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Signed-off-by: Jakub Sztandera <kubuxu@protocol.ai>
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Jakub Sztandera 2020-06-22 17:46:09 +02:00
parent 8fea872345
commit d92362f96e
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1 changed files with 10 additions and 0 deletions
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10
chain/types/electionproof.go
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@ -120,10 +120,15 @@ type poiss struct {
// returns (instance, `1-poisscdf(0, lambda)`)
// CDF value returend is reused when calling `next`
func newPoiss(lambda *big.Int) (*poiss, *big.Int) {
// e^-lambda
elam := expneg(lambda) // Q.256
// pmf(k) = (lambda^k)*(e^lambda) / k!
// k = 0 here so it similifies to just e^labda
pmf := new(big.Int).Set(elam) // Q.256
// icdf(k) = 1 - ∑ᵏᵢ₌₀ pmf(i)
// icdf(0) = 1 - pmf(0)
icdf := big.NewInt(1)
icdf = icdf.Lsh(icdf, precision) // Q.256
icdf = icdf.Sub(icdf, pmf) // Q.256
@ -148,6 +153,10 @@ func newPoiss(lambda *big.Int) (*poiss, *big.Int) {
// next computes next `k++, 1-poisscdf(k, lam)`
// return is in Q.256 format
func (p *poiss) next() *big.Int {
// incrementally compute next pfm and icdf
// pmf(k) = (lambda^k)*(e^lambda) / k!
// so pmf(k) = pmf(k-1) * lambda / k
p.k++
p.kBig = p.kBig.SetUint64(p.k) // Q.0
@ -157,6 +166,7 @@ func (p *poiss) next() *big.Int {
p.pmf = p.pmf.Rsh(p.tmp, precision) // Q.512 >> 256 => Q.256
// calculate output
// icdf(k) = icdf(k-1) - pmf(k)
p.icdf = p.icdf.Sub(p.icdf, p.pmf) // Q.256
return p.icdf
}