199 lines
6.3 KiB
Go
199 lines
6.3 KiB
Go
// Copyright 2020 The go-ethereum Authors
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// This file is part of the go-ethereum library.
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//
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// The go-ethereum library is free software: you can redistribute it and/or modify
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// it under the terms of the GNU Lesser General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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//
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// The go-ethereum library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public License
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// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
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package utils
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import (
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"math"
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"github.com/ethereum/go-ethereum/common/mclock"
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)
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// ExpiredValue is a scalar value that is continuously expired (decreased
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// exponentially) based on the provided logarithmic expiration offset value.
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//
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// The formula for value calculation is: base*2^(exp-logOffset). In order to
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// simplify the calculation of ExpiredValue, its value is expressed in the form
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// of an exponent with a base of 2.
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//
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// Also here is a trick to reduce a lot of calculations. In theory, when a value X
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// decays over time and then a new value Y is added, the final result should be
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// X*2^(exp-logOffset)+Y. However it's very hard to represent in memory.
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// So the trick is using the idea of inflation instead of exponential decay. At this
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// moment the temporary value becomes: X*2^exp+Y*2^logOffset_1, apply the exponential
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// decay when we actually want to calculate the value.
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//
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// e.g.
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// t0: V = 100
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// t1: add 30, inflationary value is: 100 + 30/0.3, 0.3 is the decay coefficient
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// t2: get value, decay coefficient is 0.2 now, final result is: 200*0.2 = 40
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type ExpiredValue struct {
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Base, Exp uint64 // rlp encoding works by default
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}
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// ExpirationFactor is calculated from logOffset. 1 <= Factor < 2 and Factor*2^Exp
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// describes the multiplier applicable for additions and the divider for readouts.
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// If logOffset changes slowly then it saves some expensive operations to not calculate
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// them for each addition and readout but cache this intermediate form for some time.
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// It is also useful for structures where multiple values are expired with the same
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// Expirer.
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type ExpirationFactor struct {
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Exp uint64
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Factor float64
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}
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// ExpFactor calculates ExpirationFactor based on logOffset
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func ExpFactor(logOffset Fixed64) ExpirationFactor {
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return ExpirationFactor{Exp: logOffset.ToUint64(), Factor: logOffset.Fraction().Pow2()}
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}
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// Value calculates the expired value based on a floating point base and integer
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// power-of-2 exponent. This function should be used by multi-value expired structures.
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func (e ExpirationFactor) Value(base float64, exp uint64) float64 {
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return base / e.Factor * math.Pow(2, float64(int64(exp-e.Exp)))
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}
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// value calculates the value at the given moment.
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func (e ExpiredValue) Value(logOffset Fixed64) uint64 {
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offset := Uint64ToFixed64(e.Exp) - logOffset
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return uint64(float64(e.Base) * offset.Pow2())
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}
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// add adds a signed value at the given moment
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func (e *ExpiredValue) Add(amount int64, logOffset Fixed64) int64 {
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integer, frac := logOffset.ToUint64(), logOffset.Fraction()
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factor := frac.Pow2()
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base := factor * float64(amount)
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if integer < e.Exp {
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base /= math.Pow(2, float64(e.Exp-integer))
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}
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if integer > e.Exp {
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e.Base >>= (integer - e.Exp)
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e.Exp = integer
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}
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if base >= 0 || uint64(-base) <= e.Base {
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// This is a temporary fix to circumvent a golang
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// uint conversion issue on arm64, which needs to
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// be investigated further. FIXME
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e.Base = uint64(int64(e.Base) + int64(base))
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return amount
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}
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net := int64(-float64(e.Base) / factor)
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e.Base = 0
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return net
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}
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// addExp adds another ExpiredValue
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func (e *ExpiredValue) AddExp(a ExpiredValue) {
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if e.Exp > a.Exp {
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a.Base >>= (e.Exp - a.Exp)
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}
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if e.Exp < a.Exp {
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e.Base >>= (a.Exp - e.Exp)
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e.Exp = a.Exp
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}
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e.Base += a.Base
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}
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// subExp subtracts another ExpiredValue
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func (e *ExpiredValue) SubExp(a ExpiredValue) {
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if e.Exp > a.Exp {
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a.Base >>= (e.Exp - a.Exp)
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}
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if e.Exp < a.Exp {
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e.Base >>= (a.Exp - e.Exp)
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e.Exp = a.Exp
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}
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if e.Base > a.Base {
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e.Base -= a.Base
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} else {
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e.Base = 0
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}
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}
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// Expirer changes logOffset with a linear rate which can be changed during operation.
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// It is not thread safe, if access by multiple goroutines is needed then it should be
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// encapsulated into a locked structure.
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// Note that if neither SetRate nor SetLogOffset are used during operation then LogOffset
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// is thread safe.
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type Expirer struct {
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logOffset Fixed64
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rate float64
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lastUpdate mclock.AbsTime
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}
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// SetRate changes the expiration rate which is the inverse of the time constant in
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// nanoseconds.
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func (e *Expirer) SetRate(now mclock.AbsTime, rate float64) {
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dt := now - e.lastUpdate
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if dt > 0 {
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e.logOffset += Fixed64(logToFixedFactor * float64(dt) * e.rate)
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}
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e.lastUpdate = now
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e.rate = rate
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}
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// SetLogOffset sets logOffset instantly.
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func (e *Expirer) SetLogOffset(now mclock.AbsTime, logOffset Fixed64) {
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e.lastUpdate = now
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e.logOffset = logOffset
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}
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// LogOffset returns the current logarithmic offset.
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func (e *Expirer) LogOffset(now mclock.AbsTime) Fixed64 {
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dt := now - e.lastUpdate
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if dt <= 0 {
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return e.logOffset
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}
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return e.logOffset + Fixed64(logToFixedFactor*float64(dt)*e.rate)
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}
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// fixedFactor is the fixed point multiplier factor used by Fixed64.
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const fixedFactor = 0x1000000
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// Fixed64 implements 64-bit fixed point arithmetic functions.
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type Fixed64 int64
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// Uint64ToFixed64 converts uint64 integer to Fixed64 format.
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func Uint64ToFixed64(f uint64) Fixed64 {
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return Fixed64(f * fixedFactor)
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}
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// float64ToFixed64 converts float64 to Fixed64 format.
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func Float64ToFixed64(f float64) Fixed64 {
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return Fixed64(f * fixedFactor)
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}
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// toUint64 converts Fixed64 format to uint64.
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func (f64 Fixed64) ToUint64() uint64 {
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return uint64(f64) / fixedFactor
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}
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// fraction returns the fractional part of a Fixed64 value.
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func (f64 Fixed64) Fraction() Fixed64 {
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return f64 % fixedFactor
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}
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var (
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logToFixedFactor = float64(fixedFactor) / math.Log(2)
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fixedToLogFactor = math.Log(2) / float64(fixedFactor)
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)
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// pow2Fixed returns the base 2 power of the fixed point value.
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func (f64 Fixed64) Pow2() float64 {
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return math.Exp(float64(f64) * fixedToLogFactor)
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}
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