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// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// W.Hormann, G.Derflinger:
// "Rejection-Inversion to Generate Variates
// from Monotone Discrete Distributions"
// http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz

package rand

import "math"

// A Zipf generates Zipf distributed variates.
type Zipf struct {
        r            *Rand
        imax         float64
        v            float64
        q            float64
        s            float64
        oneminusQ    float64
        oneminusQinv float64
        hxm          float64
        hx0minusHxm  float64
}

func (z *Zipf) h(x float64) float64 {
        return math.Exp(z.oneminusQ*math.Log(z.v+x)) * z.oneminusQinv
}

func (z *Zipf) hinv(x float64) float64 {
        return math.Exp(z.oneminusQinv*math.Log(z.oneminusQ*x)) - z.v
}

// NewZipf returns a Zipf generating variates p(k) on [0, imax]
// proportional to (v+k)**(-s) where s>1 and k>=0, and v>=1.
//
func NewZipf(r *Rand, s float64, v float64, imax uint64) *Zipf {
        z := new(Zipf)
        if s <= 1.0 || v < 1 {
                return nil
        }
        z.r = r
        z.imax = float64(imax)
        z.v = v
        z.q = s
        z.oneminusQ = 1.0 - z.q
        z.oneminusQinv = 1.0 / z.oneminusQ
        z.hxm = z.h(z.imax + 0.5)
        z.hx0minusHxm = z.h(0.5) - math.Exp(math.Log(z.v)*(-z.q)) - z.hxm
        z.s = 1 - z.hinv(z.h(1.5)-math.Exp(-z.q*math.Log(z.v+1.0)))
        return z
}

// Uint64 returns a value drawn from the Zipf distributed described
// by the Zipf object.
func (z *Zipf) Uint64() uint64 {
        k := 0.0

        for {
                r := z.r.Float64() // r on [0,1]
                ur := z.hxm + r*z.hx0minusHxm
                x := z.hinv(ur)
                k = math.Floor(x + 0.5)
                if k-x <= z.s {
                        break
                }
                if ur >= z.h(k+0.5)-math.Exp(-math.Log(k+z.v)*z.q) {
                        break
                }
        }
        return uint64(k)
}