lbcd/difficulty.go

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// Copyright (c) 2013-2014 Conformal Systems LLC.
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// Use of this source code is governed by an ISC
// license that can be found in the LICENSE file.
package btcchain
import (
"fmt"
"math/big"
"time"
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"github.com/btcsuite/btcwire"
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)
const (
// targetTimespan is the desired amount of time that should elapse
// before block difficulty requirement is examined to determine how
// it should be changed in order to maintain the desired block
// generation rate.
targetTimespan = time.Hour * 24 * 14
// targetSpacing is the desired amount of time to generate each block.
targetSpacing = time.Minute * 10
// BlocksPerRetarget is the number of blocks between each difficulty
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// retarget. It is calculated based on the desired block generation
// rate.
BlocksPerRetarget = int64(targetTimespan / targetSpacing)
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// retargetAdjustmentFactor is the adjustment factor used to limit
// the minimum and maximum amount of adjustment that can occur between
// difficulty retargets.
retargetAdjustmentFactor = 4
// minRetargetTimespan is the minimum amount of adjustment that can
// occur between difficulty retargets. It equates to 25% of the
// previous difficulty.
minRetargetTimespan = int64(targetTimespan / retargetAdjustmentFactor)
// maxRetargetTimespan is the maximum amount of adjustment that can
// occur between difficulty retargets. It equates to 400% of the
// previous difficulty.
maxRetargetTimespan = int64(targetTimespan * retargetAdjustmentFactor)
)
var (
// bigOne is 1 represented as a big.Int. It is defined here to avoid
// the overhead of creating it multiple times.
bigOne = big.NewInt(1)
// oneLsh256 is 1 shifted left 256 bits. It is defined here to avoid
// the overhead of creating it multiple times.
oneLsh256 = new(big.Int).Lsh(bigOne, 256)
)
// ShaHashToBig converts a btcwire.ShaHash into a big.Int that can be used to
// perform math comparisons.
func ShaHashToBig(hash *btcwire.ShaHash) *big.Int {
// A ShaHash is in little-endian, but the big package wants the bytes
// in big-endian. Reverse them. ShaHash.Bytes makes a copy, so it
// is safe to modify the returned buffer.
buf := hash.Bytes()
blen := len(buf)
for i := 0; i < blen/2; i++ {
buf[i], buf[blen-1-i] = buf[blen-1-i], buf[i]
}
return new(big.Int).SetBytes(buf)
}
// CompactToBig converts a compact representation of a whole number N to an
// unsigned 32-bit number. The representation is similar to IEEE754 floating
// point numbers.
//
// Like IEEE754 floating point, there are three basic components: the sign,
// the exponent, and the mantissa. They are broken out as follows:
//
// * the most significant 8 bits represent the unsigned base 256 exponent
// * bit 23 (the 24th bit) represents the sign bit
// * the least significant 23 bits represent the mantissa
//
// -------------------------------------------------
// | Exponent | Sign | Mantissa |
// -------------------------------------------------
// | 8 bits [31-24] | 1 bit [23] | 23 bits [22-00] |
// -------------------------------------------------
//
// The formula to calculate N is:
// N = (-1^sign) * mantissa * 256^(exponent-3)
//
// This compact form is only used in bitcoin to encode unsigned 256-bit numbers
// which represent difficulty targets, thus there really is not a need for a
// sign bit, but it is implemented here to stay consistent with bitcoind.
func CompactToBig(compact uint32) *big.Int {
// Extract the mantissa, sign bit, and exponent.
mantissa := compact & 0x007fffff
isNegative := compact&0x00800000 != 0
exponent := uint(compact >> 24)
// Since the base for the exponent is 256, the exponent can be treated
// as the number of bytes to represent the full 256-bit number. So,
// treat the exponent as the number of bytes and shift the mantissa
// right or left accordingly. This is equivalent to:
// N = mantissa * 256^(exponent-3)
var bn *big.Int
if exponent <= 3 {
mantissa >>= 8 * (3 - exponent)
bn = big.NewInt(int64(mantissa))
} else {
bn = big.NewInt(int64(mantissa))
bn.Lsh(bn, 8*(exponent-3))
}
// Make it negative if the sign bit is set.
if isNegative {
bn = bn.Neg(bn)
}
return bn
}
// BigToCompact converts a whole number N to a compact representation using
// an unsigned 32-bit number. The compact representation only provides 23 bits
// of precision, so values larger than (2^23 - 1) only encode the most
// significant digits of the number. See CompactToBig for details.
func BigToCompact(n *big.Int) uint32 {
// No need to do any work if it's zero.
if n.Sign() == 0 {
return 0
}
// Since the base for the exponent is 256, the exponent can be treated
// as the number of bytes. So, shift the number right or left
// accordingly. This is equivalent to:
// mantissa = mantissa / 256^(exponent-3)
var mantissa uint32
exponent := uint(len(n.Bytes()))
if exponent <= 3 {
mantissa = uint32(n.Bits()[0])
mantissa <<= 8 * (3 - exponent)
} else {
// Use a copy to avoid modifying the caller's original number.
tn := new(big.Int).Set(n)
mantissa = uint32(tn.Rsh(tn, 8*(exponent-3)).Bits()[0])
}
// When the mantissa already has the sign bit set, the number is too
// large to fit into the available 23-bits, so divide the number by 256
// and increment the exponent accordingly.
if mantissa&0x00800000 != 0 {
mantissa >>= 8
exponent++
}
// Pack the exponent, sign bit, and mantissa into an unsigned 32-bit
// int and return it.
compact := uint32(exponent<<24) | mantissa
if n.Sign() < 0 {
compact |= 0x00800000
}
return compact
}
// CalcWork calculates a work value from difficulty bits. Bitcoin increases
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// the difficulty for generating a block by decreasing the value which the
// generated hash must be less than. This difficulty target is stored in each
// block header using a compact representation as described in the documenation
// for CompactToBig. The main chain is selected by choosing the chain that has
// the most proof of work (highest difficulty). Since a lower target difficulty
// value equates to higher actual difficulty, the work value which will be
// accumulated must be the inverse of the difficulty. Also, in order to avoid
// potential division by zero and really small floating point numbers, the
// result adds 1 to the denominator and multiplies the numerator by 2^256.
func CalcWork(bits uint32) *big.Int {
// Return a work value of zero if the passed difficulty bits represent
// a negative number. Note this should not happen in practice with valid
// blocks, but an invalid block could trigger it.
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difficultyNum := CompactToBig(bits)
if difficultyNum.Sign() <= 0 {
return big.NewInt(0)
}
// (1 << 256) / (difficultyNum + 1)
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denominator := new(big.Int).Add(difficultyNum, bigOne)
return new(big.Int).Div(oneLsh256, denominator)
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}
// calcEasiestDifficulty calculates the easiest possible difficulty that a block
// can have given starting difficulty bits and a duration. It is mainly used to
// verify that claimed proof of work by a block is sane as compared to a
// known good checkpoint.
func (b *BlockChain) calcEasiestDifficulty(bits uint32, duration time.Duration) uint32 {
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// Convert types used in the calculations below.
durationVal := int64(duration)
adjustmentFactor := big.NewInt(retargetAdjustmentFactor)
// The test network rules allow minimum difficulty blocks after more
// than twice the desired amount of time needed to generate a block has
// elapsed.
if b.netParams.ResetMinDifficulty {
if durationVal > int64(targetSpacing)*2 {
return b.netParams.PowLimitBits
}
}
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// Since easier difficulty equates to higher numbers, the easiest
// difficulty for a given duration is the largest value possible given
// the number of retargets for the duration and starting difficulty
// multiplied by the max adjustment factor.
newTarget := CompactToBig(bits)
for durationVal > 0 && newTarget.Cmp(b.netParams.PowLimit) < 0 {
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newTarget.Mul(newTarget, adjustmentFactor)
durationVal -= maxRetargetTimespan
}
// Limit new value to the proof of work limit.
if newTarget.Cmp(b.netParams.PowLimit) > 0 {
newTarget.Set(b.netParams.PowLimit)
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}
return BigToCompact(newTarget)
}
// findPrevTestNetDifficulty returns the difficulty of the previous block which
// did not have the special testnet minimum difficulty rule applied.
func (b *BlockChain) findPrevTestNetDifficulty(startNode *blockNode) (uint32, error) {
// Search backwards through the chain for the last block without
// the special rule applied.
iterNode := startNode
for iterNode != nil && iterNode.height%BlocksPerRetarget != 0 &&
iterNode.bits == b.netParams.PowLimitBits {
// Get the previous block node. This function is used over
// simply accessing iterNode.parent directly as it will
// dynamically create previous block nodes as needed. This
// helps allow only the pieces of the chain that are needed
// to remain in memory.
var err error
iterNode, err = b.getPrevNodeFromNode(iterNode)
if err != nil {
log.Errorf("getPrevNodeFromNode: %v", err)
return 0, err
}
}
// Return the found difficulty or the minimum difficulty if no
// appropriate block was found.
lastBits := b.netParams.PowLimitBits
if iterNode != nil {
lastBits = iterNode.bits
}
return lastBits, nil
}
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// calcNextRequiredDifficulty calculates the required difficulty for the block
// after the passed previous block node based on the difficulty retarget rules.
// This function differs from the exported CalcNextRequiredDifficulty in that
// the exported version uses the current best chain as the previous block node
// while this function accepts any block node.
func (b *BlockChain) calcNextRequiredDifficulty(lastNode *blockNode, newBlockTime time.Time) (uint32, error) {
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// Genesis block.
if lastNode == nil {
return b.netParams.PowLimitBits, nil
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}
// Return the previous block's difficulty requirements if this block
// is not at a difficulty retarget interval.
if (lastNode.height+1)%BlocksPerRetarget != 0 {
// The test network rules allow minimum difficulty blocks after
// more than twice the desired amount of time needed to generate
// a block has elapsed.
if b.netParams.ResetMinDifficulty {
// Return minimum difficulty when more than twice the
// desired amount of time needed to generate a block has
// elapsed.
allowMinTime := lastNode.timestamp.Add(targetSpacing * 2)
if newBlockTime.After(allowMinTime) {
return b.netParams.PowLimitBits, nil
}
// The block was mined within the desired timeframe, so
// return the difficulty for the last block which did
// not have the special minimum difficulty rule applied.
prevBits, err := b.findPrevTestNetDifficulty(lastNode)
if err != nil {
return 0, err
}
return prevBits, nil
}
// For the main network (or any unrecognized networks), simply
// return the previous block's difficulty requirements.
return lastNode.bits, nil
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}
// Get the block node at the previous retarget (targetTimespan days
// worth of blocks).
firstNode := lastNode
for i := int64(0); i < BlocksPerRetarget-1 && firstNode != nil; i++ {
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// Get the previous block node. This function is used over
// simply accessing firstNode.parent directly as it will
// dynamically create previous block nodes as needed. This
// helps allow only the pieces of the chain that are needed
// to remain in memory.
var err error
firstNode, err = b.getPrevNodeFromNode(firstNode)
if err != nil {
return 0, err
}
}
if firstNode == nil {
return 0, fmt.Errorf("unable to obtain previous retarget block")
}
// Limit the amount of adjustment that can occur to the previous
// difficulty.
actualTimespan := lastNode.timestamp.UnixNano() - firstNode.timestamp.UnixNano()
adjustedTimespan := actualTimespan
if actualTimespan < minRetargetTimespan {
adjustedTimespan = minRetargetTimespan
} else if actualTimespan > maxRetargetTimespan {
adjustedTimespan = maxRetargetTimespan
}
// Calculate new target difficulty as:
// currentDifficulty * (adjustedTimespan / targetTimespan)
// The result uses integer division which means it will be slightly
// rounded down. Bitcoind also uses integer division to calculate this
// result.
oldTarget := CompactToBig(lastNode.bits)
newTarget := new(big.Int).Mul(oldTarget, big.NewInt(adjustedTimespan))
newTarget.Div(newTarget, big.NewInt(int64(targetTimespan)))
// Limit new value to the proof of work limit.
if newTarget.Cmp(b.netParams.PowLimit) > 0 {
newTarget.Set(b.netParams.PowLimit)
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}
// Log new target difficulty and return it. The new target logging is
// intentionally converting the bits back to a number instead of using
// newTarget since conversion to the compact representation loses
// precision.
newTargetBits := BigToCompact(newTarget)
log.Debugf("Difficulty retarget at block height %d", lastNode.height+1)
log.Debugf("Old target %08x (%064x)", lastNode.bits, oldTarget)
log.Debugf("New target %08x (%064x)", newTargetBits, CompactToBig(newTargetBits))
log.Debugf("Actual timespan %v, adjusted timespan %v, target timespan %v",
time.Duration(actualTimespan), time.Duration(adjustedTimespan),
targetTimespan)
return newTargetBits, nil
}
// CalcNextRequiredDifficulty calculates the required difficulty for the block
// after the end of the current best chain based on the difficulty retarget
// rules.
//
// This function is NOT safe for concurrent access.
func (b *BlockChain) CalcNextRequiredDifficulty(timestamp time.Time) (uint32, error) {
return b.calcNextRequiredDifficulty(b.bestChain, timestamp)
}