package ope

import (
	"math"
)

// uniformRand returns a random number in [0, 1]
// len(coins) >= 32
func uniformRand(coins []byte) float64 {
	b := int64(0)
	for i := 0; i < 32; i++ {
		b <<= 1
		b |= int64(coins[i])
	}
	return float64(b) / float64(uint64(1)<<32-1)
}

// hypergeometric10 returns a sample in hypergeometric distribution.
// Pr[X=x] = choose(y, x) * choose(N-y, M-x) / choose(N, M)
func hypergeometricSmall(M int64, N int64, y int64, coins []byte) int64 {
	d1 := N - y
	d2 := min(M, N-M)

	Y := d2
	K := y
	for Y > 0.0 && K != 0 {
		U := uniformRand(coins)
		Y -= int64(U + float64(Y)/float64(d1+K))
		K--
	}
	Z := d2 - Y
	if N-M < M {
		Z = y - Z
	}
	return Z
}

func loggam[T int | int64 | float32 | float64](x T) float64 {
	return math.Log(math.Gamma(float64(x)))
}

func hypergeometric(M int64, N int64, y int64, coins []byte) int64 {
	if y > 10 {
		return hypergeometricSmall(M, N, y, coins)
	}
	return hypergeometricBig(M, N, y, coins)
}

func hypergeometricBig(M int64, N int64, y int64, coins []byte) int64 {
	D1 := 1.7155277699214135
	D2 := 0.8989161620588988
	// # long mingoodbad, maxgoodbad, popsize, m, d9;
	// # double d4, d5, d6, d7, d8, d10, d11;
	// # long Z;
	// # double T, W, X, Y;
	good := M
	bad := N - M
	sample := y

	mingoodbad := min(good, bad)
	popsize := N
	maxgoodbad := max(good, bad)
	m := min(sample, popsize-sample)
	d4 := float64(mingoodbad) / float64(popsize)
	d5 := 1.0 - d4
	d6 := float64(m)*d4 + 0.5
	d7 := math.Sqrt(float64(popsize-m)*float64(sample)*d4*d5/float64(popsize-1) + 0.5)
	d8 := D1*d7 + D2
	d9 := (m + 1) * (mingoodbad + 1) / (popsize + 2)
	d10 := loggam(d9+1) + loggam(mingoodbad-d9+1) + loggam(m-d9+1) + loggam(maxgoodbad-m+d9+1)
	d11 := min(float64(min(m, mingoodbad)+1), math.Floor(d6+16*d7))
	// # 16 for 16-decimal-digit precision in D1 and D2

	var Z int64
	for {
		X := uniformRand(coins)
		Y := uniformRand(coins)
		W := d6 + d8*(Y-0.5)/X

		// # fast rejection:
		if W < 0.0 || W >= d11 {
			continue
		}

		Z = int64(math.Floor(W))
		T := d10 - (loggam(Z+1) + loggam(mingoodbad-Z+1) + loggam(m-Z+1) + loggam(maxgoodbad-m+Z+1))

		// # fast acceptance:
		if (X*(4.0-X) - 3.0) <= T {
			break
		}

		// # fast rejection:
		if X*(X-T) >= 1 {
			continue
		}

		// # acceptance:
		if 2.0*math.Log(X) <= T {
			break
		}
	}

	// # this is a correction to HRUA* by Ivan Frohne in rv.py
	if good > bad {
		Z = m - Z
	}

	// # another fix from rv.py to allow sample to exceed popsize/2
	if m < sample {
		Z = good - Z
	}

	return Z
}