# Source file src/math/rand/zipf.go

```     1  // Copyright 2009 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
4
5  // W.Hormann, G.Derflinger:
6  // "Rejection-Inversion to Generate Variates
7  // from Monotone Discrete Distributions"
8  // http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz
9
10  package rand
11
12  import "math"
13
14  // A Zipf generates Zipf distributed variates.
15  type Zipf struct {
16  	r            *Rand
17  	imax         float64
18  	v            float64
19  	q            float64
20  	s            float64
21  	oneminusQ    float64
22  	oneminusQinv float64
23  	hxm          float64
24  	hx0minusHxm  float64
25  }
26
27  func (z *Zipf) h(x float64) float64 {
28  	return math.Exp(z.oneminusQ*math.Log(z.v+x)) * z.oneminusQinv
29  }
30
31  func (z *Zipf) hinv(x float64) float64 {
32  	return math.Exp(z.oneminusQinv*math.Log(z.oneminusQ*x)) - z.v
33  }
34
35  // NewZipf returns a [Zipf] variate generator.
36  // The generator generates values k ∈ [0, imax]
37  // such that P(k) is proportional to (v + k) ** (-s).
38  // Requirements: s > 1 and v >= 1.
39  func NewZipf(r *Rand, s float64, v float64, imax uint64) *Zipf {
40  	z := new(Zipf)
41  	if s <= 1.0 || v < 1 {
42  		return nil
43  	}
44  	z.r = r
45  	z.imax = float64(imax)
46  	z.v = v
47  	z.q = s
48  	z.oneminusQ = 1.0 - z.q
49  	z.oneminusQinv = 1.0 / z.oneminusQ
50  	z.hxm = z.h(z.imax + 0.5)
51  	z.hx0minusHxm = z.h(0.5) - math.Exp(math.Log(z.v)*(-z.q)) - z.hxm
52  	z.s = 1 - z.hinv(z.h(1.5)-math.Exp(-z.q*math.Log(z.v+1.0)))
53  	return z
54  }
55
56  // Uint64 returns a value drawn from the [Zipf] distribution described
57  // by the [Zipf] object.
58  func (z *Zipf) Uint64() uint64 {
59  	if z == nil {
60  		panic("rand: nil Zipf")
61  	}
62  	k := 0.0
63
64  	for {
65  		r := z.r.Float64() // r on [0,1]
66  		ur := z.hxm + r*z.hx0minusHxm
67  		x := z.hinv(ur)
68  		k = math.Floor(x + 0.5)
69  		if k-x <= z.s {
70  			break
71  		}
72  		if ur >= z.h(k+0.5)-math.Exp(-math.Log(k+z.v)*z.q) {
73  			break
74  		}
75  	}
76  	return uint64(k)
77  }
78
```

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