blob: 9adf9ea6c3673a2ed98d6ff194e3e4c0d525d655 (
plain)
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
|
// SPDX-License-Identifier: Apache-2.0
//
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------
//! \addtogroup constants
//! @{
namespace priv
{
class Datum_helper
{
public:
template<typename eT>
static
typename arma_real_only<eT>::result
nan(typename arma_real_only<eT>::result* junk = nullptr)
{
arma_ignore(junk);
return (std::numeric_limits<eT>::has_quiet_NaN) ? eT(std::numeric_limits<eT>::quiet_NaN()) : eT(0);
}
template<typename eT>
static
typename arma_cx_only<eT>::result
nan(typename arma_cx_only<eT>::result* junk = nullptr)
{
arma_ignore(junk);
typedef typename get_pod_type<eT>::result T;
return eT( Datum_helper::nan<T>(), Datum_helper::nan<T>() );
}
template<typename eT>
static
typename arma_integral_only<eT>::result
nan(typename arma_integral_only<eT>::result* junk = nullptr)
{
arma_ignore(junk);
return eT(0);
}
template<typename eT>
static
typename arma_real_only<eT>::result
inf(typename arma_real_only<eT>::result* junk = nullptr)
{
arma_ignore(junk);
return (std::numeric_limits<eT>::has_infinity) ? eT(std::numeric_limits<eT>::infinity()) : eT(std::numeric_limits<eT>::max());
}
template<typename eT>
static
typename arma_cx_only<eT>::result
inf(typename arma_cx_only<eT>::result* junk = nullptr)
{
arma_ignore(junk);
typedef typename get_pod_type<eT>::result T;
return eT( Datum_helper::inf<T>(), Datum_helper::inf<T>() );
}
template<typename eT>
static
typename arma_integral_only<eT>::result
inf(typename arma_integral_only<eT>::result* junk = nullptr)
{
arma_ignore(junk);
return std::numeric_limits<eT>::max();
}
};
}
//! various constants.
//! Physical constants taken from NIST 2018 CODATA values, and some from WolframAlpha (values provided as of 2009-06-23)
//! http://physics.nist.gov/cuu/Constants
//! http://www.wolframalpha.com
//! See also http://en.wikipedia.org/wiki/Physical_constant
template<typename eT>
class Datum
{
public:
static const eT pi; //!< ratio of any circle's circumference to its diameter
static const eT tau; //!< ratio of any circle's circumference to its radius (replacement of 2*pi)
static const eT e; //!< base of the natural logarithm
static const eT euler; //!< Euler's constant, aka Euler-Mascheroni constant
static const eT gratio; //!< golden ratio
static const eT sqrt2; //!< square root of 2
static const eT sqrt2pi; //!< square root of 2*pi
static const eT log_sqrt2pi; //!< log of square root of 2*pi
static const eT eps; //!< the difference between 1 and the least value greater than 1 that is representable
static const eT log_min; //!< log of the minimum representable value
static const eT log_max; //!< log of the maximum representable value
static const eT nan; //!< "not a number"
static const eT inf; //!< infinity
//
static const eT m_u; //!< atomic mass constant (in kg)
static const eT N_A; //!< Avogadro constant
static const eT k; //!< Boltzmann constant (in joules per kelvin)
static const eT k_evk; //!< Boltzmann constant (in eV/K)
static const eT a_0; //!< Bohr radius (in meters)
static const eT mu_B; //!< Bohr magneton
static const eT Z_0; //!< characteristic impedance of vacuum (in ohms)
static const eT G_0; //!< conductance quantum (in siemens)
static const eT k_e; //!< Coulomb's constant (in meters per farad)
static const eT eps_0; //!< electric constant (in farads per meter)
static const eT m_e; //!< electron mass (in kg)
static const eT eV; //!< electron volt (in joules)
static const eT ec; //!< elementary charge (in coulombs)
static const eT F; //!< Faraday constant (in coulombs)
static const eT alpha; //!< fine-structure constant
static const eT alpha_inv; //!< inverse fine-structure constant
static const eT K_J; //!< Josephson constant
static const eT mu_0; //!< magnetic constant (in henries per meter)
static const eT phi_0; //!< magnetic flux quantum (in webers)
static const eT R; //!< molar gas constant (in joules per mole kelvin)
static const eT G; //!< Newtonian constant of gravitation (in newton square meters per kilogram squared)
static const eT h; //!< Planck constant (in joule seconds)
static const eT h_bar; //!< Planck constant over 2 pi, aka reduced Planck constant (in joule seconds)
static const eT m_p; //!< proton mass (in kg)
static const eT R_inf; //!< Rydberg constant (in reciprocal meters)
static const eT c_0; //!< speed of light in vacuum (in meters per second)
static const eT sigma; //!< Stefan-Boltzmann constant
static const eT R_k; //!< von Klitzing constant (in ohms)
static const eT b; //!< Wien wavelength displacement law constant
};
// the long lengths of the constants are for future support of "long double"
// and any smart compiler that does high-precision computation at compile-time
template<typename eT> const eT Datum<eT>::pi = eT(3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679);
template<typename eT> const eT Datum<eT>::tau = eT(6.2831853071795864769252867665590057683943387987502116419498891846156328125724179972560696506842341359);
template<typename eT> const eT Datum<eT>::e = eT(2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274);
template<typename eT> const eT Datum<eT>::euler = eT(0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495);
template<typename eT> const eT Datum<eT>::gratio = eT(1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374);
template<typename eT> const eT Datum<eT>::sqrt2 = eT(1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727);
template<typename eT> const eT Datum<eT>::sqrt2pi = eT(2.5066282746310005024157652848110452530069867406099383166299235763422936546078419749465958383780572661);
template<typename eT> const eT Datum<eT>::log_sqrt2pi = eT(0.9189385332046727417803297364056176398613974736377834128171515404827656959272603976947432986359541976);
template<typename eT> const eT Datum<eT>::eps = std::numeric_limits<eT>::epsilon();
template<typename eT> const eT Datum<eT>::log_min = std::log(std::numeric_limits<eT>::min());
template<typename eT> const eT Datum<eT>::log_max = std::log(std::numeric_limits<eT>::max());
template<typename eT> const eT Datum<eT>::nan = priv::Datum_helper::nan<eT>();
template<typename eT> const eT Datum<eT>::inf = priv::Datum_helper::inf<eT>();
template<typename eT> const eT Datum<eT>::m_u = eT(1.66053906660e-27);
template<typename eT> const eT Datum<eT>::N_A = eT(6.02214076e23);
template<typename eT> const eT Datum<eT>::k = eT(1.380649e-23);
template<typename eT> const eT Datum<eT>::k_evk = eT(8.617333262e-5);
template<typename eT> const eT Datum<eT>::a_0 = eT(5.29177210903e-11);
template<typename eT> const eT Datum<eT>::mu_B = eT(9.2740100783e-24);
template<typename eT> const eT Datum<eT>::Z_0 = eT(376.730313668);
template<typename eT> const eT Datum<eT>::G_0 = eT(7.748091729e-5);
template<typename eT> const eT Datum<eT>::k_e = eT(8.9875517923e9);
template<typename eT> const eT Datum<eT>::eps_0 = eT(8.8541878128e-12);
template<typename eT> const eT Datum<eT>::m_e = eT(9.1093837015e-31);
template<typename eT> const eT Datum<eT>::eV = eT(1.602176634e-19);
template<typename eT> const eT Datum<eT>::ec = eT(1.602176634e-19);
template<typename eT> const eT Datum<eT>::F = eT(96485.33212);
template<typename eT> const eT Datum<eT>::alpha = eT(7.2973525693e-3);
template<typename eT> const eT Datum<eT>::alpha_inv = eT(137.035999084);
template<typename eT> const eT Datum<eT>::K_J = eT(483597.8484e9);
template<typename eT> const eT Datum<eT>::mu_0 = eT(1.25663706212e-6);
template<typename eT> const eT Datum<eT>::phi_0 = eT(2.067833848e-15);
template<typename eT> const eT Datum<eT>::R = eT(8.314462618);
template<typename eT> const eT Datum<eT>::G = eT(6.67430e-11);
template<typename eT> const eT Datum<eT>::h = eT(6.62607015e-34);
template<typename eT> const eT Datum<eT>::h_bar = eT(1.054571817e-34);
template<typename eT> const eT Datum<eT>::m_p = eT(1.67262192369e-27);
template<typename eT> const eT Datum<eT>::R_inf = eT(10973731.568160);
template<typename eT> const eT Datum<eT>::c_0 = eT(299792458.0);
template<typename eT> const eT Datum<eT>::sigma = eT(5.670374419e-8);
template<typename eT> const eT Datum<eT>::R_k = eT(25812.80745);
template<typename eT> const eT Datum<eT>::b = eT(2.897771955e-3);
typedef Datum<float > fdatum;
typedef Datum<double> datum;
namespace priv
{
template<typename eT>
static
constexpr
typename arma_real_only<eT>::result
most_neg()
{
return (std::numeric_limits<eT>::has_infinity) ? -(std::numeric_limits<eT>::infinity()) : std::numeric_limits<eT>::lowest();
}
template<typename eT>
static
constexpr
typename arma_integral_only<eT>::result
most_neg()
{
return std::numeric_limits<eT>::lowest();
}
template<typename eT>
static
constexpr
typename arma_real_only<eT>::result
most_pos()
{
return (std::numeric_limits<eT>::has_infinity) ? std::numeric_limits<eT>::infinity() : std::numeric_limits<eT>::max();
}
template<typename eT>
static
constexpr
typename arma_integral_only<eT>::result
most_pos()
{
return std::numeric_limits<eT>::max();
}
}
//! @}
|
