// 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
)
// 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 verification 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("seed", hexutil.Bytes(seed))
logger.Debug("Generating ethash verification cache")
start := time.Now()
defer func() {
logger.Info("Generated ethash verification cache", "elapsed", common.PrettyDuration(time.Since(start)))
}()
// Calculate the number of thoretical rows (we'll store in one buffer nonetheless)
rows := int(size) / hashBytes
// Start a monitoring goroutine to report progress on low end devices
var progress uint32
done := make(chan struct{})
defer close(done)
go func() {
for {
select {
case <-done:
return
case <-time.After(3 * time.Second):
logger.Info("Generating ethash verification cache", "percentage", atomic.LoadUint32(&progress)*100/uint32(rows)/4, "elapsed", common.PrettyDuration(time.Since(start)))
}
}
}()
// 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]))
atomic.AddUint32(&progress, 1)
}
// 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))
atomic.AddUint32(&progress, 1)
}
}
return cache
}
// prepare converts 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,
5771358592, 5779748224, 5788137856, 5796527488, 5804911232,
5813300608, 5821692544, 5830082176, 5838468992, 5846855552,
5855247488, 5863636096, 5872024448, 5880411008, 5888799872,
5897186432, 5905576832, 5913966976, 5922352768, 5930744704,
5939132288, 5947522432, 5955911296, 5964299392, 5972688256,
5981074304, 5989465472, 5997851008, 6006241408, 6014627968,
6023015552, 6031408256, 6039796096, 6048185216, 6056574848,
6064963456, 6073351808, 6081736064, 6090128768, 6098517632,
6106906496, 6115289216, 6123680896, 6132070016, 6140459648,
6148849024, 6157237376, 6165624704, 6174009728, 6182403712,
6190792064, 6199176064, 6207569792, 6215952256, 6224345216,
6232732544, 6241124224, 6249510272, 6257899136, 6266287744,
6274676864, 6283065728, 6291454336, 6299843456, 6308232064,
6316620928, 6325006208, 6333395584, 6341784704, 6350174848,
6358562176, 6366951296, 6375337856, 6383729536, 6392119168,
6400504192, 6408895616, 6417283456, 6425673344, 6434059136,
6442444672, 6450837376, 6459223424, 6467613056, 6476004224,
6484393088, 6492781952, 6501170048, 6509555072, 6517947008,
6526336384, 6534725504, 6543112832, 6551500672, 6559888768,
6568278656, 6576662912, 6585055616, 6593443456, 6601834112,
6610219648, 6618610304, 6626999168, 6635385472, 6643777408,
6652164224, 6660552832, 6668941952, 6677330048, 6685719424,
6694107776, 6702493568, 6710882176, 6719274112, 6727662976,
6736052096, 6744437632, 6752825984, 6761213824, 6769604224,
6777993856, 6786383488, 6794770816, 6803158144, 6811549312,
6819937664, 6828326528, 6836706176, 6845101696, 6853491328,
6861880448, 6870269312, 6878655104, 6887046272, 6895433344,
6903822208, 6912212864, 6920596864, 6928988288, 6937377152,
6945764992, 6954149248, 6962544256, 6970928768, 6979317376,
6987709312, 6996093824, 7004487296, 7012875392, 7021258624,
7029652352, 7038038912, 7046427776, 7054818944, 7063207808,
7071595136, 7079980928, 7088372608, 7096759424, 7105149824,
7113536896, 7121928064, 7130315392, 7138699648, 7147092352,
7155479168, 7163865728, 7172249984, 7180648064, 7189036672,
7197424768, 7205810816, 7214196608, 7222589824, 7230975104,
7239367552, 7247755904, 7256145536, 7264533376, 7272921472,
7281308032, 7289694848, 7298088832, 7306471808, 7314864512,
7323253888, 7331643008, 7340029568, 7348419712, 7356808832,
7365196672, 7373585792, 7381973888, 7390362752, 7398750592,
7407138944, 7415528576, 7423915648, 7432302208, 7440690304,
7449080192, 7457472128, 7465860992, 7474249088, 7482635648,
7491023744, 7499412608, 7507803008, 7516192384, 7524579968,
7532967296, 7541358464, 7549745792, 7558134656, 7566524032,
7574912896, 7583300992, 7591690112, 7600075136, 7608466816,
7616854912, 7625244544, 7633629824, 7642020992, 7650410368,
7658794112, 7667187328, 7675574912, 7683961984, 7692349568,
7700739712, 7709130368, 7717519232, 7725905536, 7734295424,
7742683264, 7751069056, 7759457408, 7767849088, 7776238208,
7784626816, 7793014912, 7801405312, 7809792128, 7818179968,
7826571136, 7834957184, 7843347328, 7851732352, 7860124544,
7868512384, 7876902016, 7885287808, 7893679744, 7902067072,
7910455936, 7918844288, 7927230848, 7935622784, 7944009344,
7952400256, 7960786048, 7969176704, 7977565312, 7985953408,
7994339968, 8002730368, 8011119488, 8019508096, 8027896192,
8036285056, 8044674688, 8053062272, 8061448832, 8069838464,
8078227328, 8086616704, 8095006592, 8103393664, 8111783552,
8120171392, 8128560256, 8136949376, 8145336704, 8153726848,
8162114944, 8170503296, 8178891904, 8187280768, 8195669632,
8204058496, 8212444544, 8220834176, 8229222272, 8237612672,
8246000768, 8254389376, 8262775168, 8271167104, 8279553664,
8287944064, 8296333184, 8304715136, 8313108352, 8321497984,
8329885568, 8338274432, 8346663296, 8355052928, 8363441536,
8371828352, 8380217984, 8388606592, 8396996224, 8405384576,
8413772672, 8422161536, 8430549376, 8438939008, 8447326592,
8455715456, 8464104832, 8472492928, 8480882048, 8489270656,
8497659776, 8506045312, 8514434944, 8522823808, 8531208832,
8539602304, 8547990656, 8556378752, 8564768384, 8573154176,
8581542784, 8589933952, 8598322816, 8606705024, 8615099264,
8623487872, 8631876992, 8640264064, 8648653952, 8657040256,
8665430656, 8673820544, 8682209152, 8690592128, 8698977152,
8707374464, 8715763328, 8724151424, 8732540032, 8740928384,
8749315712, 8757704576, 8766089344, 8774480768, 8782871936,
8791260032, 8799645824, 8808034432, 8816426368, 8824812928,
8833199488, 8841591424, 8849976448, 8858366336, 8866757248,
8875147136, 8883532928, 8891923328, 8900306816, 8908700288,
8917088384, 8925478784, 8933867392, 8942250368, 8950644608,
8959032704, 8967420544, 8975809664, 8984197504, 8992584064,
9000976256, 9009362048, 9017752448, 9026141312, 9034530688,
9042917504, 9051307904, 9059694208, 9068084864, 9076471424,
9084861824, 9093250688, 9101638528, 9110027648, 9118416512,
9126803584, 9135188096, 9143581312, 9151969664, 9160356224,
9168747136, 9177134464, 9185525632, 9193910144, 9202302848,
9210690688, 9219079552, 9227465344, 9235854464, 9244244864,
9252633472, 9261021824, 9269411456, 9277799296, 9286188928,
9294574208, 9302965888, 9311351936, 9319740032, 9328131968,
9336516736, 9344907392, 9353296768, 9361685888, 9370074752,
9378463616, 9386849408, 9395239808, 9403629184, 9412016512,
9420405376, 9428795008, 9437181568, 9445570688, 9453960832,
9462346624, 9470738048, 9479121536, 9487515008, 9495903616,
9504289664, 9512678528, 9521067904, 9529456256, 9537843584,
9546233728, 9554621312, 9563011456, 9571398784, 9579788672,
9588178304, 9596567168, 9604954496, 9613343104, 9621732992,
9630121856, 9638508416, 9646898816, 9655283584, 9663675776,
9672061312, 9680449664, 9688840064, 9697230464, 9705617536,
9714003584, 9722393984, 9730772608, 9739172224, 9747561088,
9755945344, 9764338816, 9772726144, 9781116544, 9789503872,
9797892992, 9806282624, 9814670464, 9823056512, 9831439232,
9839833984, 9848224384, 9856613504, 9865000576, 9873391232,
9881772416, 9890162816, 9898556288, 9906940544, 9915333248,
9923721088, 9932108672, 9940496512, 9948888448, 9957276544,
9965666176, 9974048384, 9982441088, 9990830464, 9999219584,
10007602816, 10015996544, 10024385152, 10032774016, 10041163648,
10049548928, 10057940096, 10066329472, 10074717824, 10083105152,
10091495296, 10099878784, 10108272256, 10116660608, 10125049216,
10133437312, 10141825664, 10150213504, 10158601088, 10166991232,
10175378816, 10183766144, 10192157312, 10200545408, 10208935552,
10217322112, 10225712768, 10234099328, 10242489472, 10250876032,
10259264896, 10267656064, 10276042624, 10284429184, 10292820352,
10301209472, 10309598848, 10317987712, 10326375296, 10334763392,
10343153536, 10351541632, 10359930752, 10368318592, 10376707456,
10385096576, 10393484672, 10401867136, 10410262144, 10418647424,
10427039104, 10435425664, 10443810176, 10452203648, 10460589952,
10468982144, 10477369472, 10485759104, 10494147712, 10502533504,
10510923392, 10519313536, 10527702656, 10536091264, 10544478592,
10552867712, 10561255808, 10569642368, 10578032768, 10586423168,
10594805632, 10603200128, 10611588992, 10619976064, 10628361344,
10636754048, 10645143424, 10653531776, 10661920384, 10670307968,
10678696832, 10687086464, 10695475072, 10703863168, 10712246144,
10720639616, 10729026688, 10737414784, 10745806208, 10754190976,
10762581376, 10770971264, 10779356288, 10787747456, 10796135552,
10804525184, 10812915584, 10821301888, 10829692288, 10838078336,
10846469248, 10854858368, 10863247232, 10871631488, 10880023424,
10888412032, 10896799616, 10905188992, 10913574016, 10921964672,
10930352768, 10938742912, 10947132544, 10955518592, 10963909504,
10972298368, 10980687488, 10989074816, 10997462912, 11005851776,
11014241152, 11022627712, 11031017344, 11039403904, 11047793024,
11056184704, 11064570752, 11072960896, 11081343872, 11089737856,
11098128256, 11106514816, 11114904448, 11123293568, 11131680128,
11140065152, 11148458368, 11156845696, 11165236864, 11173624192,
11182013824, 11190402688, 11198790784, 11207179136, 11215568768,
11223957376, 11232345728, 11240734592, 11249122688, 11257511296,
11265899648, 11274285952, 11282675584, 11291065472, 11299452544,
11307842432, 11316231296, 11324616832, 11333009024, 11341395584,
11349782656, 11358172288, 11366560384, 11374950016, 11383339648,
11391721856, 11400117376, 11408504192, 11416893568, 11425283456,
11433671552, 11442061184, 11450444672, 11458837888, 11467226752,
11475611776, 11484003968, 11492392064, 11500780672, 11509169024,
11517550976, 11525944448, 11534335616, 11542724224, 11551111808,
11559500672, 11567890304, 11576277376, 11584667008, 11593056128,
11601443456, 11609830016, 11618221952, 11626607488, 11634995072,
11643387776, 11651775104, 11660161664, 11668552576, 11676940928,
11685330304, 11693718656, 11702106496, 11710496128, 11718882688,
11727273088, 11735660416, 11744050048, 11752437376, 11760824704,
11769216128, 11777604736, 11785991296, 11794381952, 11802770048,
11811157888, 11819548544, 11827932544, 11836324736, 11844713344,
11853100928, 11861486464, 11869879936, 11878268032, 11886656896,
11895044992, 11903433088, 11911822976, 11920210816, 11928600448,
11936987264, 11945375872, 11953761152, 11962151296, 11970543488,
11978928512, 11987320448, 11995708288, 12004095104, 12012486272,
12020875136, 12029255552, 12037652096, 12046039168, 12054429568,
12062813824, 12071206528, 12079594624, 12087983744, 12096371072,
12104759936, 12113147264, 12121534592, 12129924992, 12138314624,
12146703232, 12155091584, 12163481216, 12171864704, 12180255872,
12188643968, 12197034112, 12205424512, 12213811328, 12222199424,
12230590336, 12238977664, 12247365248, 12255755392, 12264143488,
12272531584, 12280920448, 12289309568, 12297694592, 12306086528,
12314475392, 12322865024, 12331253632, 12339640448, 12348029312,
12356418944, 12364805248, 12373196672, 12381580928, 12389969024,
12398357632, 12406750592, 12415138432, 12423527552, 12431916416,
12440304512, 12448692352, 12457081216, 12465467776, 12473859968,
12482245504, 12490636672, 12499025536, 12507411584, 12515801728,
12524190592, 12532577152, 12540966272, 12549354368, 12557743232,
12566129536, 12574523264, 12582911872, 12591299456, 12599688064,
12608074624, 12616463488, 12624845696, 12633239936, 12641631616,
12650019968, 12658407296, 12666795136, 12675183232, 12683574656,
12691960192, 12700350592, 12708740224, 12717128576, 12725515904,
12733906816, 12742295168, 12750680192, 12759071872, 12767460736,
12775848832, 12784236928, 12792626816, 12801014656, 12809404288,
12817789312, 12826181504, 12834568832, 12842954624, 12851345792,
12859732352, 12868122496, 12876512128, 12884901248, 12893289088,
12901672832, 12910067584, 12918455168, 12926842496, 12935232896,
12943620736, 12952009856, 12960396928, 12968786816, 12977176192,
12985563776, 12993951104, 13002341504, 13010730368, 13019115392,
13027506304, 13035895168, 13044272512, 13052673152, 13061062528,
13069446272, 13077838976, 13086227072, 13094613632, 13103000192,
13111393664, 13119782528, 13128157568, 13136559232, 13144945024,
13153329536, 13161724288, 13170111872, 13178502784, 13186884736,
13195279744, 13203667072, 13212057472, 13220445824, 13228832128,
13237221248, 13245610624, 13254000512, 13262388352, 13270777472,
13279166336, 13287553408, 13295943296, 13304331904, 13312719488,
13321108096, 13329494656, 13337885824, 13346274944, 13354663808,
13363051136, 13371439232, 13379825024, 13388210816, 13396605056,
13404995456, 13413380224, 13421771392, 13430159744, 13438546048,
13446937216, 13455326848, 13463708288, 13472103808, 13480492672,
13488875648, 13497269888, 13505657728, 13514045312, 13522435712,
13530824576, 13539210112, 13547599232, 13555989376, 13564379008,
13572766336, 13581154432, 13589544832, 13597932928, 13606320512,
13614710656, 13623097472, 13631477632, 13639874944, 13648264064,
13656652928, 13665041792, 13673430656, 13681818496, 13690207616,
13698595712, 13706982272, 13715373184, 13723762048, 13732150144,
13740536704, 13748926592, 13757316224, 13765700992, 13774090112,
13782477952, 13790869376, 13799259008, 13807647872, 13816036736,
13824425344, 13832814208, 13841202304, 13849591424, 13857978752,
13866368896, 13874754688, 13883145344, 13891533184, 13899919232,
13908311168, 13916692096, 13925085056, 13933473152, 13941866368,
13950253696, 13958643584, 13967032192, 13975417216, 13983807616,
13992197504, 14000582272, 14008973696, 14017363072, 14025752192,
14034137984, 14042528384, 14050918016, 14059301504, 14067691648,
14076083584, 14084470144, 14092852352, 14101249664, 14109635968,
14118024832, 14126407552, 14134804352, 14143188608, 14151577984,
14159968384, 14168357248, 14176741504, 14185127296, 14193521024,
14201911424, 14210301824, 14218685056, 14227067264, 14235467392,
14243855488, 14252243072, 14260630144, 14269021568, 14277409408,
14285799296, 14294187904, 14302571392, 14310961792, 14319353728,
14327738752, 14336130944, 14344518784, 14352906368, 14361296512,
14369685376, 14378071424, 14386462592, 14394848128, 14403230848,
14411627392, 14420013952, 14428402304, 14436793472, 14445181568,
14453569664, 14461959808, 14470347904, 14478737024, 14487122816,
14495511424, 14503901824, 14512291712, 14520677504, 14529064832,
14537456768, 14545845632, 14554234496, 14562618496, 14571011456,
14579398784, 14587789184, 14596172672, 14604564608, 14612953984,
14621341312, 14629724288, 14638120832, 14646503296, 14654897536,
14663284864, 14671675264, 14680061056, 14688447616, 14696835968,
14705228416, 14713616768, 14722003328, 14730392192, 14738784128,
14747172736, 14755561088, 14763947648, 14772336512, 14780725376,
14789110144, 14797499776, 14805892736, 14814276992, 14822670208,
14831056256, 14839444352, 14847836032, 14856222848, 14864612992,
14872997504, 14881388672, 14889775744, 14898165376, 14906553472,
14914944896, 14923329664, 14931721856, 14940109696, 14948497024,
14956887424, 14965276544, 14973663616, 14982053248, 14990439808,
14998830976, 15007216768, 15015605888, 15023995264, 15032385152,
15040768384, 15049154944, 15057549184, 15065939072, 15074328448,
15082715008, 15091104128, 15099493504, 15107879296, 15116269184,
15124659584, 15133042304, 15141431936, 15149824384, 15158214272,
15166602368, 15174991232, 15183378304, 15191760512, 15200154496,
15208542592, 15216931712, 15225323392, 15233708416, 15242098048,
15250489216, 15258875264, 15267265408, 15275654528, 15284043136,
15292431488, 15300819584, 15309208192, 15317596544, 15325986176,
15334374784, 15342763648, 15351151744, 15359540608, 15367929728,
15376318336, 15384706432, 15393092992, 15401481856, 15409869952,
15418258816, 15426649984, 15435037568, 15443425664, 15451815296,
15460203392, 15468589184, 15476979328, 15485369216, 15493755776,
15502146944, 15510534272, 15518924416, 15527311232, 15535699072,
15544089472, 15552478336, 15560866688, 15569254528, 15577642624,
15586031488, 15594419072, 15602809472, 15611199104, 15619586432,
15627975296, 15636364928, 15644753792, 15653141888, 15661529216,
15669918848, 15678305152, 15686696576, 15695083136, 15703474048,
15711861632, 15720251264, 15728636288, 15737027456, 15745417088,
15753804928, 15762194048, 15770582656, 15778971008, 15787358336,
15795747712, 15804132224, 15812523392, 15820909696, 15829300096,
15837691264, 15846071936, 15854466944, 15862855808, 15871244672,
15879634816, 15888020608, 15896409728, 15904799104, 15913185152,
15921577088, 15929966464, 15938354816, 15946743424, 15955129472,
15963519872, 15971907968, 15980296064, 15988684928, 15997073024,
16005460864, 16013851264, 16022241152, 16030629248, 16039012736,
16047406976, 16055794816, 16064181376, 16072571264, 16080957824,
16089346688, 16097737856, 16106125184, 16114514816, 16122904192,
16131292544, 16139678848, 16148066944, 16156453504, 16164839552,
16173236096, 16181623424, 16190012032, 16198401152, 16206790528,
16215177344, 16223567744, 16231956352, 16240344704, 16248731008,
16257117824, 16265504384, 16273898624, 16282281856, 16290668672,
16299064192, 16307449216, 16315842176, 16324230016, 16332613504,
16341006464, 16349394304, 16357783168, 16366172288, 16374561664,
16382951296, 16391337856, 16399726208, 16408116352, 16416505472,
16424892032, 16433282176, 16441668224, 16450058624, 16458448768,
16466836864, 16475224448, 16483613056, 16492001408, 16500391808,
16508779648, 16517166976, 16525555328, 16533944192, 16542330752,
16550719616, 16559110528, 16567497088, 16575888512, 16584274816,
16592665472, 16601051008, 16609442944, 16617832064, 16626218624,
16634607488, 16642996096, 16651385728, 16659773824, 16668163712,
16676552576, 16684938112, 16693328768, 16701718144, 16710095488,
16718492288, 16726883968, 16735272832, 16743661184, 16752049792,
16760436608, 16768827008, 16777214336, 16785599104, 16793992832,
16802381696, 16810768768, 16819151744, 16827542656, 16835934848,
16844323712, 16852711552, 16861101952, 16869489536, 16877876864,
16886265728, 16894653056, 16903044736, 16911431296, 16919821696,
16928207488, 16936592768, 16944987776, 16953375616, 16961763968,
16970152832, 16978540928, 16986929536, 16995319168, 17003704448,
17012096896, 17020481152, 17028870784, 17037262208, 17045649536,
17054039936, 17062426496, 17070814336, 17079205504, 17087592064,
17095978112, 17104369024, 17112759424, 17121147776, 17129536384,
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,
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