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import quincy beta 17.1.0
[ceph.git] / ceph / src / boost / libs / math / test / test_constants.cpp
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7c673cae
FG		 1// Copyright Paul Bristow 2007, 2011.
2// Copyright John Maddock 2006, 2011.
3
4// Use, modification and distribution are subject to the
5// Boost Software License, Version 1.0.
6// (See accompanying file LICENSE_1_0.txt
7// or copy at http://www.boost.org/LICENSE_1_0.txt)
8
7c673cae
FG		 9// Check values of constants are drawn from an independent source, or calculated.
10// Both must be at long double precision for the most precise compilers floating-point implementation.
11// So all values use static_cast<RealType>() of values at least 40 decimal digits
12// and that have suffix L to ensure floating-point type is long double.
13
14// Steve Moshier's command interpreter V1.3 100 digits calculator used for some values.
15
16#ifdef _MSC_VER
17# pragma warning(disable : 4127) // conditional expression is constant.
18#endif
20effc67 19#include "math_unit_test.hpp"
7c673cae 20#include <boost/math/concepts/real_concept.hpp> // for real_concept
7c673cae 21#include <boost/math/constants/constants.hpp>
7c673cae 22#include <boost/utility/enable_if.hpp>
20effc67
TL		 23#include <boost/multiprecision/cpp_bin_float.hpp>
24#ifdef BOOST_MATH_HAS_FLOAT128
25#include <boost/multiprecision/float128.hpp>
26#endif
7c673cae 27
20effc67
TL		 28#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900)
29#include <boost/math/tools/agm.hpp>
7c673cae 30// Check at compile time that the construction method for constants of type float, is "construct from a float", or "construct from a double", ...
20effc67
TL		 31static_assert((boost::is_same<boost::math::constants::construction_traits<float, boost::math::policies::policy<> >::type, boost::integral_constant<int, boost::math::constants::construct_from_float> >::value), "Need to be able to construct from float");
32static_assert((boost::is_same<boost::math::constants::construction_traits<double, boost::math::policies::policy<> >::type, boost::integral_constant<int, boost::math::constants::construct_from_double> >::value), "Need to be able to construct from double");
33static_assert((boost::is_same<boost::math::constants::construction_traits<long double, boost::math::policies::policy<> >::type, boost::integral_constant<int, (sizeof(double) == sizeof(long double) ? boost::math::constants::construct_from_double : boost::math::constants::construct_from_long_double)> >::value), "Need to be able to construct from long double");
34static_assert((boost::is_same<boost::math::constants::construction_traits<boost::math::concepts::real_concept, boost::math::policies::policy<> >::type, boost::integral_constant<int, 0> >::value), "Need to be able to construct from real_concept");
7c673cae
FG		 35
36// Policy to set precision at maximum possible using long double.
37typedef boost::math::policies::policy<boost::math::policies::digits2<std::numeric_limits<long double>::digits> > real_concept_policy_1;
38// Policy with precision +2 (could be any reasonable value),
39// forces the precision of the policy to be greater than
40// that of a long double, and therefore triggers different code (construct from string).
41#ifdef BOOST_MATH_USE_FLOAT128
42typedef boost::math::policies::policy<boost::math::policies::digits2<115> > real_concept_policy_2;
43#else
44typedef boost::math::policies::policy<boost::math::policies::digits2<std::numeric_limits<long double>::digits + 2> > real_concept_policy_2;
45#endif
46// Policy with precision greater than the string representations, forces computation of values (i.e. different code path):
47typedef boost::math::policies::policy<boost::math::policies::digits2<400> > real_concept_policy_3;
48
20effc67
TL		 49static_assert((boost::is_same<boost::math::constants::construction_traits<boost::math::concepts::real_concept, real_concept_policy_1 >::type, boost::integral_constant<int, (sizeof(double) == sizeof(long double) ? boost::math::constants::construct_from_double : boost::math::constants::construct_from_long_double) > >::value), "Need to be able to construct from long double");
50static_assert((boost::is_same<boost::math::constants::construction_traits<boost::math::concepts::real_concept, real_concept_policy_2 >::type, boost::integral_constant<int, boost::math::constants::construct_from_string> >::value), "Need to be able to construct integer from string");
51static_assert((boost::math::constants::construction_traits<boost::math::concepts::real_concept, real_concept_policy_3>::type::value >= 5), "Nee 5 digits");
52#endif // C++11
7c673cae
FG		 53
54// We need to declare a conceptual type whose precision is unknown at
55// compile time, and is so enormous when checked at runtime,
56// that we're forced to calculate the values of the constants ourselves.
57
58namespace boost{ namespace math{ namespace concepts{
59
60class big_real_concept : public real_concept
61{
62public:
63 big_real_concept() {}
64 template <class T>
65 big_real_concept(const T& t, typename enable_if<is_convertible<T, real_concept> >::type* = 0) : real_concept(t) {}
66};
67
68inline int itrunc(const big_real_concept& val)
69{
70 BOOST_MATH_STD_USING
71 return itrunc(val.value());
72}
73
74}
75namespace tools{
76
77template <>
78inline BOOST_MATH_CONSTEXPR int digits<concepts::big_real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) BOOST_NOEXCEPT
79{
80 return 2 * boost::math::constants::max_string_digits;
81}
82
83}}}
84
85template <class RealType>
86void test_spots(RealType)
87{
88 // Basic sanity checks for constants,
89 // where template parameter RealType can be float, double, long double,
90 // or real_concept, a prototype for user-defined floating-point types.
91
92 // Parameter RealType is only used to communicate the RealType,
20effc67 93 // and is an arbitrary zero for all tests.
7c673cae 94
20effc67 95 //typedef typename boost::math::constants::construction_traits<RealType, boost::math::policies::policy<> >::type construction_type;
7c673cae
FG		 96 using namespace boost::math::constants;
97 BOOST_MATH_STD_USING
98
20effc67
TL		 99 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), 2);
100 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), 2);
101 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L/2), root_half_pi<RealType>(), 2);
102 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), root_two_pi<RealType>(), 2);
103 CHECK_ULP_CLOSE(sqrt(log(4.0L)), root_ln_four<RealType>(), 2);
104 CHECK_ULP_CLOSE(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), 2);
105 CHECK_ULP_CLOSE(0.5L, half<RealType>(), 2);
106 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104259335L, euler<RealType>(), 2);
107 CHECK_ULP_CLOSE(sqrt(2.0L), root_two<RealType>(), 2);
108 CHECK_ULP_CLOSE(log(2.0L), ln_two<RealType>(), 2);
109 CHECK_ULP_CLOSE(log(10.0L), ln_ten<RealType>(), 2);
110 CHECK_ULP_CLOSE(log(log(2.0L)), ln_ln_two<RealType>(), 2);
111
112 CHECK_ULP_CLOSE(static_cast<long double>(1)/3, third<RealType>(), 2);
113 CHECK_ULP_CLOSE(static_cast<long double>(2)/3, twothirds<RealType>(), 2);
114 CHECK_ULP_CLOSE(0.14159265358979323846264338327950288419716939937510L, pi_minus_three<RealType>(), 2);
115 CHECK_ULP_CLOSE(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi<RealType>(), 2);
7c673cae 116#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
20effc67
TL		 117 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e<RealType>(), 2);
118 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), cbrt_pi<RealType>(), 2);
119 CHECK_ULP_CLOSE(exp(-0.5L), exp_minus_half<RealType>(), 2);
120 CHECK_ULP_CLOSE(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), e_pow_pi<RealType>(), 2);
7c673cae
FG		 121
122
123#else // Only double, so no suffix L.
20effc67
TL		 124 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), pi_pow_e<RealType>(), 2);
125 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), cbrt_pi<RealType>(), 2);
126 CHECK_ULP_CLOSE(exp(-0.5), exp_minus_half<RealType>(), 2);
7c673cae
FG		 127#endif
128 // Rational fractions.
20effc67
TL		 129 CHECK_ULP_CLOSE(0.333333333333333333333333333333333333333L, third<RealType>(), 2);
130 CHECK_ULP_CLOSE(0.666666666666666666666666666666666666667L, two_thirds<RealType>(), 2);
131 CHECK_ULP_CLOSE(0.75L, three_quarters<RealType>(), 2);
132 CHECK_ULP_CLOSE(0.1666666666666666666666666666666666666667L, sixth<RealType>(), 2);
92f5a8d4 133
7c673cae 134 // Two and related.
20effc67
TL		 135 CHECK_ULP_CLOSE(sqrt(2.L), root_two<RealType>(), 2);
136 CHECK_ULP_CLOSE(sqrt(3.L), root_three<RealType>(), 2);
137 CHECK_ULP_CLOSE(sqrt(2.L)/2, half_root_two<RealType>(), 2);
138 CHECK_ULP_CLOSE(log(2.L), ln_two<RealType>(), 2);
139 CHECK_ULP_CLOSE(log(log(2.0L)), ln_ln_two<RealType>(), 2);
140 CHECK_ULP_CLOSE(sqrt(log(4.0L)), root_ln_four<RealType>(), 2);
141 CHECK_ULP_CLOSE(1/sqrt(2.0L), one_div_root_two<RealType>(), 2);
7c673cae
FG		 142
143 // pi.
20effc67
TL		 144 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), 2);
145 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/2, half_pi<RealType>(), 2);
146 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/4, quarter_pi<RealType>(), 2);
147 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/3, third_pi<RealType>(), 2);
148 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/4, quarter_pi<RealType>(), 2);
149 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/6, sixth_pi<RealType>(), 2);
150 CHECK_ULP_CLOSE(2 * 3.14159265358979323846264338327950288419716939937510L, two_pi<RealType>(), 2);
151 CHECK_ULP_CLOSE(3 * 3.14159265358979323846264338327950288419716939937510L / 4, three_quarters_pi<RealType>(), 2);
152 CHECK_ULP_CLOSE(4 * 3.14159265358979323846264338327950288419716939937510L / 3, four_thirds_pi<RealType>(), 2);
153 CHECK_ULP_CLOSE(1 / (3.14159265358979323846264338327950288419716939937510L), one_div_pi<RealType>(), 2);
154 CHECK_ULP_CLOSE(2 / (3.14159265358979323846264338327950288419716939937510L), two_div_pi<RealType>(), 2);
155 CHECK_ULP_CLOSE(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), one_div_two_pi<RealType>(), 2);
156 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), 2);
157 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), root_half_pi<RealType>(), 2);
158 CHECK_ULP_CLOSE(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), root_two_pi<RealType>(), 2);
159 CHECK_ULP_CLOSE(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), one_div_root_pi<RealType>(), 2);
160 CHECK_ULP_CLOSE(2 / sqrt(3.14159265358979323846264338327950288419716939937510L), two_div_root_pi<RealType>(), 2);
161 CHECK_ULP_CLOSE(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), one_div_root_two_pi<RealType>(), 2);
162 CHECK_ULP_CLOSE(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), root_one_div_pi<RealType>(), 2);
163 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L - 3.L, pi_minus_three<RealType>(), 4 * 4 ); // 4 * 2 because of cancellation loss.
164 CHECK_ULP_CLOSE(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi<RealType>(), 4 );
7c673cae 165 //
20effc67
TL		 166 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e<RealType>(), 2); // See above.
167 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, pi_sqr<RealType>(), 2); // See above.
168 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L/6, pi_sqr_div_six<RealType>(), 2); // See above.
169 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, pi_cubed<RealType>(), 2); // See above.
7c673cae 170
20effc67
TL		 171 // CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, cbrt_pi<RealType>(), 2); // See above.
172 CHECK_ULP_CLOSE(cbrt_pi<RealType>() * cbrt_pi<RealType>() * cbrt_pi<RealType>(), pi<RealType>(), 2);
173 CHECK_ULP_CLOSE((1)/cbrt_pi<RealType>(), one_div_cbrt_pi<RealType>(), 2);
7c673cae
FG		 174
175 // Euler
20effc67
TL		 176 CHECK_ULP_CLOSE(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), 2);
177 //CHECK_ULP_CLOSE(exp(-0.5L), exp_minus_half<RealType>(), 2); // See above.
178 CHECK_ULP_CLOSE(exp(-1.L), exp_minus_one<RealType>(), 2);
179 CHECK_ULP_CLOSE(pow(e<RealType>(), pi<RealType>()), e_pow_pi<RealType>(), 2); // See also above.
180 CHECK_ULP_CLOSE(sqrt(e<RealType>()), root_e<RealType>(), 2);
181 CHECK_ULP_CLOSE(log10(e<RealType>()), log10_e<RealType>(), 2);
182 CHECK_ULP_CLOSE(1/log10(e<RealType>()), one_div_log10_e<RealType>(), 2);
183 CHECK_ULP_CLOSE((1/ln_two<RealType>()), log2_e<RealType>(), 2);
7c673cae 184
f67539c2 185 // Trigonometric
20effc67
TL		 186 CHECK_ULP_CLOSE(pi<RealType>()/180, degree<RealType>(), 2);
187 CHECK_ULP_CLOSE(180 / pi<RealType>(), radian<RealType>(), 2);
188 CHECK_ULP_CLOSE(sin(1.L), sin_one<RealType>(), 2);
189 CHECK_ULP_CLOSE(cos(1.L), cos_one<RealType>(), 2);
190 CHECK_ULP_CLOSE(sinh(1.L), sinh_one<RealType>(), 2);
191 CHECK_ULP_CLOSE(cosh(1.L), cosh_one<RealType>(), 2);
7c673cae
FG		 192
193 // Phi
20effc67
TL		 194 CHECK_ULP_CLOSE((1.L + sqrt(5.L)) /2, phi<RealType>(), 2);
195 CHECK_ULP_CLOSE(log((1.L + sqrt(5.L)) /2), ln_phi<RealType>(), 2);
196 CHECK_ULP_CLOSE(1.L / log((1.L + sqrt(5.L)) /2), one_div_ln_phi<RealType>(), 2);
7c673cae
FG		 197
198 //Euler's Gamma
20effc67
TL		 199 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992L, euler<RealType>(), 2); // (sequence A001620 in OEIS).
200 CHECK_ULP_CLOSE(1.L/ 0.57721566490153286060651209008240243104215933593992L, one_div_euler<RealType>(), 2); // (from sequence A001620 in OEIS).
201 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992L * 0.57721566490153286060651209008240243104215933593992L, euler_sqr<RealType>(), 2); // (from sequence A001620 in OEIS).
7c673cae
FG		 202
203 // Misc
20effc67
TL		 204 CHECK_ULP_CLOSE(1.644934066848226436472415166646025189218949901206L, zeta_two<RealType>(), 2); // A013661 as a constant (usually base 10) in OEIS.
205 CHECK_ULP_CLOSE(1.20205690315959428539973816151144999076498629234049888179227L, zeta_three<RealType>(), 2); // (sequence A002117 in OEIS)
206 CHECK_ULP_CLOSE(.91596559417721901505460351493238411077414937428167213L, catalan<RealType>(), 2); // A006752 as a constant in OEIS.
207 CHECK_ULP_CLOSE(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness<RealType>(), 2); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
208 CHECK_ULP_CLOSE(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness<RealType>(), 2); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
209 CHECK_ULP_CLOSE(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess<RealType>(), 4 * 2);
210 CHECK_ULP_CLOSE(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin<RealType>(), 4 ); // A002210 as a constant https://oeis.org/A002210/constant
211 CHECK_ULP_CLOSE(1.2824271291006226368753425688697917277676889273250011L, glaisher<RealType>(), 4 ); // https://oeis.org/A074962/constant
7c673cae
FG		 212
213 //
214 // Last of all come the test cases that behave differently if we're calculating the constants on the fly:
215 //
216 if(boost::math::tools::digits<RealType>() > boost::math::constants::max_string_digits)
217 {
20effc67
TL		 218 // This suffers from cancellation error, so increased 4:
219 CHECK_ULP_CLOSE(static_cast<RealType>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi<RealType>(), 4 * 3);
220 CHECK_ULP_CLOSE(static_cast<RealType>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three<RealType>(), 4 * 3);
7c673cae
FG		 221 }
222 else
223 {
20effc67
TL		 224 CHECK_ULP_CLOSE(static_cast<RealType>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi<RealType>(), 2);
225 CHECK_ULP_CLOSE(static_cast<RealType>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three<RealType>(), 2);
7c673cae
FG		 226 }
227} // template <class RealType>void test_spots(RealType)
228
229void test_float_spots()
230{
231 // Basic sanity checks for constants in boost::math::float_constants::
232 // for example: boost::math::float_constants::pi
233 // (rather than boost::math::constants::pi<float>() ).
7c673cae
FG		 234 using namespace boost::math::float_constants;
235 BOOST_MATH_STD_USING
236
20effc67
TL		 237 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, 2);
238 CHECK_ULP_CLOSE(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, 2);
239 CHECK_ULP_CLOSE(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F/2)), root_half_pi, 2);
240 CHECK_ULP_CLOSE(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F * 2)), root_two_pi, 2);
241 CHECK_ULP_CLOSE(static_cast<float>(sqrt(log(4.0F))), root_ln_four, 2);
242 CHECK_ULP_CLOSE(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, 2);
243 CHECK_ULP_CLOSE(static_cast<float>(0.5), half, 2);
244 CHECK_ULP_CLOSE(static_cast<float>(0.57721566490153286060651209008240243104259335F), euler, 2);
245 CHECK_ULP_CLOSE(static_cast<float>(sqrt(2.0F)), root_two, 2);
246 CHECK_ULP_CLOSE(static_cast<float>(log(2.0F)), ln_two, 2);
247 CHECK_ULP_CLOSE(static_cast<float>(log(log(2.0F))), ln_ln_two, 2);
248 CHECK_ULP_CLOSE(static_cast<float>(1)/3, third, 2);
249 CHECK_ULP_CLOSE(static_cast<float>(2)/3, twothirds, 2);
250 CHECK_ULP_CLOSE(static_cast<float>(0.14159265358979323846264338327950288419716939937510F), pi_minus_three, 2);
251 CHECK_ULP_CLOSE(static_cast<float>(4.F - 3.14159265358979323846264338327950288419716939937510F), four_minus_pi, 2);
7c673cae 252#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
20effc67
TL		 253 CHECK_ULP_CLOSE(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, 2);
254 CHECK_ULP_CLOSE(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 0.33333333333333333333333333333333333333333333333333F)), cbrt_pi, 2);
255 CHECK_ULP_CLOSE(static_cast<float>(exp(-0.5F)), exp_minus_half, 2);
256 CHECK_ULP_CLOSE(static_cast<float>(pow(2.71828182845904523536028747135266249775724709369995F, 3.14159265358979323846264338327950288419716939937510F)), e_pow_pi, 2);
7c673cae
FG		 257
258
259#else // Only double, so no suffix F.
20effc67
TL		 260 CHECK_ULP_CLOSE(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, 2);
261 CHECK_ULP_CLOSE(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, 2);
262 CHECK_ULP_CLOSE(static_cast<float>(exp(-0.5)), exp_minus_half, 2);
7c673cae
FG		 263#endif
264 // Rational fractions.
20effc67
TL		 265 CHECK_ULP_CLOSE(static_cast<float>(0.333333333333333333333333333333333333333F), third, 2);
266 CHECK_ULP_CLOSE(static_cast<float>(0.666666666666666666666666666666666666667F), two_thirds, 2);
267 CHECK_ULP_CLOSE(static_cast<float>(0.75F), three_quarters, 2);
7c673cae 268 // Two and related.
20effc67
TL		 269 CHECK_ULP_CLOSE(static_cast<float>(sqrt(2.F)), root_two, 2);
270 CHECK_ULP_CLOSE(static_cast<float>(sqrt(3.F)), root_three, 2);
271 CHECK_ULP_CLOSE(static_cast<float>(sqrt(2.F)/2), half_root_two, 2);
272 CHECK_ULP_CLOSE(static_cast<float>(log(2.F)), ln_two, 2);
273 CHECK_ULP_CLOSE(static_cast<float>(log(log(2.0F))), ln_ln_two, 2);
274 CHECK_ULP_CLOSE(static_cast<float>(sqrt(log(4.0F))), root_ln_four, 2);
275 CHECK_ULP_CLOSE(static_cast<float>(1/sqrt(2.0F)), one_div_root_two, 2);
7c673cae
FG		 276
277 // pi.
20effc67
TL		 278 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, 2);
279 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/2), half_pi, 2);
280 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/4), quarter_pi, 2);
281 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/3), third_pi, 2);
282 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/6), sixth_pi, 2);
283 CHECK_ULP_CLOSE(static_cast<float>(2 * 3.14159265358979323846264338327950288419716939937510F), two_pi, 2);
284 CHECK_ULP_CLOSE(static_cast<float>(3 * 3.14159265358979323846264338327950288419716939937510F / 4), three_quarters_pi, 2);
285 CHECK_ULP_CLOSE(static_cast<float>(4 * 3.14159265358979323846264338327950288419716939937510F / 3), four_thirds_pi, 2);
286 CHECK_ULP_CLOSE(static_cast<float>(1 / (3.14159265358979323846264338327950288419716939937510F)), one_div_pi, 2);
287 CHECK_ULP_CLOSE(static_cast<float>(2 / (3.14159265358979323846264338327950288419716939937510F)), two_div_pi, 2);
288 CHECK_ULP_CLOSE(static_cast<float>(1 / (2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_two_pi, 2);
289 CHECK_ULP_CLOSE(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, 2);
290 CHECK_ULP_CLOSE(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F / 2)), root_half_pi, 2);
291 CHECK_ULP_CLOSE(static_cast<float>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), root_two_pi, 2);
292 CHECK_ULP_CLOSE(static_cast<float>(1 / sqrt(3.14159265358979323846264338327950288419716939937510F)), one_div_root_pi, 2);
293 CHECK_ULP_CLOSE(static_cast<float>(2 / sqrt(3.14159265358979323846264338327950288419716939937510F)), two_div_root_pi, 2);
294 CHECK_ULP_CLOSE(static_cast<float>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_root_two_pi, 2);
295 CHECK_ULP_CLOSE(static_cast<float>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510F)), root_one_div_pi, 2);
296 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510L - 3.L), pi_minus_three, 4 * 2 ); // 4 * 2 because of cancellation loss.
297 CHECK_ULP_CLOSE(static_cast<float>(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, 4 );
7c673cae 298 //
20effc67
TL		 299 CHECK_ULP_CLOSE(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, 2); // See above.
300 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), pi_sqr, 2); // See above.
301 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F/6), pi_sqr_div_six, 2); // See above.
302 CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), pi_cubed, 2); // See above.
7c673cae 303
20effc67
TL		 304 // CHECK_ULP_CLOSE(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), cbrt_pi, 2); // See above.
305 CHECK_ULP_CLOSE(cbrt_pi * cbrt_pi * cbrt_pi, pi, 2);
306 CHECK_ULP_CLOSE((static_cast<float>(1)/cbrt_pi), one_div_cbrt_pi, 2);
7c673cae
FG		 307
308 // Euler
20effc67 309 CHECK_ULP_CLOSE(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, 2);
7c673cae 310
20effc67
TL		 311 //CHECK_ULP_CLOSE(static_cast<float>(exp(-0.5F)), exp_minus_half, 2); // See above.
312 CHECK_ULP_CLOSE(pow(e, pi), e_pow_pi, 2); // See also above.
313 CHECK_ULP_CLOSE(sqrt(e), root_e, 2);
314 CHECK_ULP_CLOSE(log10(e), log10_e, 2);
315 CHECK_ULP_CLOSE(static_cast<float>(1)/log10(e), one_div_log10_e, 2);
7c673cae 316
f67539c2 317 // Trigonometric
20effc67
TL		 318 CHECK_ULP_CLOSE(pi/180, degree, 2);
319 CHECK_ULP_CLOSE(180 / pi, radian, 2);
320 CHECK_ULP_CLOSE(sin(1.F), sin_one, 2);
321 CHECK_ULP_CLOSE(cos(1.F), cos_one, 2);
322 CHECK_ULP_CLOSE(sinh(1.F), sinh_one, 2);
323 CHECK_ULP_CLOSE(cosh(1.F), cosh_one, 2);
7c673cae
FG		 324
325 // Phi
20effc67
TL		 326 CHECK_ULP_CLOSE((1.F + sqrt(5.F)) /2, phi, 2);
327 CHECK_ULP_CLOSE(log((1.F + sqrt(5.F)) /2), ln_phi, 2);
328 CHECK_ULP_CLOSE(1.F / log((1.F + sqrt(5.F)) /2), one_div_ln_phi, 2);
7c673cae
FG		 329
330 // Euler's Gamma
20effc67
TL		 331 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992F, euler, 2); // (sequence A001620 in OEIS).
332 CHECK_ULP_CLOSE(1.F/ 0.57721566490153286060651209008240243104215933593992F, one_div_euler, 2); // (from sequence A001620 in OEIS).
333 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992F * 0.57721566490153286060651209008240243104215933593992F, euler_sqr, 2); // (from sequence A001620 in OEIS).
7c673cae
FG		 334
335 // Misc
20effc67
TL		 336 CHECK_ULP_CLOSE(1.644934066848226436472415166646025189218949901206F, zeta_two, 2); // A013661 as a constant (usually base 10) in OEIS.
337 CHECK_ULP_CLOSE(1.20205690315959428539973816151144999076498629234049888179227F, zeta_three, 2); // (sequence A002117 in OEIS)
338 CHECK_ULP_CLOSE(.91596559417721901505460351493238411077414937428167213F, catalan, 2); // A006752 as a constant in OEIS.
339 CHECK_ULP_CLOSE(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150F, extreme_value_skewness, 2); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
340 CHECK_ULP_CLOSE(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067F, rayleigh_skewness, 2); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
341 CHECK_ULP_CLOSE(2.450893006876380628486604106197544154e-01F, rayleigh_kurtosis_excess, 2);
342 CHECK_ULP_CLOSE(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515F, khinchin, 4 ); // A002210 as a constant https://oeis.org/A002210/constant
343 CHECK_ULP_CLOSE(1.2824271291006226368753425688697917277676889273250011F, glaisher, 4 ); // https://oeis.org/A074962/constant
344 CHECK_ULP_CLOSE(4.66920160910299067185320382046620161725F, first_feigenbaum, 1);
7c673cae
FG		 345} // template <class RealType>void test_spots(RealType)
346
347void test_double_spots()
348{
349 // Basic sanity checks for constants in boost::math::double_constants::
350 // for example: boost::math::double_constants::pi
351 // (rather than boost::math::constants::pi<double>() ).
7c673cae
FG		 352 using namespace boost::math::double_constants;
353 BOOST_MATH_STD_USING
354
20effc67
TL		 355 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, 2);
356 CHECK_ULP_CLOSE(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, 2);
357 CHECK_ULP_CLOSE(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510/2)), root_half_pi, 2);
358 CHECK_ULP_CLOSE(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 * 2)), root_two_pi, 2);
359 CHECK_ULP_CLOSE(static_cast<double>(sqrt(log(4.0))), root_ln_four, 2);
360 CHECK_ULP_CLOSE(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, 2);
361 CHECK_ULP_CLOSE(static_cast<double>(0.5), half, 2);
362 CHECK_ULP_CLOSE(static_cast<double>(0.57721566490153286060651209008240243104259335), euler, 2);
363 CHECK_ULP_CLOSE(static_cast<double>(sqrt(2.0)), root_two, 2);
364 CHECK_ULP_CLOSE(static_cast<double>(log(2.0)), ln_two, 2);
365 CHECK_ULP_CLOSE(static_cast<double>(log(log(2.0))), ln_ln_two, 2);
366 CHECK_ULP_CLOSE(static_cast<double>(1)/3, third, 2);
367 CHECK_ULP_CLOSE(static_cast<double>(2)/3, twothirds, 2);
368 CHECK_ULP_CLOSE(static_cast<double>(0.14159265358979323846264338327950288419716939937510), pi_minus_three, 2);
369 CHECK_ULP_CLOSE(static_cast<double>(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, 2);
7c673cae 370#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
20effc67
TL		 371 CHECK_ULP_CLOSE(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, 2);
372 CHECK_ULP_CLOSE(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, 2);
373 CHECK_ULP_CLOSE(static_cast<double>(exp(-0.5)), exp_minus_half, 2);
374 CHECK_ULP_CLOSE(static_cast<double>(pow(2.71828182845904523536028747135266249775724709369995, 3.14159265358979323846264338327950288419716939937510)), e_pow_pi, 2);
7c673cae
FG		 375
376
377#else // Only double, so no suffix .
20effc67
TL		 378 CHECK_ULP_CLOSE(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, 2);
379 CHECK_ULP_CLOSE(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, 2);
380 CHECK_ULP_CLOSE(static_cast<double>(exp(-0.5)), exp_minus_half, 2);
7c673cae
FG		 381#endif
382 // Rational fractions.
20effc67
TL		 383 CHECK_ULP_CLOSE(static_cast<double>(0.333333333333333333333333333333333333333), third, 2);
384 CHECK_ULP_CLOSE(static_cast<double>(0.666666666666666666666666666666666666667), two_thirds, 2);
385 CHECK_ULP_CLOSE(static_cast<double>(0.75), three_quarters, 2);
7c673cae 386 // Two and related.
20effc67
TL		 387 CHECK_ULP_CLOSE(static_cast<double>(sqrt(2.)), root_two, 2);
388 CHECK_ULP_CLOSE(static_cast<double>(sqrt(3.)), root_three, 2);
389 CHECK_ULP_CLOSE(static_cast<double>(sqrt(2.)/2), half_root_two, 2);
390 CHECK_ULP_CLOSE(static_cast<double>(log(2.)), ln_two, 2);
391 CHECK_ULP_CLOSE(static_cast<double>(log(log(2.0))), ln_ln_two, 2);
392 CHECK_ULP_CLOSE(static_cast<double>(sqrt(log(4.0))), root_ln_four, 2);
393 CHECK_ULP_CLOSE(static_cast<double>(1/sqrt(2.0)), one_div_root_two, 2);
7c673cae
FG		 394
395 // pi.
20effc67
TL		 396 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, 2);
397 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510/2), half_pi, 2);
398 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510/4), quarter_pi, 2);
399 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510/3), third_pi, 2);
400 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510/6), sixth_pi, 2);
401 CHECK_ULP_CLOSE(static_cast<double>(2 * 3.14159265358979323846264338327950288419716939937510), two_pi, 2);
402 CHECK_ULP_CLOSE(static_cast<double>(3 * 3.14159265358979323846264338327950288419716939937510 / 4), three_quarters_pi, 2);
403 CHECK_ULP_CLOSE(static_cast<double>(4 * 3.14159265358979323846264338327950288419716939937510 / 3), four_thirds_pi, 2);
404 CHECK_ULP_CLOSE(static_cast<double>(1 / (3.14159265358979323846264338327950288419716939937510)), one_div_pi, 2);
405 CHECK_ULP_CLOSE(static_cast<double>(2 / (3.14159265358979323846264338327950288419716939937510)), two_div_pi, 2);
406 CHECK_ULP_CLOSE(static_cast<double>(1 / (2 * 3.14159265358979323846264338327950288419716939937510)), one_div_two_pi, 2);
407 CHECK_ULP_CLOSE(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, 2);
408 CHECK_ULP_CLOSE(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 / 2)), root_half_pi, 2);
409 CHECK_ULP_CLOSE(static_cast<double>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), root_two_pi, 2);
410 CHECK_ULP_CLOSE(static_cast<double>(1 / sqrt(3.14159265358979323846264338327950288419716939937510)), one_div_root_pi, 2);
411 CHECK_ULP_CLOSE(static_cast<double>(2 / sqrt(3.14159265358979323846264338327950288419716939937510)), two_div_root_pi, 2);
412 CHECK_ULP_CLOSE(static_cast<double>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), one_div_root_two_pi, 2);
413 CHECK_ULP_CLOSE(static_cast<double>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510)), root_one_div_pi, 2);
414 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510 - 3.), pi_minus_three, 4 * 2 ); // 4 * 2 because of cancellation loss.
415 CHECK_ULP_CLOSE(static_cast<double>(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, 4 );
7c673cae 416 //
20effc67
TL		 417 CHECK_ULP_CLOSE(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, 2); // See above.
418 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), pi_sqr, 2); // See above.
419 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510/6), pi_sqr_div_six, 2); // See above.
420 CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), pi_cubed, 2); // See above.
7c673cae 421
20effc67
TL		 422 // CHECK_ULP_CLOSE(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), cbrt_pi, 2); // See above.
423 CHECK_ULP_CLOSE(cbrt_pi * cbrt_pi * cbrt_pi, pi, 2);
424 CHECK_ULP_CLOSE((static_cast<double>(1)/cbrt_pi), one_div_cbrt_pi, 2);
7c673cae
FG		 425
426 // Euler
20effc67 427 CHECK_ULP_CLOSE(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, 2);
7c673cae 428
20effc67
TL		 429 //CHECK_ULP_CLOSE(static_cast<double>(exp(-0.5)), exp_minus_half, 2); // See above.
430 CHECK_ULP_CLOSE(pow(e, pi), e_pow_pi, 2); // See also above.
431 CHECK_ULP_CLOSE(sqrt(e), root_e, 2);
432 CHECK_ULP_CLOSE(log10(e), log10_e, 2);
433 CHECK_ULP_CLOSE(static_cast<double>(1)/log10(e), one_div_log10_e, 2);
7c673cae 434
f67539c2 435 // Trigonometric
20effc67
TL		 436 CHECK_ULP_CLOSE(pi/180, degree, 2);
437 CHECK_ULP_CLOSE(180 / pi, radian, 2);
438 CHECK_ULP_CLOSE(sin(1.), sin_one, 2);
439 CHECK_ULP_CLOSE(cos(1.), cos_one, 2);
440 CHECK_ULP_CLOSE(sinh(1.), sinh_one, 2);
441 CHECK_ULP_CLOSE(cosh(1.), cosh_one, 2);
7c673cae
FG		 442
443 // Phi
20effc67
TL		 444 CHECK_ULP_CLOSE((1. + sqrt(5.)) /2, phi, 2);
445 CHECK_ULP_CLOSE(log((1. + sqrt(5.)) /2), ln_phi, 2);
446 CHECK_ULP_CLOSE(1. / log((1. + sqrt(5.)) /2), one_div_ln_phi, 2);
7c673cae
FG		 447
448 //Euler's Gamma
20effc67
TL		 449 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992, euler, 2); // (sequence A001620 in OEIS).
450 CHECK_ULP_CLOSE(1./ 0.57721566490153286060651209008240243104215933593992, one_div_euler, 2); // (from sequence A001620 in OEIS).
451 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992 * 0.57721566490153286060651209008240243104215933593992, euler_sqr, 2); // (from sequence A001620 in OEIS).
7c673cae
FG		 452
453 // Misc
20effc67
TL		 454 CHECK_ULP_CLOSE(1.644934066848226436472415166646025189218949901206, zeta_two, 2); // A013661 as a constant (usually base 10) in OEIS.
455 CHECK_ULP_CLOSE(1.20205690315959428539973816151144999076498629234049888179227, zeta_three, 2); // (sequence A002117 in OEIS)
456 CHECK_ULP_CLOSE(.91596559417721901505460351493238411077414937428167213, catalan, 2); // A006752 as a constant in OEIS.
457 CHECK_ULP_CLOSE(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150, extreme_value_skewness, 2); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
458 CHECK_ULP_CLOSE(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067, rayleigh_skewness, 2); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
459 CHECK_ULP_CLOSE(2.450893006876380628486604106197544154e-01, rayleigh_kurtosis_excess, 2);
460 CHECK_ULP_CLOSE(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515, khinchin, 4 ); // A002210 as a constant https://oeis.org/A002210/constant
461 CHECK_ULP_CLOSE(1.2824271291006226368753425688697917277676889273250011, glaisher, 4 ); // https://oeis.org/A074962/constant
7c673cae
FG		 462
463} // template <class RealType>void test_spots(RealType)
464
465void test_long_double_spots()
466{
467 // Basic sanity checks for constants in boost::math::long double_constants::
468 // for example: boost::math::long_double_constants::pi
469 // (rather than boost::math::constants::pi<long double>() ).
470
20effc67
TL		 471 // All constants are tested here using at least long double precision
472 // with independent calculated or listed values,
473 // or calculations using long double (sometime a little less accurate).
7c673cae
FG		 474 using namespace boost::math::long_double_constants;
475 BOOST_MATH_STD_USING
476
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TL		 477 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L), pi, 2);
478 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, 2);
479 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi, 2);
480 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi, 2);
481 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(log(4.0L))), root_ln_four, 2);
482 CHECK_ULP_CLOSE(static_cast<long double>(2.71828182845904523536028747135266249775724709369995L), e, 2);
483 CHECK_ULP_CLOSE(static_cast<long double>(0.5), half, 2);
484 CHECK_ULP_CLOSE(static_cast<long double>(0.57721566490153286060651209008240243104259335L), euler, 2);
485 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(2.0L)), root_two, 2);
486 CHECK_ULP_CLOSE(static_cast<long double>(log(2.0L)), ln_two, 2);
487 CHECK_ULP_CLOSE(static_cast<long double>(log(log(2.0L))), ln_ln_two, 2);
488 CHECK_ULP_CLOSE(static_cast<long double>(1)/3, third, 2);
489 CHECK_ULP_CLOSE(static_cast<long double>(2)/3, twothirds, 2);
490 CHECK_ULP_CLOSE(static_cast<long double>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three, 2);
491 CHECK_ULP_CLOSE(static_cast<long double>(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, 2);
7c673cae 492#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
20effc67
TL		 493 CHECK_ULP_CLOSE(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L)), pi_pow_e, 2);
494 CHECK_ULP_CLOSE(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L)), cbrt_pi, 2);
495 CHECK_ULP_CLOSE(static_cast<long double>(exp(-0.5L)), exp_minus_half, 2);
496 CHECK_ULP_CLOSE(static_cast<long double>(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L)), e_pow_pi, 2);
7c673cae
FG		 497
498
499#else // Only double, so no suffix L.
20effc67
TL		 500 CHECK_ULP_CLOSE(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, 2);
501 CHECK_ULP_CLOSE(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, 2);
502 CHECK_ULP_CLOSE(static_cast<long double>(exp(-0.5)), exp_minus_half, 2);
7c673cae
FG		 503#endif
504 // Rational fractions.
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TL		 505 CHECK_ULP_CLOSE(static_cast<long double>(0.333333333333333333333333333333333333333L), third, 2);
506 CHECK_ULP_CLOSE(static_cast<long double>(0.666666666666666666666666666666666666667L), two_thirds, 2);
507 CHECK_ULP_CLOSE(static_cast<long double>(0.75L), three_quarters, 2);
7c673cae 508 // Two and related.
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TL		 509 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(2.L)), root_two, 2);
510 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(3.L)), root_three, 2);
511 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(2.L)/2), half_root_two, 2);
512 CHECK_ULP_CLOSE(static_cast<long double>(log(2.L)), ln_two, 2);
513 CHECK_ULP_CLOSE(static_cast<long double>(log(log(2.0L))), ln_ln_two, 2);
514 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(log(4.0L))), root_ln_four, 2);
515 CHECK_ULP_CLOSE(static_cast<long double>(1/sqrt(2.0L)), one_div_root_two, 2);
7c673cae
FG		 516
517 // pi.
20effc67
TL		 518 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L), pi, 2);
519 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/2), half_pi, 2);
520 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/4), quarter_pi, 2);
521 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/3), third_pi, 2);
522 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/6), sixth_pi, 2);
523 CHECK_ULP_CLOSE(static_cast<long double>(2 * 3.14159265358979323846264338327950288419716939937510L), two_pi, 2);
524 CHECK_ULP_CLOSE(static_cast<long double>(3 * 3.14159265358979323846264338327950288419716939937510L / 4), three_quarters_pi, 2);
525 CHECK_ULP_CLOSE(static_cast<long double>(4 * 3.14159265358979323846264338327950288419716939937510L / 3), four_thirds_pi, 2);
526 CHECK_ULP_CLOSE(static_cast<long double>(1 / (3.14159265358979323846264338327950288419716939937510L)), one_div_pi, 2);
527 CHECK_ULP_CLOSE(static_cast<long double>(2 / (3.14159265358979323846264338327950288419716939937510L)), two_div_pi, 2);
528 CHECK_ULP_CLOSE(static_cast<long double>(1 / (2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_two_pi, 2);
529 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, 2);
530 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L / 2)), root_half_pi, 2);
531 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), root_two_pi, 2);
532 CHECK_ULP_CLOSE(static_cast<long double>(1 / sqrt(3.14159265358979323846264338327950288419716939937510L)), one_div_root_pi, 2);
533 CHECK_ULP_CLOSE(static_cast<long double>(2 / sqrt(3.14159265358979323846264338327950288419716939937510L)), two_div_root_pi, 2);
534 CHECK_ULP_CLOSE(static_cast<long double>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_root_two_pi, 2);
535 CHECK_ULP_CLOSE(static_cast<long double>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L)), root_one_div_pi, 2);
536 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L - 3.L), pi_minus_three, 4 * 4 ); // 4 * 2 because of cancellation loss.
537 CHECK_ULP_CLOSE(static_cast<long double>(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, 4 );
7c673cae 538 //
20effc67
TL		 539 CHECK_ULP_CLOSE(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L)), pi_pow_e, 2); // See above.
540 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L), pi_sqr, 2); // See above.
541 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L/6), pi_sqr_div_six, 2); // See above.
542 CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L), pi_cubed, 2); // See above.
7c673cae 543
20effc67
TL		 544 // CHECK_ULP_CLOSE(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L), cbrt_pi, 2); // See above.
545 CHECK_ULP_CLOSE(cbrt_pi * cbrt_pi * cbrt_pi, pi, 2);
546 CHECK_ULP_CLOSE((static_cast<long double>(1)/cbrt_pi), one_div_cbrt_pi, 2);
7c673cae 547
20effc67
TL		 548 CHECK_ULP_CLOSE(static_cast<long double>(6.366197723675813430755350534900574481378385829618257E-1L), two_div_pi, 4 * 3); // 2/pi
549 CHECK_ULP_CLOSE(static_cast<long double>(7.97884560802865355879892119868763736951717262329869E-1L), root_two_div_pi, 4 * 3); // sqrt(2/pi)
7c673cae
FG		 550
551 // Euler
20effc67 552 CHECK_ULP_CLOSE(static_cast<long double>(2.71828182845904523536028747135266249775724709369995L), e, 2);
7c673cae 553
20effc67
TL		 554 //CHECK_ULP_CLOSE(static_cast<long double>(exp(-0.5L)), exp_minus_half, 2); // See above.
555 CHECK_ULP_CLOSE(pow(e, pi), e_pow_pi, 2); // See also above.
556 CHECK_ULP_CLOSE(sqrt(e), root_e, 2);
557 CHECK_ULP_CLOSE(log10(e), log10_e, 2);
558 CHECK_ULP_CLOSE(static_cast<long double>(1)/log10(e), one_div_log10_e, 2);
7c673cae 559
f67539c2 560 // Trigonometric
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TL		 561 CHECK_ULP_CLOSE(pi/180, degree, 2);
562 CHECK_ULP_CLOSE(180 / pi, radian, 2);
563 CHECK_ULP_CLOSE(sin(1.L), sin_one, 2);
564 CHECK_ULP_CLOSE(cos(1.L), cos_one, 2);
565 CHECK_ULP_CLOSE(sinh(1.L), sinh_one, 2);
566 CHECK_ULP_CLOSE(cosh(1.L), cosh_one, 2);
7c673cae
FG		 567
568 // Phi
20effc67
TL		 569 CHECK_ULP_CLOSE((1.L + sqrt(5.L)) /2, phi, 2);
570 CHECK_ULP_CLOSE(log((1.L + sqrt(5.L)) /2), ln_phi, 2);
571 CHECK_ULP_CLOSE(1.L / log((1.L + sqrt(5.L)) /2), one_div_ln_phi, 2);
7c673cae
FG		 572
573 //Euler's Gamma
20effc67
TL		 574 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992L, euler, 2); // (sequence A001620 in OEIS).
575 CHECK_ULP_CLOSE(1.L/ 0.57721566490153286060651209008240243104215933593992L, one_div_euler, 2); // (from sequence A001620 in OEIS).
576 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992L * 0.57721566490153286060651209008240243104215933593992L, euler_sqr, 2); // (from sequence A001620 in OEIS).
7c673cae
FG		 577
578 // Misc
20effc67
TL		 579 CHECK_ULP_CLOSE(1.644934066848226436472415166646025189218949901206L, zeta_two, 2); // A013661 as a constant (usually base 10) in OEIS.
580 CHECK_ULP_CLOSE(1.20205690315959428539973816151144999076498629234049888179227L, zeta_three, 2); // (sequence A002117 in OEIS)
581 CHECK_ULP_CLOSE(.91596559417721901505460351493238411077414937428167213L, catalan, 2); // A006752 as a constant in OEIS.
582 CHECK_ULP_CLOSE(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness, 2); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
583 CHECK_ULP_CLOSE(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness, 2); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
584 CHECK_ULP_CLOSE(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess, 2);
585 CHECK_ULP_CLOSE(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin, 4 ); // A002210 as a constant https://oeis.org/A002210/constant
586 CHECK_ULP_CLOSE(1.2824271291006226368753425688697917277676889273250011L, glaisher, 4 ); // https://oeis.org/A074962/constant
7c673cae
FG		 587
588} // template <class RealType>void test_spots(RealType)
589
590template <class Policy>
591void test_real_concept_policy(const Policy&)
592{
593 // Basic sanity checks for constants using real_concept.
594 // Parameter Policy is used to control precision.
595
596 using boost::math::concepts::real_concept;
7c673cae
FG		 597 //typedef typename boost::math::policies::precision<boost::math::concepts::real_concept, boost::math::policies::policy<> >::type t1;
598 // A precision of zero means we don't know what the precision of this type is until runtime.
599 //std::cout << "Precision for type " << typeid(boost::math::concepts::real_concept).name() << " is " << t1::value << "." << std::endl;
600
601 using namespace boost::math::constants;
602 BOOST_MATH_STD_USING
603
20effc67
TL		 604 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), 2);
605 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), 2);
606 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L/2), (root_half_pi<real_concept, Policy>)(), 2);
607 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), (root_two_pi<real_concept, Policy>)(), 2);
608 CHECK_ULP_CLOSE(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), 2);
609 CHECK_ULP_CLOSE(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), 2);
610 CHECK_ULP_CLOSE(0.5, (half<real_concept, Policy>)(), 2);
611 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104259335L, (euler<real_concept, Policy>)(), 2);
612 CHECK_ULP_CLOSE(sqrt(2.0L), (root_two<real_concept, Policy>)(), 2);
613 CHECK_ULP_CLOSE(log(2.0L), (ln_two<real_concept, Policy>)(), 2);
614 CHECK_ULP_CLOSE(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), 2);
615 CHECK_ULP_CLOSE(static_cast<long double>(1)/3, (third<real_concept, Policy>)(), 2);
616 CHECK_ULP_CLOSE(static_cast<long double>(2)/3, (twothirds<real_concept, Policy>)(), 2);
617 CHECK_ULP_CLOSE(0.14159265358979323846264338327950288419716939937510L, (pi_minus_three<real_concept, Policy>)(), 2);
618 CHECK_ULP_CLOSE(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi<real_concept, Policy>)(), 2);
7c673cae 619#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
20effc67
TL		 620 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e<real_concept, Policy>)(), 2);
621 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), (cbrt_pi<real_concept, Policy>)(), 2);
622 CHECK_ULP_CLOSE(exp(-0.5L), (exp_minus_half<real_concept, Policy>)(), 2);
623 CHECK_ULP_CLOSE(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), (e_pow_pi<real_concept, Policy>)(), 2);
7c673cae
FG		 624
625
626#else // Only double, so no suffix L.
20effc67
TL		 627 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), (pi_pow_e<real_concept, Policy>)(), 2);
628 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), (cbrt_pi<real_concept, Policy>)(), 2);
629 CHECK_ULP_CLOSE(exp(-0.5), (exp_minus_half<real_concept, Policy>)(), 2);
7c673cae
FG		 630#endif
631 // Rational fractions.
20effc67
TL		 632 CHECK_ULP_CLOSE(0.333333333333333333333333333333333333333L, (third<real_concept, Policy>)(), 2);
633 CHECK_ULP_CLOSE(0.666666666666666666666666666666666666667L, (two_thirds<real_concept, Policy>)(), 2);
634 CHECK_ULP_CLOSE(0.75L, (three_quarters<real_concept, Policy>)(), 2);
7c673cae 635 // Two and related.
20effc67
TL		 636 CHECK_ULP_CLOSE(sqrt(2.L), (root_two<real_concept, Policy>)(), 2);
637 CHECK_ULP_CLOSE(sqrt(3.L), (root_three<real_concept, Policy>)(), 2);
638 CHECK_ULP_CLOSE(sqrt(2.L)/2, (half_root_two<real_concept, Policy>)(), 2);
639 CHECK_ULP_CLOSE(log(2.L), (ln_two<real_concept, Policy>)(), 2);
640 CHECK_ULP_CLOSE(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), 2);
641 CHECK_ULP_CLOSE(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), 2);
642 CHECK_ULP_CLOSE(1/sqrt(2.0L), (one_div_root_two<real_concept, Policy>)(), 2);
7c673cae
FG		 643
644 // pi.
20effc67
TL		 645 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), 2);
646 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/2, (half_pi<real_concept, Policy>)(), 2);
647 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/4, (quarter_pi<real_concept, Policy>)(), 2);
648 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/3, (third_pi<real_concept, Policy>)(), 2);
649 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L/6, (sixth_pi<real_concept, Policy>)(), 2);
650 CHECK_ULP_CLOSE(2 * 3.14159265358979323846264338327950288419716939937510L, (two_pi<real_concept, Policy>)(), 2);
651 CHECK_ULP_CLOSE(3 * 3.14159265358979323846264338327950288419716939937510L / 4, (three_quarters_pi<real_concept, Policy>)(), 2);
652 CHECK_ULP_CLOSE(4 * 3.14159265358979323846264338327950288419716939937510L / 3, (four_thirds_pi<real_concept, Policy>)(), 2);
653 CHECK_ULP_CLOSE(1 / (3.14159265358979323846264338327950288419716939937510L), (one_div_pi<real_concept, Policy>)(), 2);
654 CHECK_ULP_CLOSE(2 / (3.14159265358979323846264338327950288419716939937510L), (two_div_pi<real_concept, Policy>)(), 2);
655 CHECK_ULP_CLOSE(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_two_pi<real_concept, Policy>)(), 2);
656 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), 2);
657 CHECK_ULP_CLOSE(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), (root_half_pi<real_concept, Policy>)(), 2);
658 CHECK_ULP_CLOSE(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (root_two_pi<real_concept, Policy>)(), 2);
659 CHECK_ULP_CLOSE(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), (one_div_root_pi<real_concept, Policy>)(), 2);
660 CHECK_ULP_CLOSE(2 / sqrt(3.14159265358979323846264338327950288419716939937510L), (two_div_root_pi<real_concept, Policy>)(), 2);
661 CHECK_ULP_CLOSE(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_root_two_pi<real_concept, Policy>)(), 2);
662 CHECK_ULP_CLOSE(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), (root_one_div_pi<real_concept, Policy>)(), 2);
663 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L - 3.L, (pi_minus_three<real_concept, Policy>)(), 4 * 4 ); // 4 * 2 because of cancellation loss.
664 CHECK_ULP_CLOSE(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi<real_concept, Policy>)(), 4 );
7c673cae 665 //
20effc67
TL		 666 CHECK_ULP_CLOSE(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e<real_concept, Policy>)(), 2); // See above.
667 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (pi_sqr<real_concept, Policy>)(), 2); // See above.
668 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L/6, (pi_sqr_div_six<real_concept, Policy>)(), 2); // See above.
669 CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (pi_cubed<real_concept, Policy>)(), 2); // See above.
7c673cae 670
20effc67
TL		 671 // CHECK_ULP_CLOSE(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (cbrt_pi<real_concept, Policy>)(), 2); // See above.
672 CHECK_ULP_CLOSE((cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)(), (pi<real_concept, Policy>)(), 2);
673 CHECK_ULP_CLOSE((1)/(cbrt_pi<real_concept, Policy>)(), (one_div_cbrt_pi<real_concept, Policy>)(), 2);
7c673cae
FG		 674
675 // Euler
20effc67 676 CHECK_ULP_CLOSE(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), 2);
7c673cae 677
20effc67
TL		 678 //CHECK_ULP_CLOSE(exp(-0.5L), (exp_minus_half<real_concept, Policy>)(), 2); // See above.
679 CHECK_ULP_CLOSE(pow(e<real_concept, Policy>(), (pi<real_concept, Policy>)()), (e_pow_pi<real_concept, Policy>)(), 2); // See also above.
680 CHECK_ULP_CLOSE(sqrt(e<real_concept, Policy>()), (root_e<real_concept, Policy>)(), 2);
681 CHECK_ULP_CLOSE(log10(e<real_concept, Policy>()), (log10_e<real_concept, Policy>)(), 2);
682 CHECK_ULP_CLOSE(1/log10(e<real_concept, Policy>()), (one_div_log10_e<real_concept, Policy>)(), 2);
683 CHECK_ULP_CLOSE((1/ln_two<real_concept, Policy>()), (log2_e<real_concept, Policy>)(), 2);
7c673cae 684
f67539c2 685 // Trigonometric
20effc67
TL		 686 CHECK_ULP_CLOSE((pi<real_concept, Policy>)()/180, (degree<real_concept, Policy>)(), 2);
687 CHECK_ULP_CLOSE(180 / (pi<real_concept, Policy>)(), (radian<real_concept, Policy>)(), 2);
688 CHECK_ULP_CLOSE(sin(1.L), (sin_one<real_concept, Policy>)(), 2);
689 CHECK_ULP_CLOSE(cos(1.L), (cos_one<real_concept, Policy>)(), 2);
690 CHECK_ULP_CLOSE(sinh(1.L), (sinh_one<real_concept, Policy>)(), 2);
691 CHECK_ULP_CLOSE(cosh(1.L), (cosh_one<real_concept, Policy>)(), 2);
7c673cae
FG		 692
693 // Phi
20effc67
TL		 694 CHECK_ULP_CLOSE((1.L + sqrt(5.L)) /2, (phi<real_concept, Policy>)(), 2);
695 CHECK_ULP_CLOSE(log((1.L + sqrt(5.L)) /2), (ln_phi<real_concept, Policy>)(), 2);
696 CHECK_ULP_CLOSE(1.L / log((1.L + sqrt(5.L)) /2), (one_div_ln_phi<real_concept, Policy>)(), 2);
7c673cae
FG		 697
698 //Euler's Gamma
20effc67
TL		 699 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992L, (euler<real_concept, Policy>)(), 2); // (sequence A001620 in OEIS).
700 CHECK_ULP_CLOSE(1.L/ 0.57721566490153286060651209008240243104215933593992L, (one_div_euler<real_concept, Policy>)(), 2); // (from sequence A001620 in OEIS).
701 CHECK_ULP_CLOSE(0.57721566490153286060651209008240243104215933593992L * 0.57721566490153286060651209008240243104215933593992L, (euler_sqr<real_concept, Policy>)(), 2); // (from sequence A001620 in OEIS).
7c673cae
FG		 702
703 // Misc
20effc67
TL		 704 CHECK_ULP_CLOSE(1.644934066848226436472415166646025189218949901206L, (zeta_two<real_concept, Policy>)(), 2); // A013661 as a constant (usually base 10) in OEIS.
705 CHECK_ULP_CLOSE(1.20205690315959428539973816151144999076498629234049888179227L, (zeta_three<real_concept, Policy>)(), 2); // (sequence A002117 in OEIS)
706 CHECK_ULP_CLOSE(.91596559417721901505460351493238411077414937428167213L, (catalan<real_concept, Policy>)(), 2); // A006752 as a constant in OEIS.
707 CHECK_ULP_CLOSE(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, (extreme_value_skewness<real_concept, Policy>)(), 2); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
708 CHECK_ULP_CLOSE(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, (rayleigh_skewness<real_concept, Policy>)(), 2); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
709 CHECK_ULP_CLOSE(2.450893006876380628486604106197544154e-01L, (rayleigh_kurtosis_excess<real_concept, Policy>)(), 2);
710 CHECK_ULP_CLOSE(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, (khinchin<real_concept, Policy>)(), 4 ); // A002210 as a constant https://oeis.org/A002210/constant
711 CHECK_ULP_CLOSE(1.2824271291006226368753425688697917277676889273250011L, (glaisher<real_concept, Policy>)(), 4 ); // https://oeis.org/A074962/constant
7c673cae
FG		 712
713 //
714 // Last of all come the test cases that behave differently if we're calculating the constants on the fly:
715 //
716 if(boost::math::tools::digits<real_concept>() > boost::math::constants::max_string_digits)
717 {
20effc67
TL		 718 // This suffers from cancellation error, so increased 4:
719 CHECK_ULP_CLOSE((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), 4 * 3);
720 CHECK_ULP_CLOSE((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), 4 * 3);
7c673cae
FG		 721 }
722 else
723 {
20effc67
TL		 724 CHECK_ULP_CLOSE((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), 2);
725 CHECK_ULP_CLOSE((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), 2);
7c673cae
FG		 726 }
727
728} // template <class boost::math::concepts::real_concept>void test_spots(boost::math::concepts::real_concept)
729
20effc67 730#ifdef BOOST_MATH_HAS_FLOAT128
7c673cae
FG		 731void test_float128()
732{
7c673cae
FG		 733 __float128 p = boost::math::constants::pi<__float128>();
734 __float128 r = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651Q;
20effc67 735 CHECK_ULP_CLOSE(boost::multiprecision::float128(p), boost::multiprecision::float128(r), 2);
7c673cae
FG		 736}
737#endif
738
739void test_constexpr()
740{
741#ifndef BOOST_NO_CXX11_CONSTEXPR
742 constexpr float f1 = boost::math::constants::pi<float>();
743 constexpr double f2 = boost::math::constants::pi<double>();
744 constexpr long double f3 = boost::math::constants::pi<long double>();
92f5a8d4
TL		 745 constexpr float fval2 = boost::math::float_constants::pi;
746 constexpr double dval2 = boost::math::double_constants::pi;
747 constexpr long double ldval2 = boost::math::long_double_constants::pi;
7c673cae
FG		 748 (void)f1;
749 (void)f2;
750 (void)f3;
92f5a8d4
TL		 751 (void) fval2;
752 (void) dval2;
753 (void) ldval2;
7c673cae
FG		 754#ifdef BOOST_MATH_USE_FLOAT128
755 constexpr __float128 f4 = boost::math::constants::pi<__float128>();
756 (void)f4;
757#endif
758#endif
759}
760
20effc67
TL		 761#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900)
762void test_feigenbaum()
7c673cae 763{
20effc67
TL		 764 // This constant takes weeks to calculate.
765 // So if the requested precision > precomputed precision, we need an error message.
766 using boost::multiprecision::cpp_bin_float;
767 using boost::multiprecision::number;
768 auto f64 = boost::math::constants::first_feigenbaum<double>();
769 using Real100 = number<cpp_bin_float<300>>;
770 auto f = boost::math::constants::first_feigenbaum<Real100>();
771 CHECK_ULP_CLOSE(static_cast<double>(f), f64, 0);
772 Real100 g{"4.6692016091029906718532038204662016172581855774757686327456513430041343302113147371386897440239480138171659848551898151344086271420279325223124429888908908599449354632367134115324817142199474556443658237932020095610583305754586176522220703854106467494942849814533917262005687556659523398756038256372256480040951071283890611844702775854285419801113440175002428585382498335715522052236087250291678860362674527213399057131606875345083433934446103706309452019115876972432273589838903794946257251289097948986768334611626889116563123474460575179539122045562472807095202198199094558581946136877445617396074115614074243754435499204869180982648652368438702799649017397793425134723808737136211601860128186102056381818354097598477964173900328936171432159878240789776614391395764037760537119096932066998361984288981837003229412030210655743295550388845849737034727532121925706958414074661841981961006129640161487712944415901405467941800198133253378592493365883070459999938375411726563553016862529032210862320550634510679399023341675"};
773 CHECK_ULP_CLOSE(f, g, 0);
774}
775
776template<typename Real>
777void test_plastic()
778{
779 Real P = boost::math::constants::plastic<Real>();
780 Real residual = P*P*P - P -1;
781 using std::abs;
782 CHECK_LE(abs(residual), 4*std::numeric_limits<Real>::epsilon());
783}
784
785template<typename Real>
786void test_gauss()
787{
788 using boost::math::tools::agm;
789 using std::sqrt;
790 Real G_computed = boost::math::constants::gauss<Real>();
791 Real G_expected = Real(1)/agm(sqrt(Real(2)), Real(1));
792 CHECK_ULP_CLOSE(G_expected, G_computed, 1);
793 CHECK_LE(G_computed, Real(0.8347));
794 CHECK_LE(Real(0.8346), G_computed);
795}
796
797template<typename Real>
798void test_dottie()
799{
800 using boost::math::constants::dottie;
801 using std::cos;
802 CHECK_ULP_CLOSE(dottie<Real>(), cos(dottie<Real>()), 1);
803}
804
805template<typename Real>
806void test_reciprocal_fibonacci()
807{
808 using boost::math::constants::reciprocal_fibonacci;
809 CHECK_LE(reciprocal_fibonacci<Real>(), Real(3.36));
810 CHECK_LE(Real(3.35), reciprocal_fibonacci<Real>());
811}
812
813template<typename Real>
814void test_laplace_limit()
815{
816 using std::exp;
817 using std::sqrt;
818 using boost::math::constants::laplace_limit;
819 Real ll = laplace_limit<Real>();
820 Real tmp = sqrt(1+ll*ll);
821 CHECK_ULP_CLOSE(ll*exp(tmp), 1 + tmp, 1);
822}
823
824#endif
7c673cae 825
20effc67
TL		 826int main()
827{
828 // Basic sanity-check spot values.
7c673cae
FG		 829 test_float_spots(); // Test float_constants, like boost::math::float_constants::pi;
830 test_double_spots(); // Test double_constants.
7c673cae 831 test_long_double_spots(); // Test long_double_constants.
20effc67 832#ifdef BOOST_MATH_HAS_FLOAT128
7c673cae
FG		 833 test_float128();
834#endif
835 test_constexpr();
836
7c673cae
FG		 837 // (Parameter value, arbitrarily zero, only communicates the floating-point type).
838 test_spots(0.0F); // Test float.
839 test_spots(0.0); // Test double.
7c673cae 840 test_spots(0.0L); // Test long double.
7c673cae 841
20effc67
TL		 842#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900)
843 test_feigenbaum();
844 test_plastic<float>();
845 test_plastic<double>();
846 test_plastic<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<400>>>();
847 test_gauss<float>();
848 test_gauss<double>();
849 test_gauss<long double>();
850 test_gauss<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<400>>>();
851 test_dottie<float>();
852 test_dottie<double>();
853 test_dottie<long double>();
854 test_dottie<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<400>>>();
855 test_laplace_limit<float>();
856 test_laplace_limit<double>();
857 test_laplace_limit<long double>();
858 test_laplace_limit<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<400>>>();
859#endif
860 return boost::math::test::report_errors();
861}
Ceph