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
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
|
//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#ifndef _LIBCPP___RANDOM_POISSON_DISTRIBUTION_H
#define _LIBCPP___RANDOM_POISSON_DISTRIBUTION_H
#include <__config>
#include <__random/clamp_to_integral.h>
#include <__random/exponential_distribution.h>
#include <__random/is_valid.h>
#include <__random/normal_distribution.h>
#include <__random/uniform_real_distribution.h>
#include <cmath>
#include <iosfwd>
#include <limits>
#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
# pragma GCC system_header
#endif
_LIBCPP_PUSH_MACROS
#include <__undef_macros>
_LIBCPP_BEGIN_NAMESPACE_STD
template<class _IntType = int>
class _LIBCPP_TEMPLATE_VIS poisson_distribution
{
static_assert(__libcpp_random_is_valid_inttype<_IntType>::value, "IntType must be a supported integer type");
public:
// types
typedef _IntType result_type;
class _LIBCPP_TEMPLATE_VIS param_type
{
double __mean_;
double __s_;
double __d_;
double __l_;
double __omega_;
double __c0_;
double __c1_;
double __c2_;
double __c3_;
double __c_;
public:
typedef poisson_distribution distribution_type;
explicit param_type(double __mean = 1.0);
_LIBCPP_INLINE_VISIBILITY
double mean() const {return __mean_;}
friend _LIBCPP_INLINE_VISIBILITY
bool operator==(const param_type& __x, const param_type& __y)
{return __x.__mean_ == __y.__mean_;}
friend _LIBCPP_INLINE_VISIBILITY
bool operator!=(const param_type& __x, const param_type& __y)
{return !(__x == __y);}
friend class poisson_distribution;
};
private:
param_type __p_;
public:
// constructors and reset functions
#ifndef _LIBCPP_CXX03_LANG
_LIBCPP_INLINE_VISIBILITY
poisson_distribution() : poisson_distribution(1.0) {}
_LIBCPP_INLINE_VISIBILITY
explicit poisson_distribution(double __mean)
: __p_(__mean) {}
#else
_LIBCPP_INLINE_VISIBILITY
explicit poisson_distribution(double __mean = 1.0)
: __p_(__mean) {}
#endif
_LIBCPP_INLINE_VISIBILITY
explicit poisson_distribution(const param_type& __p) : __p_(__p) {}
_LIBCPP_INLINE_VISIBILITY
void reset() {}
// generating functions
template<class _URNG>
_LIBCPP_INLINE_VISIBILITY
result_type operator()(_URNG& __g)
{return (*this)(__g, __p_);}
template<class _URNG> result_type operator()(_URNG& __g, const param_type& __p);
// property functions
_LIBCPP_INLINE_VISIBILITY
double mean() const {return __p_.mean();}
_LIBCPP_INLINE_VISIBILITY
param_type param() const {return __p_;}
_LIBCPP_INLINE_VISIBILITY
void param(const param_type& __p) {__p_ = __p;}
_LIBCPP_INLINE_VISIBILITY
result_type min() const {return 0;}
_LIBCPP_INLINE_VISIBILITY
result_type max() const {return numeric_limits<result_type>::max();}
friend _LIBCPP_INLINE_VISIBILITY
bool operator==(const poisson_distribution& __x,
const poisson_distribution& __y)
{return __x.__p_ == __y.__p_;}
friend _LIBCPP_INLINE_VISIBILITY
bool operator!=(const poisson_distribution& __x,
const poisson_distribution& __y)
{return !(__x == __y);}
};
template<class _IntType>
poisson_distribution<_IntType>::param_type::param_type(double __mean)
// According to the standard `inf` is a valid input, but it causes the
// distribution to hang, so we replace it with the maximum representable
// mean.
: __mean_(isinf(__mean) ? numeric_limits<double>::max() : __mean)
{
if (__mean_ < 10)
{
__s_ = 0;
__d_ = 0;
__l_ = _VSTD::exp(-__mean_);
__omega_ = 0;
__c3_ = 0;
__c2_ = 0;
__c1_ = 0;
__c0_ = 0;
__c_ = 0;
}
else
{
__s_ = _VSTD::sqrt(__mean_);
__d_ = 6 * __mean_ * __mean_;
__l_ = _VSTD::trunc(__mean_ - 1.1484);
__omega_ = .3989423 / __s_;
double __b1_ = .4166667E-1 / __mean_;
double __b2_ = .3 * __b1_ * __b1_;
__c3_ = .1428571 * __b1_ * __b2_;
__c2_ = __b2_ - 15. * __c3_;
__c1_ = __b1_ - 6. * __b2_ + 45. * __c3_;
__c0_ = 1. - __b1_ + 3. * __b2_ - 15. * __c3_;
__c_ = .1069 / __mean_;
}
}
template <class _IntType>
template<class _URNG>
_IntType
poisson_distribution<_IntType>::operator()(_URNG& __urng, const param_type& __pr)
{
static_assert(__libcpp_random_is_valid_urng<_URNG>::value, "");
double __tx;
uniform_real_distribution<double> __urd;
if (__pr.__mean_ < 10)
{
__tx = 0;
for (double __p = __urd(__urng); __p > __pr.__l_; ++__tx)
__p *= __urd(__urng);
}
else
{
double __difmuk;
double __g = __pr.__mean_ + __pr.__s_ * normal_distribution<double>()(__urng);
double __u;
if (__g > 0)
{
__tx = _VSTD::trunc(__g);
if (__tx >= __pr.__l_)
return _VSTD::__clamp_to_integral<result_type>(__tx);
__difmuk = __pr.__mean_ - __tx;
__u = __urd(__urng);
if (__pr.__d_ * __u >= __difmuk * __difmuk * __difmuk)
return _VSTD::__clamp_to_integral<result_type>(__tx);
}
exponential_distribution<double> __edist;
for (bool __using_exp_dist = false; true; __using_exp_dist = true)
{
double __e;
if (__using_exp_dist || __g <= 0)
{
double __t;
do
{
__e = __edist(__urng);
__u = __urd(__urng);
__u += __u - 1;
__t = 1.8 + (__u < 0 ? -__e : __e);
} while (__t <= -.6744);
__tx = _VSTD::trunc(__pr.__mean_ + __pr.__s_ * __t);
__difmuk = __pr.__mean_ - __tx;
__using_exp_dist = true;
}
double __px;
double __py;
if (__tx < 10 && __tx >= 0)
{
const double __fac[] = {1, 1, 2, 6, 24, 120, 720, 5040,
40320, 362880};
__px = -__pr.__mean_;
__py = _VSTD::pow(__pr.__mean_, (double)__tx) / __fac[static_cast<int>(__tx)];
}
else
{
double __del = .8333333E-1 / __tx;
__del -= 4.8 * __del * __del * __del;
double __v = __difmuk / __tx;
if (_VSTD::abs(__v) > 0.25)
__px = __tx * _VSTD::log(1 + __v) - __difmuk - __del;
else
__px = __tx * __v * __v * (((((((.1250060 * __v + -.1384794) *
__v + .1421878) * __v + -.1661269) * __v + .2000118) *
__v + -.2500068) * __v + .3333333) * __v + -.5) - __del;
__py = .3989423 / _VSTD::sqrt(__tx);
}
double __r = (0.5 - __difmuk) / __pr.__s_;
double __r2 = __r * __r;
double __fx = -0.5 * __r2;
double __fy = __pr.__omega_ * (((__pr.__c3_ * __r2 + __pr.__c2_) *
__r2 + __pr.__c1_) * __r2 + __pr.__c0_);
if (__using_exp_dist)
{
if (__pr.__c_ * _VSTD::abs(__u) <= __py * _VSTD::exp(__px + __e) -
__fy * _VSTD::exp(__fx + __e))
break;
}
else
{
if (__fy - __u * __fy <= __py * _VSTD::exp(__px - __fx))
break;
}
}
}
return _VSTD::__clamp_to_integral<result_type>(__tx);
}
template <class _CharT, class _Traits, class _IntType>
basic_ostream<_CharT, _Traits>&
operator<<(basic_ostream<_CharT, _Traits>& __os,
const poisson_distribution<_IntType>& __x)
{
__save_flags<_CharT, _Traits> __lx(__os);
typedef basic_ostream<_CharT, _Traits> _OStream;
__os.flags(_OStream::dec | _OStream::left | _OStream::fixed |
_OStream::scientific);
return __os << __x.mean();
}
template <class _CharT, class _Traits, class _IntType>
basic_istream<_CharT, _Traits>&
operator>>(basic_istream<_CharT, _Traits>& __is,
poisson_distribution<_IntType>& __x)
{
typedef poisson_distribution<_IntType> _Eng;
typedef typename _Eng::param_type param_type;
__save_flags<_CharT, _Traits> __lx(__is);
typedef basic_istream<_CharT, _Traits> _Istream;
__is.flags(_Istream::dec | _Istream::skipws);
double __mean;
__is >> __mean;
if (!__is.fail())
__x.param(param_type(__mean));
return __is;
}
_LIBCPP_END_NAMESPACE_STD
_LIBCPP_POP_MACROS
#endif // _LIBCPP___RANDOM_POISSON_DISTRIBUTION_H
|
