github.com/Aodurkeen/go-ubiq@v2.3.0+incompatible/core/headerchain.go (about)

     1  // Copyright 2015 The go-ethereum Authors
     2  // This file is part of the go-ethereum library.
     3  //
     4  // The go-ethereum library is free software: you can redistribute it and/or modify
     5  // it under the terms of the GNU Lesser General Public License as published by
     6  // the Free Software Foundation, either version 3 of the License, or
     7  // (at your option) any later version.
     8  //
     9  // The go-ethereum library is distributed in the hope that it will be useful,
    10  // but WITHOUT ANY WARRANTY; without even the implied warranty of
    11  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    12  // GNU Lesser General Public License for more details.
    13  //
    14  // You should have received a copy of the GNU Lesser General Public License
    15  // along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
    16  
    17  package core
    18  
    19  import (
    20  	crand "crypto/rand"
    21  	"errors"
    22  	"fmt"
    23  	"math"
    24  	"math/big"
    25  	mrand "math/rand"
    26  	"sync/atomic"
    27  	"sort"
    28  	"time"
    29  
    30  	"github.com/ubiq/go-ubiq/common"
    31  	"github.com/ubiq/go-ubiq/consensus"
    32  	"github.com/ubiq/go-ubiq/core/rawdb"
    33  	"github.com/ubiq/go-ubiq/core/types"
    34  	"github.com/ubiq/go-ubiq/ethdb"
    35  	"github.com/ubiq/go-ubiq/log"
    36  	"github.com/ubiq/go-ubiq/params"
    37  	"github.com/hashicorp/golang-lru"
    38  )
    39  
    40  const (
    41  	headerCacheLimit = 512
    42  	tdCacheLimit     = 1024
    43  	numberCacheLimit = 2048
    44  	hashCacheLimit   = 64
    45  	medianTimeBlocks = 11
    46  )
    47  
    48  // HeaderChain implements the basic block header chain logic that is shared by
    49  // core.BlockChain and light.LightChain. It is not usable in itself, only as
    50  // a part of either structure.
    51  // It is not thread safe either, the encapsulating chain structures should do
    52  // the necessary mutex locking/unlocking.
    53  type HeaderChain struct {
    54  	config *params.ChainConfig
    55  
    56  	chainDb       ethdb.Database
    57  	genesisHeader *types.Header
    58  
    59  	currentHeader     atomic.Value // Current head of the header chain (may be above the block chain!)
    60  	currentHeaderHash common.Hash  // Hash of the current head of the header chain (prevent recomputing all the time)
    61  
    62  	headerCache *lru.Cache // Cache for the most recent block headers
    63  	tdCache     *lru.Cache // Cache for the most recent block total difficulties
    64  	numberCache *lru.Cache // Cache for the most recent block numbers
    65  	hashCache   *lru.Cache
    66  
    67  	procInterrupt func() bool
    68  
    69  	rand   *mrand.Rand
    70  	engine consensus.Engine
    71  }
    72  
    73  // NewHeaderChain creates a new HeaderChain structure.
    74  //  getValidator should return the parent's validator
    75  //  procInterrupt points to the parent's interrupt semaphore
    76  //  wg points to the parent's shutdown wait group
    77  func NewHeaderChain(chainDb ethdb.Database, config *params.ChainConfig, engine consensus.Engine, procInterrupt func() bool) (*HeaderChain, error) {
    78  	headerCache, _ := lru.New(headerCacheLimit)
    79  	tdCache, _ := lru.New(tdCacheLimit)
    80  	numberCache, _ := lru.New(numberCacheLimit)
    81  	hashCache, _ := lru.New(hashCacheLimit)
    82  
    83  	// Seed a fast but crypto originating random generator
    84  	seed, err := crand.Int(crand.Reader, big.NewInt(math.MaxInt64))
    85  	if err != nil {
    86  		return nil, err
    87  	}
    88  
    89  	hc := &HeaderChain{
    90  		config:        config,
    91  		chainDb:       chainDb,
    92  		headerCache:   headerCache,
    93  		tdCache:       tdCache,
    94  		numberCache:   numberCache,
    95  		hashCache:     hashCache,
    96  		procInterrupt: procInterrupt,
    97  		rand:          mrand.New(mrand.NewSource(seed.Int64())),
    98  		engine:        engine,
    99  	}
   100  
   101  	hc.genesisHeader = hc.GetHeaderByNumber(0)
   102  	if hc.genesisHeader == nil {
   103  		return nil, ErrNoGenesis
   104  	}
   105  
   106  	hc.currentHeader.Store(hc.genesisHeader)
   107  	if head := rawdb.ReadHeadBlockHash(chainDb); head != (common.Hash{}) {
   108  		if chead := hc.GetHeaderByHash(head); chead != nil {
   109  			hc.currentHeader.Store(chead)
   110  		}
   111  	}
   112  	hc.currentHeaderHash = hc.CurrentHeader().Hash()
   113  
   114  	return hc, nil
   115  }
   116  
   117  // GetBlockNumber retrieves the block number belonging to the given hash
   118  // from the cache or database
   119  func (hc *HeaderChain) GetBlockNumber(hash common.Hash) *uint64 {
   120  	if cached, ok := hc.numberCache.Get(hash); ok {
   121  		number := cached.(uint64)
   122  		return &number
   123  	}
   124  	number := rawdb.ReadHeaderNumber(hc.chainDb, hash)
   125  	if number != nil {
   126  		hc.numberCache.Add(hash, *number)
   127  	}
   128  	return number
   129  }
   130  
   131  // WriteHeader writes a header into the local chain, given that its parent is
   132  // already known. If the total difficulty of the newly inserted header becomes
   133  // greater than the current known TD, the canonical chain is re-routed.
   134  //
   135  // Note: This method is not concurrent-safe with inserting blocks simultaneously
   136  // into the chain, as side effects caused by reorganisations cannot be emulated
   137  // without the real blocks. Hence, writing headers directly should only be done
   138  // in two scenarios: pure-header mode of operation (light clients), or properly
   139  // separated header/block phases (non-archive clients).
   140  func (hc *HeaderChain) WriteHeader(header *types.Header) (status WriteStatus, err error) {
   141  	// Cache some values to prevent constant recalculation
   142  	var (
   143  		hash   = header.Hash()
   144  		number = header.Number.Uint64()
   145  	)
   146  	// Calculate the total difficulty of the header
   147  	ptd := hc.GetTd(header.ParentHash, number-1)
   148  	if ptd == nil {
   149  		return NonStatTy, consensus.ErrUnknownAncestor
   150  	}
   151  	localTd := hc.GetTd(hc.currentHeaderHash, hc.CurrentHeader().Number.Uint64())
   152  	externTd := new(big.Int).Add(header.Difficulty, ptd)
   153  
   154  	// Irrelevant of the canonical status, write the td and header to the database
   155  	if err := hc.WriteTd(hash, number, externTd); err != nil {
   156  		log.Crit("Failed to write header total difficulty", "err", err)
   157  	}
   158  	rawdb.WriteHeader(hc.chainDb, header)
   159  
   160  	// If the total difficulty is higher than our known, add it to the canonical chain
   161  	// Second clause in the if statement reduces the vulnerability to selfish mining.
   162  	// Please refer to http://www.cs.cornell.edu/~ie53/publications/btcProcFC.pdf
   163  	if externTd.Cmp(localTd) > 0 || (externTd.Cmp(localTd) == 0 && mrand.Float64() < 0.5) {
   164  		// Delete any canonical number assignments above the new head
   165  		batch := hc.chainDb.NewBatch()
   166  		for i := number + 1; ; i++ {
   167  			hash := rawdb.ReadCanonicalHash(hc.chainDb, i)
   168  			if hash == (common.Hash{}) {
   169  				break
   170  			}
   171  			rawdb.DeleteCanonicalHash(batch, i)
   172  		}
   173  		batch.Write()
   174  
   175  		// Overwrite any stale canonical number assignments
   176  		var (
   177  			headHash   = header.ParentHash
   178  			headNumber = header.Number.Uint64() - 1
   179  			headHeader = hc.GetHeader(headHash, headNumber)
   180  		)
   181  		for rawdb.ReadCanonicalHash(hc.chainDb, headNumber) != headHash {
   182  			rawdb.WriteCanonicalHash(hc.chainDb, headHash, headNumber)
   183  
   184  			headHash = headHeader.ParentHash
   185  			headNumber = headHeader.Number.Uint64() - 1
   186  			headHeader = hc.GetHeader(headHash, headNumber)
   187  		}
   188  		// Extend the canonical chain with the new header
   189  		rawdb.WriteCanonicalHash(hc.chainDb, hash, number)
   190  		rawdb.WriteHeadHeaderHash(hc.chainDb, hash)
   191  
   192  		hc.currentHeaderHash = hash
   193  		hc.currentHeader.Store(types.CopyHeader(header))
   194  
   195  		status = CanonStatTy
   196  	} else {
   197  		status = SideStatTy
   198  	}
   199  
   200  	hc.headerCache.Add(hash, header)
   201  	hc.numberCache.Add(hash, number)
   202  	hc.hashCache.Add(number, hash)
   203  
   204  	return
   205  }
   206  
   207  // WhCallback is a callback function for inserting individual headers.
   208  // A callback is used for two reasons: first, in a LightChain, status should be
   209  // processed and light chain events sent, while in a BlockChain this is not
   210  // necessary since chain events are sent after inserting blocks. Second, the
   211  // header writes should be protected by the parent chain mutex individually.
   212  type WhCallback func(*types.Header) error
   213  
   214  func (hc *HeaderChain) ValidateHeaderChain(chain []*types.Header, checkFreq int) (int, error) {
   215  	// Do a sanity check that the provided chain is actually ordered and linked
   216  	for i := 1; i < len(chain); i++ {
   217  		if chain[i].Number.Uint64() != chain[i-1].Number.Uint64()+1 || chain[i].ParentHash != chain[i-1].Hash() {
   218  			// Chain broke ancestry, log a message (programming error) and skip insertion
   219  			log.Error("Non contiguous header insert", "number", chain[i].Number, "hash", chain[i].Hash(),
   220  				"parent", chain[i].ParentHash, "prevnumber", chain[i-1].Number, "prevhash", chain[i-1].Hash())
   221  
   222  			return 0, fmt.Errorf("non contiguous insert: item %d is #%d [%x…], item %d is #%d [%x…] (parent [%x…])", i-1, chain[i-1].Number,
   223  				chain[i-1].Hash().Bytes()[:4], i, chain[i].Number, chain[i].Hash().Bytes()[:4], chain[i].ParentHash[:4])
   224  		}
   225  	}
   226  
   227  	// Generate the list of seal verification requests, and start the parallel verifier
   228  	seals := make([]bool, len(chain))
   229  	for i := 0; i < len(seals)/checkFreq; i++ {
   230  		index := i*checkFreq + hc.rand.Intn(checkFreq)
   231  		if index >= len(seals) {
   232  			index = len(seals) - 1
   233  		}
   234  		seals[index] = true
   235  	}
   236  	seals[len(seals)-1] = true // Last should always be verified to avoid junk
   237  
   238  	abort, results := hc.engine.VerifyHeaders(hc, chain, seals)
   239  	defer close(abort)
   240  
   241  	// Iterate over the headers and ensure they all check out
   242  	for i, header := range chain {
   243  		// If the chain is terminating, stop processing blocks
   244  		if hc.procInterrupt() {
   245  			log.Debug("Premature abort during headers verification")
   246  			return 0, errors.New("aborted")
   247  		}
   248  		// If the header is a banned one, straight out abort
   249  		if BadHashes[header.Hash()] {
   250  			return i, ErrBlacklistedHash
   251  		}
   252  		// Otherwise wait for headers checks and ensure they pass
   253  		if err := <-results; err != nil {
   254  			return i, err
   255  		}
   256  	}
   257  
   258  	return 0, nil
   259  }
   260  
   261  // InsertHeaderChain attempts to insert the given header chain in to the local
   262  // chain, possibly creating a reorg. If an error is returned, it will return the
   263  // index number of the failing header as well an error describing what went wrong.
   264  //
   265  // The verify parameter can be used to fine tune whether nonce verification
   266  // should be done or not. The reason behind the optional check is because some
   267  // of the header retrieval mechanisms already need to verfy nonces, as well as
   268  // because nonces can be verified sparsely, not needing to check each.
   269  func (hc *HeaderChain) InsertHeaderChain(chain []*types.Header, writeHeader WhCallback, start time.Time) (int, error) {
   270  	// Collect some import statistics to report on
   271  	stats := struct{ processed, ignored int }{}
   272  	// All headers passed verification, import them into the database
   273  	for i, header := range chain {
   274  		// Short circuit insertion if shutting down
   275  		if hc.procInterrupt() {
   276  			log.Debug("Premature abort during headers import")
   277  			return i, errors.New("aborted")
   278  		}
   279  		// If the header's already known, skip it, otherwise store
   280  		if hc.HasHeader(header.Hash(), header.Number.Uint64()) {
   281  			stats.ignored++
   282  			continue
   283  		}
   284  		if err := writeHeader(header); err != nil {
   285  			return i, err
   286  		}
   287  		stats.processed++
   288  	}
   289  	// Report some public statistics so the user has a clue what's going on
   290  	last := chain[len(chain)-1]
   291  
   292  	context := []interface{}{
   293  		"count", stats.processed, "elapsed", common.PrettyDuration(time.Since(start)),
   294  		"number", last.Number, "hash", last.Hash(),
   295  	}
   296  	if timestamp := time.Unix(int64(last.Time), 0); time.Since(timestamp) > time.Minute {
   297  		context = append(context, []interface{}{"age", common.PrettyAge(timestamp)}...)
   298  	}
   299  	if stats.ignored > 0 {
   300  		context = append(context, []interface{}{"ignored", stats.ignored}...)
   301  	}
   302  	log.Info("Imported new block headers", context...)
   303  
   304  	return 0, nil
   305  }
   306  
   307  // GetBlockHashesFromHash retrieves a number of block hashes starting at a given
   308  // hash, fetching towards the genesis block.
   309  func (hc *HeaderChain) GetBlockHashesFromHash(hash common.Hash, max uint64) []common.Hash {
   310  	// Get the origin header from which to fetch
   311  	header := hc.GetHeaderByHash(hash)
   312  	if header == nil {
   313  		return nil
   314  	}
   315  	// Iterate the headers until enough is collected or the genesis reached
   316  	chain := make([]common.Hash, 0, max)
   317  	for i := uint64(0); i < max; i++ {
   318  		next := header.ParentHash
   319  		if header = hc.GetHeader(next, header.Number.Uint64()-1); header == nil {
   320  			break
   321  		}
   322  		chain = append(chain, next)
   323  		if header.Number.Sign() == 0 {
   324  			break
   325  		}
   326  	}
   327  	return chain
   328  }
   329  
   330  // GetAncestor retrieves the Nth ancestor of a given block. It assumes that either the given block or
   331  // a close ancestor of it is canonical. maxNonCanonical points to a downwards counter limiting the
   332  // number of blocks to be individually checked before we reach the canonical chain.
   333  //
   334  // Note: ancestor == 0 returns the same block, 1 returns its parent and so on.
   335  func (hc *HeaderChain) GetAncestor(hash common.Hash, number, ancestor uint64, maxNonCanonical *uint64) (common.Hash, uint64) {
   336  	if ancestor > number {
   337  		return common.Hash{}, 0
   338  	}
   339  	if ancestor == 1 {
   340  		// in this case it is cheaper to just read the header
   341  		if header := hc.GetHeader(hash, number); header != nil {
   342  			return header.ParentHash, number - 1
   343  		} else {
   344  			return common.Hash{}, 0
   345  		}
   346  	}
   347  	for ancestor != 0 {
   348  		if rawdb.ReadCanonicalHash(hc.chainDb, number) == hash {
   349  			number -= ancestor
   350  			return rawdb.ReadCanonicalHash(hc.chainDb, number), number
   351  		}
   352  		if *maxNonCanonical == 0 {
   353  			return common.Hash{}, 0
   354  		}
   355  		*maxNonCanonical--
   356  		ancestor--
   357  		header := hc.GetHeader(hash, number)
   358  		if header == nil {
   359  			return common.Hash{}, 0
   360  		}
   361  		hash = header.ParentHash
   362  		number--
   363  	}
   364  	return hash, number
   365  }
   366  
   367  // GetTd retrieves a block's total difficulty in the canonical chain from the
   368  // database by hash and number, caching it if found.
   369  func (hc *HeaderChain) GetTd(hash common.Hash, number uint64) *big.Int {
   370  	// Short circuit if the td's already in the cache, retrieve otherwise
   371  	if cached, ok := hc.tdCache.Get(hash); ok {
   372  		return cached.(*big.Int)
   373  	}
   374  	td := rawdb.ReadTd(hc.chainDb, hash, number)
   375  	if td == nil {
   376  		return nil
   377  	}
   378  	// Cache the found body for next time and return
   379  	hc.tdCache.Add(hash, td)
   380  	return td
   381  }
   382  
   383  // GetTdByHash retrieves a block's total difficulty in the canonical chain from the
   384  // database by hash, caching it if found.
   385  func (hc *HeaderChain) GetTdByHash(hash common.Hash) *big.Int {
   386  	number := hc.GetBlockNumber(hash)
   387  	if number == nil {
   388  		return nil
   389  	}
   390  	return hc.GetTd(hash, *number)
   391  }
   392  
   393  // calcPastMedianTime calculates the median time of the previous few blocks
   394  // prior to, and including, the passed block node.
   395  //
   396  // Modified from btcsuite
   397  func (hc *HeaderChain) CalcPastMedianTime(number uint64, parent *types.Header) *big.Int {
   398  
   399  	// Genesis block.
   400  	if number == 0 {
   401  		return big.NewInt(int64(hc.GetHeaderByNumber(0).Time))
   402  	}
   403  
   404  	timestamps := make([]*big.Int, medianTimeBlocks)
   405  	numNodes := 0
   406  	limit := uint64(0)
   407  	if number >= medianTimeBlocks {
   408  		limit = number - medianTimeBlocks + 1
   409  	}
   410  
   411  	for i := number; i >= limit; i-- {
   412  		if parent != nil && i == number {
   413  			timestamps[numNodes] = big.NewInt(int64(parent.Time))
   414  		} else {
   415  			header := hc.GetHeaderByNumber(i)
   416  			timestamps[numNodes] = big.NewInt(int64(header.Time))
   417  		}
   418  		numNodes++
   419  		if i == 0 {
   420  			break
   421  		}
   422  	}
   423  
   424  	// Prune the slice to the actual number of available timestamps which
   425  	// will be fewer than desired near the beginning of the block chain
   426  	// and sort them.
   427  	timestamps = timestamps[:numNodes]
   428  	sort.Sort(BigIntSlice(timestamps))
   429  
   430  	medianTimestamp := timestamps[numNodes/2]
   431  	return medianTimestamp
   432  }
   433  
   434  // WriteTd stores a block's total difficulty into the database, also caching it
   435  // along the way.
   436  func (hc *HeaderChain) WriteTd(hash common.Hash, number uint64, td *big.Int) error {
   437  	rawdb.WriteTd(hc.chainDb, hash, number, td)
   438  	hc.tdCache.Add(hash, new(big.Int).Set(td))
   439  	return nil
   440  }
   441  
   442  // GetHeader retrieves a block header from the database by hash and number,
   443  // caching it if found.
   444  func (hc *HeaderChain) GetHeader(hash common.Hash, number uint64) *types.Header {
   445  	// Short circuit if the header's already in the cache, retrieve otherwise
   446  	if header, ok := hc.headerCache.Get(hash); ok {
   447  		return header.(*types.Header)
   448  	}
   449  	header := rawdb.ReadHeader(hc.chainDb, hash, number)
   450  	if header == nil {
   451  		return nil
   452  	}
   453  	// Cache the found header for next time and return
   454  	hc.headerCache.Add(hash, header)
   455  	return header
   456  }
   457  
   458  // GetHeaderByHash retrieves a block header from the database by hash, caching it if
   459  // found.
   460  func (hc *HeaderChain) GetHeaderByHash(hash common.Hash) *types.Header {
   461  	number := hc.GetBlockNumber(hash)
   462  	if number == nil {
   463  		return nil
   464  	}
   465  	return hc.GetHeader(hash, *number)
   466  }
   467  
   468  // HasHeader checks if a block header is present in the database or not.
   469  func (hc *HeaderChain) HasHeader(hash common.Hash, number uint64) bool {
   470  	if hc.numberCache.Contains(hash) || hc.headerCache.Contains(hash) {
   471  		return true
   472  	}
   473  	return rawdb.HasHeader(hc.chainDb, hash, number)
   474  }
   475  
   476  // GetHeaderByNumber retrieves a block header from the database by number,
   477  // caching it (associated with its hash) if found.
   478  func (hc *HeaderChain) GetHeaderByNumber(number uint64) *types.Header {
   479  	hash := rawdb.ReadCanonicalHash(hc.chainDb, number)
   480  	if hash == (common.Hash{}) {
   481  		return nil
   482  	}
   483  	return hc.GetHeader(hash, number)
   484  }
   485  
   486  // CurrentHeader retrieves the current head header of the canonical chain. The
   487  // header is retrieved from the HeaderChain's internal cache.
   488  func (hc *HeaderChain) CurrentHeader() *types.Header {
   489  	return hc.currentHeader.Load().(*types.Header)
   490  }
   491  
   492  // SetCurrentHeader sets the current head header of the canonical chain.
   493  func (hc *HeaderChain) SetCurrentHeader(head *types.Header) {
   494  	rawdb.WriteHeadHeaderHash(hc.chainDb, head.Hash())
   495  
   496  	hc.currentHeader.Store(head)
   497  	hc.currentHeaderHash = head.Hash()
   498  }
   499  
   500  // DeleteCallback is a callback function that is called by SetHead before
   501  // each header is deleted.
   502  type DeleteCallback func(rawdb.DatabaseDeleter, common.Hash, uint64)
   503  
   504  // SetHead rewinds the local chain to a new head. Everything above the new head
   505  // will be deleted and the new one set.
   506  func (hc *HeaderChain) SetHead(head uint64, delFn DeleteCallback) {
   507  	height := uint64(0)
   508  
   509  	if hdr := hc.CurrentHeader(); hdr != nil {
   510  		height = hdr.Number.Uint64()
   511  	}
   512  	batch := hc.chainDb.NewBatch()
   513  	for hdr := hc.CurrentHeader(); hdr != nil && hdr.Number.Uint64() > head; hdr = hc.CurrentHeader() {
   514  		hash := hdr.Hash()
   515  		num := hdr.Number.Uint64()
   516  		if delFn != nil {
   517  			delFn(batch, hash, num)
   518  		}
   519  		rawdb.DeleteHeader(batch, hash, num)
   520  		rawdb.DeleteTd(batch, hash, num)
   521  
   522  		hc.currentHeader.Store(hc.GetHeader(hdr.ParentHash, hdr.Number.Uint64()-1))
   523  	}
   524  	// Roll back the canonical chain numbering
   525  	for i := height; i > head; i-- {
   526  		rawdb.DeleteCanonicalHash(batch, i)
   527  	}
   528  	batch.Write()
   529  
   530  	// Clear out any stale content from the caches
   531  	hc.headerCache.Purge()
   532  	hc.tdCache.Purge()
   533  	hc.numberCache.Purge()
   534  	hc.hashCache.Purge()
   535  
   536  	if hc.CurrentHeader() == nil {
   537  		hc.currentHeader.Store(hc.genesisHeader)
   538  	}
   539  	hc.currentHeaderHash = hc.CurrentHeader().Hash()
   540  
   541  	rawdb.WriteHeadHeaderHash(hc.chainDb, hc.currentHeaderHash)
   542  }
   543  
   544  // SetGenesis sets a new genesis block header for the chain
   545  func (hc *HeaderChain) SetGenesis(head *types.Header) {
   546  	hc.genesisHeader = head
   547  }
   548  
   549  // Config retrieves the header chain's chain configuration.
   550  func (hc *HeaderChain) Config() *params.ChainConfig { return hc.config }
   551  
   552  // Engine retrieves the header chain's consensus engine.
   553  func (hc *HeaderChain) Engine() consensus.Engine { return hc.engine }
   554  
   555  // GetBlock implements consensus.ChainReader, and returns nil for every input as
   556  // a header chain does not have blocks available for retrieval.
   557  func (hc *HeaderChain) GetBlock(hash common.Hash, number uint64) *types.Block {
   558  	return nil
   559  }
   560  
   561  // BigIntSlice attaches the methods of sort.Interface to []*big.Int, sorting in increasing order. (used by CalcPastMedianTime)
   562  type BigIntSlice []*big.Int
   563  
   564  func (s BigIntSlice) Len() int           { return len(s) }
   565  func (s BigIntSlice) Less(i, j int) bool { return s[i].Cmp(s[j]) < 0 }
   566  func (s BigIntSlice) Swap(i, j int)      { s[i], s[j] = s[j], s[i] }