1// Copyright 2009 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package rand
6
7import (
8	"math"
9)
10
11/*
12 * Normal distribution
13 *
14 * See "The Ziggurat Method for Generating Random Variables"
15 * (Marsaglia & Tsang, 2000)
16 * http://www.jstatsoft.org/v05/i08/paper [pdf]
17 */
18
19const (
20	rn = 3.442619855899
21)
22
23func absInt32(i int32) uint32 {
24	if i < 0 {
25		return uint32(-i)
26	}
27	return uint32(i)
28}
29
30// NormFloat64 returns a normally distributed float64 in
31// the range -math.MaxFloat64 through +math.MaxFloat64 inclusive,
32// with standard normal distribution (mean = 0, stddev = 1).
33// To produce a different normal distribution, callers can
34// adjust the output using:
35//
36//	sample = NormFloat64() * desiredStdDev + desiredMean
37func (r *Rand) NormFloat64() float64 {
38	for {
39		u := r.Uint64()
40		j := int32(u) // Possibly negative
41		i := u >> 32 & 0x7F
42		x := float64(j) * float64(wn[i])
43		if absInt32(j) < kn[i] {
44			// This case should be hit better than 99% of the time.
45			return x
46		}
47
48		if i == 0 {
49			// This extra work is only required for the base strip.
50			for {
51				x = -math.Log(r.Float64()) * (1.0 / rn)
52				y := -math.Log(r.Float64())
53				if y+y >= x*x {
54					break
55				}
56			}
57			if j > 0 {
58				return rn + x
59			}
60			return -rn - x
61		}
62		if fn[i]+float32(r.Float64())*(fn[i-1]-fn[i]) < float32(math.Exp(-.5*x*x)) {
63			return x
64		}
65	}
66}
67
68var kn = [128]uint32{
69	0x76ad2212, 0x0, 0x600f1b53, 0x6ce447a6, 0x725b46a2,
70	0x7560051d, 0x774921eb, 0x789a25bd, 0x799045c3, 0x7a4bce5d,
71	0x7adf629f, 0x7b5682a6, 0x7bb8a8c6, 0x7c0ae722, 0x7c50cce7,
72	0x7c8cec5b, 0x7cc12cd6, 0x7ceefed2, 0x7d177e0b, 0x7d3b8883,
73	0x7d5bce6c, 0x7d78dd64, 0x7d932886, 0x7dab0e57, 0x7dc0dd30,
74	0x7dd4d688, 0x7de73185, 0x7df81cea, 0x7e07c0a3, 0x7e163efa,
75	0x7e23b587, 0x7e303dfd, 0x7e3beec2, 0x7e46db77, 0x7e51155d,
76	0x7e5aabb3, 0x7e63abf7, 0x7e6c222c, 0x7e741906, 0x7e7b9a18,
77	0x7e82adfa, 0x7e895c63, 0x7e8fac4b, 0x7e95a3fb, 0x7e9b4924,
78	0x7ea0a0ef, 0x7ea5b00d, 0x7eaa7ac3, 0x7eaf04f3, 0x7eb3522a,
79	0x7eb765a5, 0x7ebb4259, 0x7ebeeafd, 0x7ec2620a, 0x7ec5a9c4,
80	0x7ec8c441, 0x7ecbb365, 0x7ece78ed, 0x7ed11671, 0x7ed38d62,
81	0x7ed5df12, 0x7ed80cb4, 0x7eda175c, 0x7edc0005, 0x7eddc78e,
82	0x7edf6ebf, 0x7ee0f647, 0x7ee25ebe, 0x7ee3a8a9, 0x7ee4d473,
83	0x7ee5e276, 0x7ee6d2f5, 0x7ee7a620, 0x7ee85c10, 0x7ee8f4cd,
84	0x7ee97047, 0x7ee9ce59, 0x7eea0eca, 0x7eea3147, 0x7eea3568,
85	0x7eea1aab, 0x7ee9e071, 0x7ee98602, 0x7ee90a88, 0x7ee86d08,
86	0x7ee7ac6a, 0x7ee6c769, 0x7ee5bc9c, 0x7ee48a67, 0x7ee32efc,
87	0x7ee1a857, 0x7edff42f, 0x7ede0ffa, 0x7edbf8d9, 0x7ed9ab94,
88	0x7ed7248d, 0x7ed45fae, 0x7ed1585c, 0x7ece095f, 0x7eca6ccb,
89	0x7ec67be2, 0x7ec22eee, 0x7ebd7d1a, 0x7eb85c35, 0x7eb2c075,
90	0x7eac9c20, 0x7ea5df27, 0x7e9e769f, 0x7e964c16, 0x7e8d44ba,
91	0x7e834033, 0x7e781728, 0x7e6b9933, 0x7e5d8a1a, 0x7e4d9ded,
92	0x7e3b737a, 0x7e268c2f, 0x7e0e3ff5, 0x7df1aa5d, 0x7dcf8c72,
93	0x7da61a1e, 0x7d72a0fb, 0x7d30e097, 0x7cd9b4ab, 0x7c600f1a,
94	0x7ba90bdc, 0x7a722176, 0x77d664e5,
95}
96var wn = [128]float32{
97	1.7290405e-09, 1.2680929e-10, 1.6897518e-10, 1.9862688e-10,
98	2.2232431e-10, 2.4244937e-10, 2.601613e-10, 2.7611988e-10,
99	2.9073963e-10, 3.042997e-10, 3.1699796e-10, 3.289802e-10,
100	3.4035738e-10, 3.5121603e-10, 3.616251e-10, 3.7164058e-10,
101	3.8130857e-10, 3.9066758e-10, 3.9975012e-10, 4.08584e-10,
102	4.1719309e-10, 4.2559822e-10, 4.338176e-10, 4.418672e-10,
103	4.497613e-10, 4.5751258e-10, 4.651324e-10, 4.7263105e-10,
104	4.8001775e-10, 4.87301e-10, 4.944885e-10, 5.015873e-10,
105	5.0860405e-10, 5.155446e-10, 5.2241467e-10, 5.2921934e-10,
106	5.359635e-10, 5.426517e-10, 5.4928817e-10, 5.5587696e-10,
107	5.624219e-10, 5.6892646e-10, 5.753941e-10, 5.818282e-10,
108	5.882317e-10, 5.946077e-10, 6.00959e-10, 6.072884e-10,
109	6.135985e-10, 6.19892e-10, 6.2617134e-10, 6.3243905e-10,
110	6.386974e-10, 6.449488e-10, 6.511956e-10, 6.5744005e-10,
111	6.6368433e-10, 6.699307e-10, 6.7618144e-10, 6.824387e-10,
112	6.8870465e-10, 6.949815e-10, 7.012715e-10, 7.075768e-10,
113	7.1389966e-10, 7.202424e-10, 7.266073e-10, 7.329966e-10,
114	7.394128e-10, 7.4585826e-10, 7.5233547e-10, 7.58847e-10,
115	7.653954e-10, 7.719835e-10, 7.7861395e-10, 7.852897e-10,
116	7.920138e-10, 7.987892e-10, 8.0561924e-10, 8.125073e-10,
117	8.194569e-10, 8.2647167e-10, 8.3355556e-10, 8.407127e-10,
118	8.479473e-10, 8.55264e-10, 8.6266755e-10, 8.7016316e-10,
119	8.777562e-10, 8.8545243e-10, 8.932582e-10, 9.0117996e-10,
120	9.09225e-10, 9.174008e-10, 9.2571584e-10, 9.341788e-10,
121	9.427997e-10, 9.515889e-10, 9.605579e-10, 9.697193e-10,
122	9.790869e-10, 9.88676e-10, 9.985036e-10, 1.0085882e-09,
123	1.0189509e-09, 1.0296151e-09, 1.0406069e-09, 1.0519566e-09,
124	1.063698e-09, 1.0758702e-09, 1.0885183e-09, 1.1016947e-09,
125	1.1154611e-09, 1.1298902e-09, 1.1450696e-09, 1.1611052e-09,
126	1.1781276e-09, 1.1962995e-09, 1.2158287e-09, 1.2369856e-09,
127	1.2601323e-09, 1.2857697e-09, 1.3146202e-09, 1.347784e-09,
128	1.3870636e-09, 1.4357403e-09, 1.5008659e-09, 1.6030948e-09,
129}
130var fn = [128]float32{
131	1, 0.9635997, 0.9362827, 0.9130436, 0.89228165, 0.87324303,
132	0.8555006, 0.8387836, 0.8229072, 0.8077383, 0.793177,
133	0.7791461, 0.7655842, 0.7524416, 0.73967725, 0.7272569,
134	0.7151515, 0.7033361, 0.69178915, 0.68049186, 0.6694277,
135	0.658582, 0.6479418, 0.63749546, 0.6272325, 0.6171434,
136	0.6072195, 0.5974532, 0.58783704, 0.5783647, 0.56903,
137	0.5598274, 0.5507518, 0.54179835, 0.5329627, 0.52424055,
138	0.5156282, 0.50712204, 0.49871865, 0.49041483, 0.48220766,
139	0.4740943, 0.46607214, 0.4581387, 0.45029163, 0.44252872,
140	0.43484783, 0.427247, 0.41972435, 0.41227803, 0.40490642,
141	0.39760786, 0.3903808, 0.3832238, 0.37613547, 0.36911446,
142	0.3621595, 0.35526937, 0.34844297, 0.34167916, 0.33497685,
143	0.3283351, 0.3217529, 0.3152294, 0.30876362, 0.30235484,
144	0.29600215, 0.28970486, 0.2834622, 0.2772735, 0.27113807,
145	0.2650553, 0.25902456, 0.2530453, 0.24711695, 0.241239,
146	0.23541094, 0.22963232, 0.2239027, 0.21822165, 0.21258877,
147	0.20700371, 0.20146611, 0.19597565, 0.19053204, 0.18513499,
148	0.17978427, 0.17447963, 0.1692209, 0.16400786, 0.15884037,
149	0.15371831, 0.14864157, 0.14361008, 0.13862377, 0.13368265,
150	0.12878671, 0.12393598, 0.119130544, 0.11437051, 0.10965602,
151	0.104987256, 0.10036444, 0.095787846, 0.0912578, 0.08677467,
152	0.0823389, 0.077950984, 0.073611505, 0.06932112, 0.06508058,
153	0.06089077, 0.056752663, 0.0526674, 0.048636295, 0.044660863,
154	0.040742867, 0.03688439, 0.033087887, 0.029356318,
155	0.025693292, 0.022103304, 0.018592102, 0.015167298,
156	0.011839478, 0.008624485, 0.005548995, 0.0026696292,
157}
158