81 lines
1.5 KiB
Go
81 lines
1.5 KiB
Go
package messagepool
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import (
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"math"
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"sync"
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)
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var noWinnersProbCache []float64
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var noWinnersProbOnce sync.Once
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func noWinnersProb() []float64 {
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noWinnersProbOnce.Do(func() {
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poissPdf := func(x float64) float64 {
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const Mu = 5
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lg, _ := math.Lgamma(x + 1)
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result := math.Exp((math.Log(Mu) * x) - lg - Mu)
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return result
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}
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out := make([]float64, 0, MaxBlocks)
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for i := 0; i < MaxBlocks; i++ {
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out = append(out, poissPdf(float64(i)))
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}
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noWinnersProbCache = out
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})
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return noWinnersProbCache
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}
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func binomialCoefficient(n, k float64) float64 {
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if k > n {
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return math.NaN()
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}
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r := 1.0
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for d := 1.0; d <= k; d++ {
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r *= n
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r /= d
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n -= 1
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}
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return r
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}
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func (mp *MessagePool) blockProbabilities(tq float64) []float64 {
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noWinners := noWinnersProb() // cache this
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p := 1 - tq
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binoPdf := func(x, trials float64) float64 {
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// based on https://github.com/atgjack/prob
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if x > trials {
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return 0
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}
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if p == 0 {
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if x == 0 {
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return 1.0
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}
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return 0.0
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}
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if p == 1 {
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if x == trials {
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return 1.0
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}
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return 0.0
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}
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coef := binomialCoefficient(trials, x)
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pow := math.Pow(p, x) * math.Pow(1-p, trials-x)
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if math.IsInf(coef, 0) {
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return 0
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}
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return coef * pow
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}
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out := make([]float64, 0, MaxBlocks)
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for place := 0; place < MaxBlocks; place++ {
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var pPlace float64
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for otherWinners, pCase := range noWinners {
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pPlace += pCase * binoPdf(float64(place), float64(otherWinners+1))
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}
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out = append(out, pPlace)
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}
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return out
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}
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