1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
|
// 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.
package rand
import (
"math"
)
/*
* Normal distribution
*
* See "The Ziggurat Method for Generating Random Variables"
* (Marsaglia & Tsang, 2000)
* http://www.jstatsoft.org/v05/i08/paper [pdf]
*/
const (
rn = 3.442619855899
)
func absInt32(i int32) uint32 {
if i < 0 {
return uint32(-i)
}
return uint32(i)
}
// NormFloat64 returns a normally distributed float64 in the range
// [-math.MaxFloat64, +math.MaxFloat64] with
// standard normal distribution (mean = 0, stddev = 1).
// To produce a different normal distribution, callers can
// adjust the output using:
//
// sample = NormFloat64() * desiredStdDev + desiredMean
//
func (r *Rand) NormFloat64() float64 {
for {
j := int32(r.Uint32()) // Possibly negative
i := j & 0x7F
x := float64(j) * float64(wn[i])
if absInt32(j) < kn[i] {
// This case should be hit better than 99% of the time.
return x
}
if i == 0 {
// This extra work is only required for the base strip.
for {
x = -math.Log(r.Float64()) * (1.0 / rn)
y := -math.Log(r.Float64())
if y+y >= x*x {
break
}
}
if j > 0 {
return rn + x
}
return -rn - x
}
if fn[i]+float32(r.Float64())*(fn[i-1]-fn[i]) < float32(math.Exp(-.5*x*x)) {
return x
}
}
}
var kn = [128]uint32{
0x76ad2212, 0x0, 0x600f1b53, 0x6ce447a6, 0x725b46a2,
0x7560051d, 0x774921eb, 0x789a25bd, 0x799045c3, 0x7a4bce5d,
0x7adf629f, 0x7b5682a6, 0x7bb8a8c6, 0x7c0ae722, 0x7c50cce7,
0x7c8cec5b, 0x7cc12cd6, 0x7ceefed2, 0x7d177e0b, 0x7d3b8883,
0x7d5bce6c, 0x7d78dd64, 0x7d932886, 0x7dab0e57, 0x7dc0dd30,
0x7dd4d688, 0x7de73185, 0x7df81cea, 0x7e07c0a3, 0x7e163efa,
0x7e23b587, 0x7e303dfd, 0x7e3beec2, 0x7e46db77, 0x7e51155d,
0x7e5aabb3, 0x7e63abf7, 0x7e6c222c, 0x7e741906, 0x7e7b9a18,
0x7e82adfa, 0x7e895c63, 0x7e8fac4b, 0x7e95a3fb, 0x7e9b4924,
0x7ea0a0ef, 0x7ea5b00d, 0x7eaa7ac3, 0x7eaf04f3, 0x7eb3522a,
0x7eb765a5, 0x7ebb4259, 0x7ebeeafd, 0x7ec2620a, 0x7ec5a9c4,
0x7ec8c441, 0x7ecbb365, 0x7ece78ed, 0x7ed11671, 0x7ed38d62,
0x7ed5df12, 0x7ed80cb4, 0x7eda175c, 0x7edc0005, 0x7eddc78e,
0x7edf6ebf, 0x7ee0f647, 0x7ee25ebe, 0x7ee3a8a9, 0x7ee4d473,
0x7ee5e276, 0x7ee6d2f5, 0x7ee7a620, 0x7ee85c10, 0x7ee8f4cd,
0x7ee97047, 0x7ee9ce59, 0x7eea0eca, 0x7eea3147, 0x7eea3568,
0x7eea1aab, 0x7ee9e071, 0x7ee98602, 0x7ee90a88, 0x7ee86d08,
0x7ee7ac6a, 0x7ee6c769, 0x7ee5bc9c, 0x7ee48a67, 0x7ee32efc,
0x7ee1a857, 0x7edff42f, 0x7ede0ffa, 0x7edbf8d9, 0x7ed9ab94,
0x7ed7248d, 0x7ed45fae, 0x7ed1585c, 0x7ece095f, 0x7eca6ccb,
0x7ec67be2, 0x7ec22eee, 0x7ebd7d1a, 0x7eb85c35, 0x7eb2c075,
0x7eac9c20, 0x7ea5df27, 0x7e9e769f, 0x7e964c16, 0x7e8d44ba,
0x7e834033, 0x7e781728, 0x7e6b9933, 0x7e5d8a1a, 0x7e4d9ded,
0x7e3b737a, 0x7e268c2f, 0x7e0e3ff5, 0x7df1aa5d, 0x7dcf8c72,
0x7da61a1e, 0x7d72a0fb, 0x7d30e097, 0x7cd9b4ab, 0x7c600f1a,
0x7ba90bdc, 0x7a722176, 0x77d664e5,
}
var wn = [128]float32{
1.7290405e-09, 1.2680929e-10, 1.6897518e-10, 1.9862688e-10,
2.2232431e-10, 2.4244937e-10, 2.601613e-10, 2.7611988e-10,
2.9073963e-10, 3.042997e-10, 3.1699796e-10, 3.289802e-10,
3.4035738e-10, 3.5121603e-10, 3.616251e-10, 3.7164058e-10,
3.8130857e-10, 3.9066758e-10, 3.9975012e-10, 4.08584e-10,
4.1719309e-10, 4.2559822e-10, 4.338176e-10, 4.418672e-10,
4.497613e-10, 4.5751258e-10, 4.651324e-10, 4.7263105e-10,
4.8001775e-10, 4.87301e-10, 4.944885e-10, 5.015873e-10,
5.0860405e-10, 5.155446e-10, 5.2241467e-10, 5.2921934e-10,
5.359635e-10, 5.426517e-10, 5.4928817e-10, 5.5587696e-10,
5.624219e-10, 5.6892646e-10, 5.753941e-10, 5.818282e-10,
5.882317e-10, 5.946077e-10, 6.00959e-10, 6.072884e-10,
6.135985e-10, 6.19892e-10, 6.2617134e-10, 6.3243905e-10,
6.386974e-10, 6.449488e-10, 6.511956e-10, 6.5744005e-10,
6.6368433e-10, 6.699307e-10, 6.7618144e-10, 6.824387e-10,
6.8870465e-10, 6.949815e-10, 7.012715e-10, 7.075768e-10,
7.1389966e-10, 7.202424e-10, 7.266073e-10, 7.329966e-10,
7.394128e-10, 7.4585826e-10, 7.5233547e-10, 7.58847e-10,
7.653954e-10, 7.719835e-10, 7.7861395e-10, 7.852897e-10,
7.920138e-10, 7.987892e-10, 8.0561924e-10, 8.125073e-10,
8.194569e-10, 8.2647167e-10, 8.3355556e-10, 8.407127e-10,
8.479473e-10, 8.55264e-10, 8.6266755e-10, 8.7016316e-10,
8.777562e-10, 8.8545243e-10, 8.932582e-10, 9.0117996e-10,
9.09225e-10, 9.174008e-10, 9.2571584e-10, 9.341788e-10,
9.427997e-10, 9.515889e-10, 9.605579e-10, 9.697193e-10,
9.790869e-10, 9.88676e-10, 9.985036e-10, 1.0085882e-09,
1.0189509e-09, 1.0296151e-09, 1.0406069e-09, 1.0519566e-09,
1.063698e-09, 1.0758702e-09, 1.0885183e-09, 1.1016947e-09,
1.1154611e-09, 1.1298902e-09, 1.1450696e-09, 1.1611052e-09,
1.1781276e-09, 1.1962995e-09, 1.2158287e-09, 1.2369856e-09,
1.2601323e-09, 1.2857697e-09, 1.3146202e-09, 1.347784e-09,
1.3870636e-09, 1.4357403e-09, 1.5008659e-09, 1.6030948e-09,
}
var fn = [128]float32{
1, 0.9635997, 0.9362827, 0.9130436, 0.89228165, 0.87324303,
0.8555006, 0.8387836, 0.8229072, 0.8077383, 0.793177,
0.7791461, 0.7655842, 0.7524416, 0.73967725, 0.7272569,
0.7151515, 0.7033361, 0.69178915, 0.68049186, 0.6694277,
0.658582, 0.6479418, 0.63749546, 0.6272325, 0.6171434,
0.6072195, 0.5974532, 0.58783704, 0.5783647, 0.56903,
0.5598274, 0.5507518, 0.54179835, 0.5329627, 0.52424055,
0.5156282, 0.50712204, 0.49871865, 0.49041483, 0.48220766,
0.4740943, 0.46607214, 0.4581387, 0.45029163, 0.44252872,
0.43484783, 0.427247, 0.41972435, 0.41227803, 0.40490642,
0.39760786, 0.3903808, 0.3832238, 0.37613547, 0.36911446,
0.3621595, 0.35526937, 0.34844297, 0.34167916, 0.33497685,
0.3283351, 0.3217529, 0.3152294, 0.30876362, 0.30235484,
0.29600215, 0.28970486, 0.2834622, 0.2772735, 0.27113807,
0.2650553, 0.25902456, 0.2530453, 0.24711695, 0.241239,
0.23541094, 0.22963232, 0.2239027, 0.21822165, 0.21258877,
0.20700371, 0.20146611, 0.19597565, 0.19053204, 0.18513499,
0.17978427, 0.17447963, 0.1692209, 0.16400786, 0.15884037,
0.15371831, 0.14864157, 0.14361008, 0.13862377, 0.13368265,
0.12878671, 0.12393598, 0.119130544, 0.11437051, 0.10965602,
0.104987256, 0.10036444, 0.095787846, 0.0912578, 0.08677467,
0.0823389, 0.077950984, 0.073611505, 0.06932112, 0.06508058,
0.06089077, 0.056752663, 0.0526674, 0.048636295, 0.044660863,
0.040742867, 0.03688439, 0.033087887, 0.029356318,
0.025693292, 0.022103304, 0.018592102, 0.015167298,
0.011839478, 0.008624485, 0.005548995, 0.0026696292,
}
|
