
114294592, 114425536, 114556864, 114687424, 114818624, 114948544,
115080512, 115212224, 115343296, 115473472, 115605184, 115736128,
115867072, 115997248, 116128576, 116260288, 116391488, 116522944,
116652992, 116784704, 116915648, 117046208, 117178304, 117308608,
117440192, 117569728, 117701824, 117833024, 117964096, 118094656,
118225984, 118357312, 118489024, 118617536, 118749632, 118882112,
119012416, 119144384, 119275328, 119406016, 119537344, 119668672,
119798464, 119928896, 120061376, 120192832, 120321728, 120454336,
120584512, 120716608, 120848192, 120979136, 121109056, 121241408,
121372352, 121502912, 121634752, 121764416, 121895744, 122027072,
122157632, 122289088, 122421184, 122550592, 122682944, 122813888,
122945344, 123075776, 123207488, 123338048, 123468736, 123600704,
123731264, 123861952, 123993664, 124124608, 124256192, 124386368,
124518208, 124649024, 124778048, 124911296, 125041088, 125173696,
125303744, 125432896, 125566912, 125696576, 125829056, 125958592,
126090304, 126221248, 126352832, 126483776, 126615232, 126746432,
126876608, 127008704, 127139392, 127270336, 127401152, 127532224,
127663552, 127794752, 127925696, 128055232, 128188096, 128319424,
128449856, 128581312, 128712256, 128843584, 128973632, 129103808,
129236288, 129365696, 129498944, 129629888, 129760832, 129892288,
130023104, 130154048, 130283968, 130416448, 130547008, 130678336,
130807616, 130939456, 131071552, 131202112, 131331776, 131464384,
131594048, 131727296, 131858368, 131987392, 132120256, 132250816,
132382528, 132513728, 132644672, 132774976, 132905792, 133038016,
133168832, 133299392, 133429312, 133562048, 133692992, 133823296,
133954624, 134086336, 134217152, 134348608, 134479808, 134607296,
134741056, 134872384, 135002944, 135134144, 135265472, 135396544,
135527872, 135659072, 135787712, 135921472, 136052416, 136182848,
136313792, 136444864, 136576448, 136707904, 136837952, 136970048,
137099584, 137232064, 137363392, 137494208, 137625536, 137755712,
137887424, 138018368, 138149824, 138280256, 138411584, 138539584,
138672832, 138804928, 138936128, 139066688, 139196864, 139328704,
139460032, 139590208, 139721024, 139852864, 139984576, 140115776,
140245696, 140376512, 140508352, 140640064, 140769856, 140902336,
141032768, 141162688, 141294016, 141426496, 141556544, 141687488,
141819584, 141949888, 142080448, 142212544, 142342336, 142474432,
142606144, 142736192, 142868288, 142997824, 143129408, 143258944,
143392448, 143523136, 143653696, 143785024, 143916992, 144045632,
144177856, 144309184, 144440768, 144570688, 144701888, 144832448,
144965056, 145096384, 145227584, 145358656, 145489856, 145620928,
145751488, 145883072, 146011456, 146144704, 146275264, 146407232,
146538176, 146668736, 146800448, 146931392, 147062336, 147193664,
147324224, 147455936, 147586624, 147717056, 147848768, 147979456,
148110784, 148242368, 148373312, 148503232, 148635584, 148766144,
148897088, 149028416, 149159488, 149290688, 149420224, 149551552,
149683136, 149814976, 149943616, 150076352, 150208064, 150338624,
150470464, 150600256, 150732224, 150862784, 150993088, 151125952,
151254976, 151388096, 151519168, 151649728, 151778752, 151911104,
152042944, 152174144, 152304704, 152435648, 152567488, 152698816,
152828992, 152960576, 153091648, 153222976, 153353792, 153484096,
153616192, 153747008, 153878336, 154008256, 154139968, 154270912,
154402624, 154533824, 154663616, 154795712, 154926272, 155057984,
155188928, 155319872, 155450816, 155580608, 155712064, 155843392,
155971136, 156106688, 156237376, 156367424, 156499264, 156630976,
156761536, 156892352, 157024064, 157155008, 157284416, 157415872,
157545536, 157677248, 157810496, 157938112, 158071744, 158203328,
158334656, 158464832, 158596288, 158727616, 158858048, 158988992,
159121216, 159252416, 159381568, 159513152, 159645632, 159776192,
159906496, 160038464, 160169536, 160300352, 160430656, 160563008,
160693952, 160822208, 160956352, 161086784, 161217344, 161349184,
161480512, 161611456, 161742272, 161873216, 162002752, 162135872,
162266432, 162397888, 162529216, 162660032, 162790976, 162922048,
163052096, 163184576, 163314752, 163446592, 163577408, 163707968,
163839296, 163969984, 164100928, 164233024, 164364224, 164494912,
164625856, 164756672, 164887616, 165019072, 165150016, 165280064,
165412672, 165543104, 165674944, 165805888, 165936832, 166067648,
166198336, 166330048, 166461248, 166591552, 166722496, 166854208,
166985408, 167116736, 167246656, 167378368, 167508416, 167641024,
167771584, 167903168, 168034112, 168164032, 168295744, 168427456,
168557632, 168688448, 168819136, 168951616, 169082176, 169213504,
169344832, 169475648, 169605952, 169738048, 169866304, 169999552,
170131264, 170262464, 170393536, 170524352, 170655424, 170782016,
170917696, 171048896, 171179072, 171310784, 171439936, 171573184,
171702976, 171835072, 171966272, 172097216, 172228288, 172359232,
172489664, 172621376, 172747712, 172883264, 173014208, 173144512,
173275072, 173407424, 173539136, 173669696, 173800768, 173931712,
174063424, 174193472, 174325696, 174455744, 174586816, 174718912,
174849728, 174977728, 175109696, 175242688, 175374272, 175504832,
175636288, 175765696, 175898432, 176028992, 176159936, 176291264,
176422592, 176552512, 176684864, 176815424, 176946496, 177076544,
177209152, 177340096, 177470528, 177600704, 177731648, 177864256,
177994816, 178126528, 178257472, 178387648, 178518464, 178650176,
178781888, 178912064, 179044288, 179174848, 179305024, 179436736,
179568448, 179698496, 179830208, 179960512, 180092608, 180223808,
180354752, 180485696, 180617152, 180748096, 180877504, 181009984,
181139264, 181272512, 181402688, 181532608, 181663168, 181795136,
181926592, 182057536, 182190016, 182320192, 182451904, 182582336,
182713792, 182843072, 182976064, 183107264, 183237056, 183368384,
183494848, 183631424, 183762752, 183893824, 184024768, 184154816,
184286656, 184417984, 184548928, 184680128, 184810816, 184941248,
185072704, 185203904, 185335616, 185465408, 185596352, 185727296,
185859904, 185989696, 186121664, 186252992, 186383552, 186514112,
186645952, 186777152, 186907328, 187037504, 187170112, 187301824,
187429184, 187562048, 187693504, 187825472, 187957184, 188087104,
188218304, 188349376, 188481344, 188609728, 188743616, 188874304,
189005248, 189136448, 189265088, 189396544, 189528128, 189660992,
189791936, 189923264, 190054208, 190182848, 190315072, 190447424,
190577984, 190709312, 190840768, 190971328, 191102656, 191233472,
191364032, 191495872, 191626816, 191758016, 191888192, 192020288,
192148928, 192282176, 192413504, 192542528, 192674752, 192805952,
192937792, 193068608, 193198912, 193330496, 193462208, 193592384,
193723456, 193854272, 193985984, 194116672, 194247232, 194379712,
194508352, 194641856, 194772544, 194900672, 195035072, 195166016,
195296704, 195428032, 195558592, 195690304, 195818176, 195952576,
196083392, 196214336, 196345792, 196476736, 196607552, 196739008,
196869952, 197000768, 197130688, 197262784, 197394368, 197523904,
197656384, 197787584, 197916608, 198049472, 198180544, 198310208,
198442432, 198573632, 198705088, 198834368, 198967232, 199097792,
199228352, 199360192, 199491392, 199621696, 199751744, 199883968,
200014016, 200146624, 200276672, 200408128, 200540096, 200671168,
200801984, 200933312, 201062464, 201194944, 201326144, 201457472,
201588544, 201719744, 201850816, 201981632, 202111552, 202244032,
202374464, 202505152, 202636352, 202767808, 202898368, 203030336,
203159872, 203292608, 203423296, 203553472, 203685824, 203816896,
203947712, 204078272, 204208192, 204341056, 204472256, 204603328,
204733888, 204864448, 204996544, 205125568, 205258304, 205388864,
205517632, 205650112, 205782208, 205913536, 206044736, 206176192,
206307008, 206434496, 206569024, 206700224, 206831168, 206961856,
207093056, 207223616, 207355328, 207486784, 207616832, 207749056,
207879104, 208010048, 208141888, 208273216, 208404032, 208534336,
208666048, 208796864, 208927424, 209059264, 209189824, 209321792,
209451584, 209582656, 209715136, 209845568, 209976896, 210106432,
210239296, 210370112, 210501568, 210630976, 210763712, 210894272,
211024832, 211156672, 211287616, 211418176, 211549376, 211679296,
211812032, 211942592, 212074432, 212204864, 212334016, 212467648,
212597824, 212727616, 212860352, 212991424, 213120832, 213253952,
213385024, 213515584, 213645632, 213777728, 213909184, 214040128,
214170688, 214302656, 214433728, 214564544, 214695232, 214826048,
214956992, 215089088, 215219776, 215350592, 215482304, 215613248,
215743552, 215874752, 216005312, 216137024, 216267328, 216399296,
216530752, 216661696, 216790592, 216923968, 217054528, 217183168,
217316672, 217448128, 217579072, 217709504, 217838912, 217972672,
218102848, 218233024, 218364736, 218496832, 218627776, 218759104,
218888896, 219021248, 219151936, 219281728, 219413056, 219545024,
219675968, 219807296, 219938624, 220069312, 220200128, 220331456,
220461632, 220592704, 220725184, 220855744, 220987072, 221117888,
221249216, 221378368, 221510336, 221642048, 221772736, 221904832,
222031808, 222166976, 222297536, 222428992, 222559936, 222690368,
222820672, 222953152, 223083968, 223213376, 223345984, 223476928,
223608512, 223738688, 223869376, 224001472, 224132672, 224262848,
224394944, 224524864, 224657344, 224788288, 224919488, 225050432,
225181504, 225312704, 225443776, 225574592, 225704768, 225834176,
225966784, 226097216, 226229824, 226360384, 226491712, 226623424,
226754368, 226885312, 227015104, 227147456, 227278528, 227409472,
227539904, 227669696, 227802944, 227932352, 228065216, 228196288,
228326464, 228457792, 228588736, 228720064, 228850112, 228981056,
229113152, 229243328, 229375936, 229505344, 229636928, 229769152,
229894976, 230030272, 230162368, 230292416, 230424512, 230553152,
230684864, 230816704, 230948416, 231079616, 231210944, 231342016,
231472448, 231603776, 231733952, 231866176, 231996736, 232127296,
232259392, 232388672, 232521664, 232652608, 232782272, 232914496,
233043904, 233175616, 233306816, 233438528, 233569984, 233699776,
233830592, 233962688, 234092224, 234221888, 234353984, 234485312,
234618304, 234749888, 234880832, 235011776, 235142464, 235274048,
235403456, 235535936, 235667392, 235797568, 235928768, 236057152,
236190272, 236322752, 236453312, 236583616, 236715712, 236846528,
236976448, 237108544, 237239104, 237371072, 237501632, 237630784,
237764416, 237895232, 238026688, 238157632, 238286912, 238419392,
238548032, 238681024, 238812608, 238941632, 239075008, 239206336,
239335232, 239466944, 239599168, 239730496, 239861312, 239992384,
240122816, 240254656, 240385856, 240516928, 240647872, 240779072,
240909632, 241040704, 241171904, 241302848, 241433408, 241565248,
241696192, 241825984, 241958848, 242088256, 242220224, 242352064,
242481856, 242611648, 242744896, 242876224, 243005632, 243138496,
243268672, 243400384, 243531712, 243662656, 243793856, 243924544,
244054592, 244187072, 244316608, 244448704, 244580032, 244710976,
244841536, 244972864, 245104448, 245233984, 245365312, 245497792,
245628736, 245759936, 245889856, 246021056, 246152512, 246284224,
246415168, 246545344, 246675904, 246808384, 246939584, 247070144,
247199552, 247331648, 247463872, 247593536, 247726016, 247857088,
247987648, 248116928, 248249536, 248380736, 248512064, 248643008,
248773312, 248901056, 249036608, 249167552, 249298624, 249429184,
249560512, 249692096, 249822784, 249954112, 250085312, 250215488,
250345792, 250478528, 250608704, 250739264, 250870976, 251002816,
251133632, 251263552, 251395136, 251523904, 251657792, 251789248,
251919424, 252051392, 252182464, 252313408, 252444224, 252575552,
252706624, 252836032, 252968512, 253099712, 253227584, 253361728,
253493056, 253623488, 253754432, 253885504, 254017216, 254148032,
254279488, 254410432, 254541376, 254672576, 254803264, 254933824,
255065792, 255196736, 255326528, 255458752, 255589952, 255721408,
255851072, 255983296, 256114624, 256244416, 256374208, 256507712,
256636096, 256768832, 256900544, 257031616, 257162176, 257294272,
257424448, 257555776, 257686976, 257818432, 257949632, 258079552,
258211136, 258342464, 258473408, 258603712, 258734656, 258867008,
258996544, 259127744, 259260224, 259391296, 259522112, 259651904,
259784384, 259915328, 260045888, 260175424, 260308544, 260438336,
260570944, 260700992, 260832448, 260963776, 261092672, 261226304,
261356864, 261487936, 261619648, 261750592, 261879872, 262011968,
262143424, 262274752, 262404416, 262537024, 262667968, 262799296,
262928704, 263061184, 263191744, 263322944, 263454656, 263585216,
263716672, 263847872, 263978944, 264108608, 264241088, 264371648,
264501184, 264632768, 264764096, 264895936, 265024576, 265158464,
265287488, 265418432, 265550528, 265681216, 265813312, 265943488,
266075968, 266206144, 266337728, 266468032, 266600384, 266731072,
266862272, 266993344, 267124288, 267255616, 267386432, 267516992,
267648704, 267777728, 267910592, 268040512, 268172096, 268302784,
268435264, 268566208, 268696256, 268828096, 268959296, 269090368,
269221312, 269352256, 269482688, 269614784, 269745856, 269876416,
270007616, 270139328, 270270272, 270401216, 270531904, 270663616,
270791744, 270924736, 271056832, 271186112, 271317184, 271449536,
271580992, 271711936, 271843136, 271973056, 272105408, 272236352,
272367296, 272498368, 272629568, 272759488, 272891456, 273022784,
273153856, 273284672, 273415616, 273547072, 273677632, 273808448,
273937088, 274071488, 274200896, 274332992, 274463296, 274595392,
274726208, 274857536, 274988992, 275118656, 275250496, 275382208,
275513024, 275643968, 275775296, 275906368, 276037184, 276167872,
276297664, 276429376, 276560576, 276692672, 276822976, 276955072,
277085632, 277216832, 277347008, 277478848, 277609664, 277740992,
277868608, 278002624, 278134336, 278265536, 278395328, 278526784,
278657728, 278789824, 278921152, 279052096, 279182912, 279313088,
279443776, 279576256, 279706048, 279838528, 279969728, 280099648,
280230976, 280361408, 280493632, 280622528, 280755392, 280887104,
281018176, 281147968, 281278912, 281411392, 281542592, 281673152,
281803712, 281935552, 282066496, 282197312, 282329024, 282458816,
282590272, 282720832, 282853184, 282983744, 283115072, 283246144,
283377344, 283508416, 283639744, 283770304, 283901504, 284032576,
284163136, 284294848, 284426176, 284556992, 284687296, 284819264,
284950208, 285081536}
pow/ethash_test.go 0 → 100644
View file @ 3b00a77d
// Copyright 2017 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// 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 pow
import (
"bytes"
"testing"
"github.com/ethereum/go-ethereum/common/hexutil"
)
// Tests whether the dataset size calculator work correctly by cross checking the
// hard coded lookup table with the value generated by it.
func TestSizeCalculations(t *testing.T) {
var tests []uint64
// Verify all the cache sizes from the lookup table
defer func(sizes []uint64) { cacheSizes = sizes }(cacheSizes)
tests, cacheSizes = cacheSizes, []uint64{}
for i, test := range tests {
if size := cacheSize(uint64(i*epochLength) + 1); size != test {
t.Errorf("cache %d: cache size mismatch: have %d, want %d", i, size, test)
}
}
// Verify all the dataset sizes from the lookup table
defer func(sizes []uint64) { datasetSizes = sizes }(datasetSizes)
tests, datasetSizes = datasetSizes, []uint64{}
for i, test := range tests {
if size := datasetSize(uint64(i*epochLength) + 1); size != test {
t.Errorf("dataset %d: dataset size mismatch: have %d, want %d", i, size, test)
}
}
}
// Tests that verification caches can be correctly generated.
func TestCacheGeneration(t *testing.T) {
tests := []struct {
size uint64
seed []byte
cache []byte
}{
{
size: 1024,
seed: make([]byte, 32),
cache: hexutil.MustDecode("0x" +
"7ce2991c951f7bf4c4c1bb119887ee07871eb5339d7b97b8588e85c742de90e5bafd5bbe6ce93a134fb6be9ad3e30db99d9528a2ea7846833f52e9ca119b6b54" +
"8979480c46e19972bd0738779c932c1b43e665a2fd3122fc3ddb2691f353ceb0ed3e38b8f51fd55b6940290743563c9f8fa8822e611924657501a12aafab8a8d" +
"88fb5fbae3a99d14792406672e783a06940a42799b1c38bc28715db6d37cb11f9f6b24e386dc52dd8c286bd8c36fa813dffe4448a9f56ebcbeea866b42f68d22" +
"6c32aae4d695a23cab28fd74af53b0c2efcc180ceaaccc0b2e280103d097a03c1d1b0f0f26ce5f32a90238f9bc49f645db001ef9cd3d13d44743f841fad11a37" +
"fa290c62c16042f703578921f30b9951465aae2af4a5dad43a7341d7b4a62750954965a47a1c3af638dc3495c4d62a9bab843168c9fc0114e79cffd1b2827b01" +
"75d30ba054658f214e946cf24c43b40d3383fbb0493408e5c5392434ca21bbcf43200dfb876c713d201813934fa485f48767c5915745cf0986b1dc0f33e57748" +
"bf483ee2aff4248dfe461ec0504a13628401020fc22638584a8f2f5206a13b2f233898c78359b21c8226024d0a7a93df5eb6c282bdbf005a4aab497e096f2847" +
"76c71cee57932a8fb89f6d6b8743b60a4ea374899a94a2e0f218d5c55818cefb1790c8529a76dba31ebb0f4592d709b49587d2317970d39c086f18dd244291d9" +
"eedb16705e53e3350591bd4ff4566a3595ac0f0ce24b5e112a3d033bc51b6fea0a92296dea7f5e20bf6ee6bc347d868fda193c395b9bb147e55e5a9f67cfe741" +
"7eea7d699b155bd13804204df7ea91fa9249e4474dddf35188f77019c67d201e4c10d7079c5ad492a71afff9a23ca7e900ba7d1bdeaf3270514d8eb35eab8a0a" +
"718bb7273aeb37768fa589ed8ab01fbf4027f4ebdbbae128d21e485f061c20183a9bc2e31edbda0727442e9d58eb0fe198440fe199e02e77c0f7b99973f1f74c" +
"c9089a51ab96c94a84d66e6aa48b2d0a4543adb5a789039a2aa7b335ca85c91026c7d3c894da53ae364188c3fd92f78e01d080399884a47385aa792e38150cda" +
"a8620b2ebeca41fbc773bb837b5e724d6eb2de570d99858df0d7d97067fb8103b21757873b735097b35d3bea8fd1c359a9e8a63c1540c76c9784cf8d975e995c" +
"778401b94a2e66e6993ad67ad3ecdc2acb17779f1ea8606827ec92b11c728f8c3b6d3f04a3e6ed05ff81dd76d5dc5695a50377bc135aaf1671cf68b750315493" +
"6c64510164d53312bf3c41740c7a237b05faf4a191bd8a95dafa068dbcf370255c725900ce5c934f36feadcfe55b687c440574c1f06f39d207a8553d39156a24" +
"845f64fd8324bb85312979dead74f764c9677aab89801ad4f927f1c00f12e28f22422bb44200d1969d9ab377dd6b099dc6dbc3222e9321b2c1e84f8e2f07731c"),
},
{
size: 1024,
seed: hexutil.MustDecode("0x290decd9548b62a8d60345a988386fc84ba6bc95484008f6362f93160ef3e563"),
cache: hexutil.MustDecode("0x" +
"1f56855d59cc5a085720899b4377a0198f1abe948d85fe5820dc0e346b7c0931b9cde8e541d751de3b2b3275d0aabfae316209d5879297d8bd99f8a033c9d4df" +
"35add1029f4e6404a022d504fb8023e42989aba985a65933b0109c7218854356f9284983c9e7de97de591828ae348b63d1fc78d8db58157344d4e06530ffd422" +
"5c7f6080d451ff94961ec2dd9e28e6d81b49102451676dbdcb6ef1094c1e8b29e7e808d47b2ba5aeb52dabf00d5f0ee08c116289cbf56d8132e5ca557c3d6220" +
"5ba3a48539acabfd4ca3c89e3aaa668e24ffeaeb9eb0136a9fc5a8a676b6d5ad76175eeda0a1fa44b5ff5591079e4b7f581569b6c82416adcb82d7e92980df67" +
"2248c4024013e7be52cf91a82491627d9e6d80eda2770ab82badc5e120cd33a4c84495f718b57396a8f397e797087fad81fa50f0e2f5da71e40816a85de35a96" +
"3cd351364905c45b3116ff25851d43a2ca1d2aa5cdb408440dabef8c57778fc18608bf431d0c7ffd37649a21a7bb9d90def39c821669dbaf165c0262434dfb08" +
"5d057a12de4a7a59fd2dfc931c29c20371abf748b69b618a9bd485b3fb3166cad4d3d27edf0197aabeceb28b96670bdf020f26d1bb9b564aaf82d866bdffd6d4" +
"1aea89e20b15a5d1264ab01d1556bfc2a266081609d60928216bd9646038f07de9fedcc9f2b86ab1b07d7bd88ba1df08b3d89b2ac789001b48a723f217debcb7" +
"090303a3ef50c1d5d99a75c640ec2b401ab149e06511753d8c49cafdde2929ae61e09cc0f0319d262869d21ead9e0cf5ff2de3dbedfb994f32432d2e4aa44c82" +
"7c42781d1477fe03ea0772998e776d63363c6c3edd2d52c89b4d2c9d89cdd90fa33b2b41c8e3f78ef06fe90bcf5cc5756d33a032f16b744141aaa8852bb4cb3a" +
"40792b93489c6d6e56c235ec4aa36c263e9b766a4daaff34b2ea709f9f811aef498a65bfbc1deffd36fcc4d1a123345fac7bf57a1fb50394843cd28976a6c7ff" +
"fe70f7b8d8f384aa06e2c9964c92a8788cef397fffdd35181b42a35d5d98cd7244bbd09e802888d7efc0311ae58e0961e3656205df4bdc553f317df4b6ede4ca" +
"846294a32aec830ab1aa5aac4e78b821c35c70fd752fec353e373bf9be656e775a0111bcbeffdfebd3bd5251d27b9f6971aa561a2bd27a99d61b2ce3965c3726" +
"1e114353e6a31b09340f4078b8a8c6ce6ff4213067a8f21020f78aff4f8b472b701ef730aacb8ce7806ea31b14abe8f8efdd6357ca299d339abc4e43ba324ad1" +
"efe6eb1a5a6e137daa6ec9f6be30931ca368a944cfcf2a0a29f9a9664188f0466e6f078c347f9fe26a9a89d2029462b19245f24ace47aecace6ef85a4e96b31b" +
"5f470eb0165c6375eb8f245d50a25d521d1e569e3b2dccce626752bb26eae624a24511e831a81fab6898a791579f462574ca4851e6588116493dbccc3072e0c5"),
},
}
for i, tt := range tests {
if cache := generateCache(tt.size, tt.seed); !bytes.Equal(cache, tt.cache) {
t.Errorf("cache %d: content mismatch: have %x, want %x", i, cache, tt.cache)
}
}
}
func TestDatasetGeneration(t *testing.T) {
tests := []struct {
cacheSize uint64
cacheSeed []byte
datasetSize uint64
dataset []byte
}{
{
cacheSize: 1024,
cacheSeed: make([]byte, 32),
datasetSize: 32 * 1024,
dataset: hexutil.MustDecode("0x" +
"4bc09fbd530a041dd2ec296110a29e8f130f179c59d223f51ecce3126e8b0c74326abc2f32ccd9d7f976bd0944e3ccf8479db39343cbbffa467046ca97e2da63" +
"da5f9d9688c7c33ab7b8aace570e422fa48b24659b72fc534669209d66389ca15b099c5604601e7581488e3bd6925cec0f12d465f8004d4fa84793f8e1e46a1b" +
"31b7298991c6142f4f0b6e6b296728ae5fa63ccb667b61fbb1b078003d18d97b906af157debed5e6c55d5a61cae90c85f9e97d565314a2f9fd9e0c08430547d0" +
"7cfcee3271f921b95c32a11596219abaa30abc62c2c72c6725078c436c677320594df6bcb92134c1b114fffec982a1f68f13a9f812f074b9fb9c78f2cd4c1c90" +
"7ebf1e447f7a422b06303921e3d54f430584d849eaa4b7d652e92a5d659bdfc462adcdd7991e8c66a19da4ddb5390463d073941491859397f135ebbbdbdf5801" +
"cafb873c383893390141ae385515504d74a33608273310c312ba468046d2e20c271a38cc0e3920b39705050e752f34f244fc23ddd17ff18677756a87671d4145" +
"3aebf97e4890da1d645f41eb20da92a8537c787ce419580073c46aa3bb154952993142ec5b4fb6e8f108fd15fc618cd5c27b45a37ee6dcd52a4ce656c0f58604" +
"717ec55f5e592355f1f20e8316f8fd77243734a8b0f50ad93c1d95b5b0482afb22cd0667d935bd6053d7198b54974e10d100df7ca3ec2e0bb5ccce5807b266e0" +
"8429d5fec2ae6ae1cc7c5efc27f19c89d4b4a6c5c0b9397886dac635ba37446ff528b582457a4fe7f803f1a47903574f8982d4a679b627396a4e97aaa12fa179" +
"0d31ba52e9010bc3c26ace81f702f86649fe9eeda9ec03b74a8a5cf540d82e22af33ab893564397dfc4edd8b1677350df5b82ab61d24db95f58fd2d78afb49c7" +
"2d2b1fefa8ff6606b8623829cc752ea37d663b945f3f1d48ad07b1416af252f81b55acd8f164da4faa9d9453721b3b795041ce7df7c77edc13865dbe04fee331" +
"47daebe18c183c4a6594a6df3a4d2dc5e3811d805102c9c49286e3d12b38927fa49a7b0cdcb1d799f57118953e31c560aae213a1799d59a78ae68f0590347061" +
"fc2668caf08f860452f6b7d3ebc1efecc2e1227d33296b1f1850360dee7236e85274eaede4d18a58b4261ce1f6a7d283dcf64e6d021813f82a566354445327e5" +
"6217279b2393fe5aa0f9eb149d4866e1105106bcc221810ceaf053f2ec733d8a22f409c1baf955e50184005c5d55de907de97f5f713b62ae10937e1a7af6267b" +
"d2a239e8589017197c343b81540bc26bc52bffd5336fb1da1202a511c7175014d2f500b9d9ce78e4b9f2b158d0fb27af352b6f78c129cad642fe909612c9d658" +
"17a8d7f9195ee97201675a918e3cf520fdc19f92b7e6a3db806d4f3799361334082cc58a22ddb4e4f5760bd1667c177b26be325166c6bbed669a158fc87acd43" +
"a2462e12578d72db6606f9e24ae659ff411ac9b31d696b8354fd08a591622967a14f8468eaaae3907b7818154ba2d6e4581589354d178bb6ae1c03651c44bbf0" +
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"87d224444245eb5b0eade5f741b025db1992a8ad0dce51b0c1af4a18a9e244f9f755891adf0f19179c7baa6c32bffc91e0b03c4ed3aaee1978b6a1f03b87ac6a" +
"fc3b9e7030bb212b17de198edfccde29d04224798c1204e47ea235f048724fac62d637d1ba0ee3922048fcf79c746b6c0c036d882e3491fd72bad6e009c6403e" +
"55876f4d31330caa02aedd0b0c121c3c41e736853a08071f0dd4ddc7412db0bbe274a9ac2932552bb37c40e72c2ef1d7cca8236942e480d709d3ea9d5ae0a1b7",
),
},
}
for i, tt := range tests {
rawCache := generateCache(tt.cacheSize, tt.cacheSeed)
cache := prepare(uint64(len(rawCache)), bytes.NewReader(rawCache))
if dataset := generateDataset(tt.datasetSize, cache); !bytes.Equal(dataset, tt.dataset) {
t.Errorf("dataset %d: content mismatch: have %x, want %x", i, dataset, tt.dataset)
}
}
}
// Tests whether the hashimoto lookup works for both light as well as the full
// datasets.
func TestHashimoto(t *testing.T) {
// Create the verification cache and mining dataset
var (
rawCache = generateCache(1024, make([]byte, 32))
cache = prepare(uint64(len(rawCache)), bytes.NewReader(rawCache))
rawDataset = generateDataset(32*1024, cache)
dataset = prepare(uint64(len(rawDataset)), bytes.NewReader(rawDataset))
)
// Create a block to verify
hash := hexutil.MustDecode("0xc9149cc0386e689d789a1c2f3d5d169a61a6218ed30e74414dc736e442ef3d1f")
nonce := uint64(0)
wantDigest := hexutil.MustDecode("0xe4073cffaef931d37117cefd9afd27ea0f1cad6a981dd2605c4a1ac97c519800")
wantResult := hexutil.MustDecode("0xd3539235ee2e6f8db665c0a72169f55b7f6c605712330b778ec3944f0eb5a557")
digest, result := hashimotoLight(32*1024, cache, hash, nonce)
if !bytes.Equal(digest, wantDigest) {
t.Errorf("light hashimoto digest mismatch: have %x, want %x", digest, wantDigest)
}
if !bytes.Equal(result, wantResult) {
t.Errorf("light hashimoto result mismatch: have %x, want %x", result, wantResult)
}
digest, result = hashimotoFull(32*1024, dataset, hash, nonce)
if !bytes.Equal(digest, wantDigest) {
t.Errorf("full hashimoto digest mismatch: have %x, want %x", digest, wantDigest)
}
if !bytes.Equal(result, wantResult) {
t.Errorf("full hashimoto result mismatch: have %x, want %x", result, wantResult)
}
}
// Becnhmarks the cache generation performance.
func BenchmarkCacheGeneration(b *testing.B) {
for i := 0; i < b.N; i++ {
generateCache(cacheSize(1), make([]byte, 32))
}
}
// Becnhmarks the dataset (small) generation performance.
func BenchmarkSmallDatasetGeneration(b *testing.B) {
rawCache := generateCache(65536, make([]byte, 32))
cache := prepare(uint64(len(rawCache)), bytes.NewReader(rawCache))
b.ResetTimer()
for i := 0; i < b.N; i++ {
generateDataset(32*65536, cache)
}
}
// Becnhmarks the light verification performace.
func BenchmarkHashimotoLight(b *testing.B) {
var (
rawCache = generateCache(cacheSize(1), make([]byte, 32))
cache = prepare(uint64(len(rawCache)), bytes.NewReader(rawCache))
hash = hexutil.MustDecode("0xc9149cc0386e689d789a1c2f3d5d169a61a6218ed30e74414dc736e442ef3d1f")
)
b.ResetTimer()
for i := 0; i < b.N; i++ {
hashimotoLight(datasetSize(1), cache, hash, 0)
}
}
// Becnhmarks the full (small) verification performace.
func BenchmarkHashimotoFullSmall(b *testing.B) {
var (
rawCache = generateCache(65536, make([]byte, 32))
cache = prepare(uint64(len(rawCache)), bytes.NewReader(rawCache))
rawDataset = generateDataset(32*65536, cache)
dataset = prepare(uint64(len(rawDataset)), bytes.NewReader(rawDataset))
hash = hexutil.MustDecode("0xc9149cc0386e689d789a1c2f3d5d169a61a6218ed30e74414dc736e442ef3d1f")
)
b.ResetTimer()
for i := 0; i < b.N; i++ {
hashimotoFull(32*65536, dataset, hash, 0)
}
}
pow/xor.go 0 → 100644
View file @ 3b00a77d
// Copyright 2013 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Source: https://golang.org/src/crypto/cipher/xor.go
package pow
import (
"runtime"
"unsafe"
)
const wordSize = int(unsafe.Sizeof(uintptr(0)))
const supportsUnaligned = runtime.GOARCH == "386" || runtime.GOARCH == "amd64" || runtime.GOARCH == "ppc64" || runtime.GOARCH == "ppc64le" || runtime.GOARCH == "s390x"
// fastXORBytes xors in bulk. It only works on architectures that
// support unaligned read/writes.
func fastXORBytes(dst, a, b []byte) int {
n := len(a)
if len(b) < n {
n = len(b)
}
w := n / wordSize
if w > 0 {
dw := *(*[]uintptr)(unsafe.Pointer(&dst))
aw := *(*[]uintptr)(unsafe.Pointer(&a))
bw := *(*[]uintptr)(unsafe.Pointer(&b))
for i := 0; i < w; i++ {
dw[i] = aw[i] ^ bw[i]
}
}
for i := (n - n%wordSize); i < n; i++ {
dst[i] = a[i] ^ b[i]
}
return n
}
func safeXORBytes(dst, a, b []byte) int {
n := len(a)
if len(b) < n {
n = len(b)
}
for i := 0; i < n; i++ {
dst[i] = a[i] ^ b[i]
}
return n
}
// xorBytes xors the bytes in a and b. The destination is assumed to have enough
// space. Returns the number of bytes xor'd.
func xorBytes(dst, a, b []byte) int {
if supportsUnaligned {
return fastXORBytes(dst, a, b)
}
// TODO(hanwen): if (dst, a, b) have common alignment
// we could still try fastXORBytes. It is not clear
// how often this happens, and it's only worth it if
// the block encryption itself is hardware
// accelerated.
return safeXORBytes(dst, a, b)
}
// fastXORWords XORs multiples of 4 or 8 bytes (depending on architecture.)
// The arguments are assumed to be of equal length.
func fastXORWords(dst, a, b []byte) {
dw := *(*[]uintptr)(unsafe.Pointer(&dst))
aw := *(*[]uintptr)(unsafe.Pointer(&a))
bw := *(*[]uintptr)(unsafe.Pointer(&b))
n := len(b) / wordSize
for i := 0; i < n; i++ {
dw[i] = aw[i] ^ bw[i]
}
}
func xorWords(dst, a, b []byte) {
if supportsUnaligned {
fastXORWords(dst, a, b)
} else {
safeXORBytes(dst, a, b)
}
}
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