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// 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 ethash

import (
    "encoding/binary"
    "hash"
    "math/big"
    "reflect"
    "runtime"
    "sync"
    "sync/atomic"
    "time"
    "unsafe"

    "github.com/ethereum/go-ethereum/common"
    "github.com/ethereum/go-ethereum/common/bitutil"
    "github.com/ethereum/go-ethereum/crypto"
    "github.com/ethereum/go-ethereum/crypto/sha3"
    "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 returns the size of the ethash verification cache that belongs to a certain
// block number.
func cacheSize(block uint64) uint64 {
    epoch := int(block / epochLength)
    if epoch < maxEpoch {
        return cacheSizes[epoch]
    }
    return calcCacheSize(epoch)
}

// calcCacheSize calculates the cache size for epoch. 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 calcCacheSize(epoch int) uint64 {
    size := cacheInitBytes + cacheGrowthBytes*uint64(epoch) - hashBytes
    for !new(big.Int).SetUint64(size / hashBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
        size -= 2 * hashBytes
    }
    return size
}

// datasetSize returns the size of the ethash mining dataset that belongs to a certain
// block number.
func datasetSize(block uint64) uint64 {
    epoch := int(block / epochLength)
    if epoch < maxEpoch {
        return datasetSizes[epoch]
    }
    return calcDatasetSize(epoch)
}

// calcDatasetSize calculates the dataset size for epoch. 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 calcDatasetSize(epoch int) uint64 {
    size := datasetInitBytes + datasetGrowthBytes*uint64(epoch) - mixBytes
    for !new(big.Int).SetUint64(size / mixBytes).ProbablyPrime(1) { // Always accurate for n < 2^64
        size -= 2 * mixBytes
    }
    return size
}

// 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(dest []byte, data []byte)

// makeHasher creates a repetitive 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 makeHasher(h hash.Hash) hasher {
    // sha3.state supports Read to get the sum, use it to avoid the overhead of Sum.
    // Read alters the state but we reset the hash before every operation.
    type readerHash interface {
        hash.Hash
        Read([]byte) (int, error)
    }
    rh, ok := h.(readerHash)
    if !ok {
        panic("can't find Read method on hash")
    }
    outputLen := rh.Size()
    return func(dest []byte, data []byte) {
        rh.Reset()
        rh.Write(data)
        rh.Read(dest[:outputLen])
    }
}

// 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 := makeHasher(sha3.NewKeccak256())
    for i := 0; i < int(block/epochLength); i++ {
        keccak256(seed, 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.
// This method places the result into dest in machine byte order.
func generateCache(dest []uint32, epoch uint64, seed []byte) {
    // Print some debug logs to allow analysis on low end devices
    logger := log.New("epoch", epoch)

    start := time.Now()
    defer func() {
        elapsed := time.Since(start)

        logFn := logger.Debug
        if elapsed > 3*time.Second {
            logFn = logger.Info
        }
        logFn("Generated ethash verification cache", "elapsed", common.PrettyDuration(elapsed))
    }()
    // Convert our destination slice to a byte buffer
    header := *(*reflect.SliceHeader)(unsafe.Pointer(&dest))
    header.Len *= 4
    header.Cap *= 4
    cache := *(*[]byte)(unsafe.Pointer(&header))

    // Calculate the number of theoretical rows (we'll store in one buffer nonetheless)
    size := uint64(len(cache))
    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 := makeHasher(sha3.NewKeccak512())

    // Sequentially produce the initial dataset
    keccak512(cache, seed)
    for offset := uint64(hashBytes); offset < size; offset += hashBytes {
        keccak512(cache[offset:], 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
            )
            bitutil.XORBytes(temp, cache[srcOff:srcOff+hashBytes], cache[xorOff:xorOff+hashBytes])
            keccak512(cache[dstOff:], temp)

            atomic.AddUint32(&progress, 1)
        }
    }
    // Swap the byte order on big endian systems and return
    if !isLittleEndian() {
        swap(cache)
    }
}

// swap changes the byte order of the buffer assuming a uint32 representation.
func swap(buffer []byte) {
    for i := 0; i < len(buffer); i += 4 {
        binary.BigEndian.PutUint32(buffer[i:], binary.LittleEndian.Uint32(buffer[i:]))
    }
}

// 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 hasher) []byte {
    // Calculate the number of theoretical 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)])
    }
    keccak512(mix, 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)
    }
    keccak512(mix, mix)
    return mix
}

// generateDataset generates the entire ethash dataset for mining.
// This method places the result into dest in machine byte order.
func generateDataset(dest []uint32, epoch uint64, cache []uint32) {
    // Print some debug logs to allow analysis on low end devices
    logger := log.New("epoch", epoch)

    start := time.Now()
    defer func() {
        elapsed := time.Since(start)

        logFn := logger.Debug
        if elapsed > 3*time.Second {
            logFn = logger.Info
        }
        logFn("Generated ethash verification cache", "elapsed", common.PrettyDuration(elapsed))
    }()

    // Figure out whether the bytes need to be swapped for the machine
    swapped := !isLittleEndian()

    // Convert our destination slice to a byte buffer
    header := *(*reflect.SliceHeader)(unsafe.Pointer(&dest))
    header.Len *= 4
    header.Cap *= 4
    dataset := *(*[]byte)(unsafe.Pointer(&header))

    // Generate the dataset on many goroutines since it takes a while
    threads := runtime.NumCPU()
    size := uint64(len(dataset))

    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 := makeHasher(sha3.NewKeccak512())

            // Calculate the data segment this thread should generate
            batch := uint32((size + hashBytes*uint64(threads) - 1) / (hashBytes * uint64(threads)))
            first := uint32(id) * batch
            limit := first + batch
            if limit > uint32(size/hashBytes) {
                limit = uint32(size / hashBytes)
            }
            // Calculate the dataset segment
            percent := uint32(size / hashBytes / 100)
            for index := first; index < limit; index++ {
                item := generateDatasetItem(cache, index, keccak512)
                if swapped {
                    swap(item)
                }
                copy(dataset[index*hashBytes:], item)

                if status := atomic.AddUint32(&progress, 1); status%percent == 0 {
                    logger.Info("Generating DAG in progress", "percentage", uint64(status*100)/(size/hashBytes), "elapsed", common.PrettyDuration(time.Since(start)))
                }
            }
        }(i)
    }
    // Wait for all the generators to finish and return
    pend.Wait()
}

// 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 theoretical 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 := makeHasher(sha3.NewKeccak512())

    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(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, uint64(len(dataset))*4, lookup)
}

const maxEpoch = 2048

// datasetSizes is a lookup table for the ethash dataset size for the first 2048
// epochs (i.e. 61440000 blocks).
var datasetSizes = [maxEpoch]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,
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    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 = [maxEpoch]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,
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