]>
git.proxmox.com Git - ceph.git/blob - ceph/src/boost/libs/math/test/test_inv_hyp.cpp
1 // (C) Copyright John Maddock 2006.
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
8 #include <boost/math/concepts/real_concept.hpp>
9 #include <boost/math/special_functions/acosh.hpp>
10 #include <boost/math/special_functions/asinh.hpp>
11 #include <boost/math/special_functions/atanh.hpp>
12 #define BOOST_TEST_MAIN
13 #include <boost/test/unit_test.hpp>
14 #include <boost/test/tools/floating_point_comparison.hpp>
15 #include <boost/math/tools/stats.hpp>
16 #include <boost/math/tools/test.hpp>
17 #include <boost/math/constants/constants.hpp>
18 #include <boost/type_traits/is_floating_point.hpp>
19 #include <boost/array.hpp>
20 #include "functor.hpp"
22 #include "handle_test_result.hpp"
23 #include "table_type.hpp"
31 // This file tests the inverse hyperbolic functions. There are two sets of tests:
32 // 1) Sanity checks: comparison to test values created with the
33 // online calculator at functions.wolfram.com
34 // 2) Accuracy tests use values generated with NTL::RR at
35 // 1000-bit precision and our generic versions of these functions.
37 // Note that when this file is first run on a new platform many of
38 // these tests will fail: the default accuracy is 1 epsilon which
39 // is too tight for most platforms. In this situation you will
40 // need to cast a human eye over the error rates reported and make
41 // a judgement as to whether they are acceptable. Either way please
42 // report the results to the Boost mailing list. Acceptable rates of
43 // error are marked up below as a series of regular expressions that
44 // identify the compiler/stdlib/platform/data-type/test-data/test-function
45 // along with the maximum expected peek and RMS mean errors for that
49 void expected_results()
52 // Define the max and mean errors expected for
53 // various compilers and platforms.
55 const char* largest_type
;
56 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
57 if(boost::math::policies::digits
<double, boost::math::policies::policy
<> >() == boost::math::policies::digits
<long double, boost::math::policies::policy
<> >())
59 largest_type
= "(long\\s+)?double|real_concept";
63 largest_type
= "long double|real_concept";
66 largest_type
= "(long\\s+)?double";
73 largest_type
, // test type(s)
74 "atanh.*", // test data group
75 ".*", 6, 1); // test function
80 "real_concept", // test type(s)
81 ".*", // test data group
82 ".*", 4, 2); // test function
87 largest_type
, // test type(s)
88 ".*", // test data group
89 ".*", 4, 1); // test function
91 std::cout
<< "Tests run with " << BOOST_COMPILER
<< ", "
92 << BOOST_STDLIB
<< ", " << BOOST_PLATFORM
<< std::endl
;
95 template <class Real
, class T
>
96 void do_test_asinh(const T
& data
, const char* type_name
, const char* test_name
)
99 // test asinh(T) against data:
102 typedef Real value_type
;
104 std::cout
<< test_name
<< " with type " << type_name
<< std::endl
;
106 typedef value_type (*pg
)(value_type
);
107 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
108 pg funcp
= boost::math::asinh
<value_type
>;
110 pg funcp
= boost::math::asinh
;
113 boost::math::tools::test_result
<value_type
> result
;
115 // test asinh against data:
117 result
= boost::math::tools::test_hetero
<Real
>(
119 bind_func
<Real
>(funcp
, 0),
120 extract_result
<Real
>(1));
121 handle_test_result(result
, data
[result
.worst()], result
.worst(), type_name
, "boost::math::asinh", test_name
);
122 std::cout
<< std::endl
;
125 template <class Real
, class T
>
126 void do_test_acosh(const T
& data
, const char* type_name
, const char* test_name
)
129 // test acosh(T) against data:
132 typedef Real value_type
;
134 std::cout
<< test_name
<< " with type " << type_name
<< std::endl
;
136 typedef value_type (*pg
)(value_type
);
137 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
138 pg funcp
= boost::math::acosh
<value_type
>;
140 pg funcp
= boost::math::acosh
;
143 boost::math::tools::test_result
<value_type
> result
;
145 // test acosh against data:
147 result
= boost::math::tools::test_hetero
<Real
>(
149 bind_func
<Real
>(funcp
, 0),
150 extract_result
<Real
>(1));
151 handle_test_result(result
, data
[result
.worst()], result
.worst(), type_name
, "boost::math::acosh", test_name
);
152 std::cout
<< std::endl
;
155 template <class Real
, class T
>
156 void do_test_atanh(const T
& data
, const char* type_name
, const char* test_name
)
159 // test atanh(T) against data:
162 typedef Real value_type
;
164 std::cout
<< test_name
<< " with type " << type_name
<< std::endl
;
166 typedef value_type (*pg
)(value_type
);
167 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
168 pg funcp
= boost::math::atanh
<value_type
>;
170 pg funcp
= boost::math::atanh
;
173 boost::math::tools::test_result
<value_type
> result
;
175 // test atanh against data:
177 result
= boost::math::tools::test_hetero
<Real
>(
179 bind_func
<Real
>(funcp
, 0),
180 extract_result
<Real
>(1));
181 handle_test_result(result
, data
[result
.worst()], result
.worst(), type_name
, "boost::math::atanh", test_name
);
182 std::cout
<< std::endl
;
186 void test_inv_hyperbolics(T
, const char* name
)
188 // function values calculated on http://functions.wolfram.com/
189 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
190 static const std::array
<std::array
<typename table_type
<T
>::type
, 2>, 16> data1
= {{
191 {{ SC_(1.0), SC_(0.0) }},
192 {{ SC_(18014398509481985.0)/SC_(18014398509481984.0), (SC_(18014398509481985.0)/SC_(18014398509481984.0) == 1 ? 0 : SC_(1.05367121277235078980001569764860129317209081216314559121044e-8)) }},
193 {{ SC_(140737488355329.0)/SC_(140737488355328.0), (SC_(140737488355329.0)/SC_(140737488355328.0) == 1 ? 0 : SC_(1.19209289550781179413921062141751258430803882725295121500042e-7)) }},
194 {{ SC_(1073741825.0)/SC_(1073741824.0), (SC_(1073741825.0)/SC_(1073741824.0) == 1 ? 0 : SC_(0.0000431583728718059579720327225039166883356735150941350459126580)) }},
195 {{ SC_(32769.0)/32768, (SC_(32769.0)/32768 == 1 ? 0 : SC_(0.00781248013192149783598227588546120945538554063153555218442060)) }},
196 {{ SC_(1025.0)/1024, SC_(0.0441905780831100944299637635287994671116916497867872322058681) }},
197 {{ SC_(513.0)/512, SC_(0.0624898319417098609694799246056217361555882834152944713872228) }},
198 {{ SC_(129.0)/128, SC_(0.124918762511080617606418193883982155828039646714882611321039) }},
199 {{ SC_(33.0)/32, SC_(0.249353493842885487851439075410018843027071727873456825299808) }},
200 {{ SC_(5.0)/4, SC_(0.693147180559945309417232121458176568075500134360255254120680) }},
201 {{ SC_(3.0)/2, SC_(0.962423650119206894995517826848736846270368668771321039322036) }},
202 {{ SC_(1.75), SC_(1.15881036042994681173087299087873019318368454205435905403767) }},
203 {{ SC_(2.0), SC_(1.31695789692481670862504634730796844402698197146751647976847) }},
204 {{ SC_(20.0), SC_(3.68825386736129666761816757203235188783315569765587425882926) }},
205 {{ SC_(200.0), SC_(5.99145829704938742305501213819154333467246121857058747847273) }},
206 {{ SC_(2000.0), SC_(8.29404957760202181151262480475259799729149903827743516943515) }},
211 // The actual test data is rather verbose, so it's in a separate file
213 #include "asinh_data.ipp"
214 do_test_asinh
<T
>(asinh_data
, name
, "asinh");
215 #include "acosh_data.ipp"
216 do_test_acosh
<T
>(data1
, name
, "acosh: Mathworld Data");
217 do_test_acosh
<T
>(acosh_data
, name
, "acosh");
218 #include "atanh_data.ipp"
219 do_test_atanh
<T
>(atanh_data
, name
, "atanh");
222 extern "C" double zetac(double);
225 void test_spots(T
, const char* t
)
227 std::cout
<< "Testing basic sanity checks for type " << t
<< std::endl
;
229 // Basic sanity checks, tolerance is either 5 or 10 epsilon
230 // expressed as a percentage:
232 T tolerance
= boost::math::tools::epsilon
<T
>() * 100 *
233 (boost::is_floating_point
<T
>::value
? 5 : 10);
234 BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T
>(262145)/262144L), static_cast<T
>(0.00276213498595136093375633956331651432309750291610866833462649L), tolerance
);
235 BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T
>(2)), static_cast<T
>(1.31695789692481670862504634730796844402698197146751647976847L), tolerance
);
236 BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T
>(40)), static_cast<T
>(4.38187034804006698696313269586603717076961771721038534547948L), tolerance
);
237 BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T
>(262145L)), static_cast<T
>(13.1698002453253126137651962522659827810753786944786303017757L), tolerance
);
239 BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T
>(0)), static_cast<T
>(0), tolerance
);
240 BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T
>(1)/262145L), static_cast<T
>(3.81468271375603081996185039385472561751449912305225962381803e-6L), tolerance
);
241 BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T
>(0.25)), static_cast<T
>(0.247466461547263452944781549788359289253766903098567696469117L), tolerance
);
242 BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T
>(1)), static_cast<T
>(0.881373587019543025232609324979792309028160328261635410753296L), tolerance
);
243 BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T
>(10)), static_cast<T
>(2.99822295029796973884659553759645347660705805487730365573446L), tolerance
);
244 BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T
>(262145L)), static_cast<T
>(13.1698002453325885158685460826511173257938039316922010439486L), tolerance
);
246 BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T
>(0)), static_cast<T
>(0), tolerance
);
247 BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T
>(1)/262145L), static_cast<T
>(3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance
);
248 BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T
>(-1)/262145L), static_cast<T
>(-3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance
);
249 BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T
>(0.5)), static_cast<T
>(0.549306144334054845697622618461262852323745278911374725867347L), tolerance
);
250 BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T
>(-0.5)), static_cast<T
>(-0.549306144334054845697622618461262852323745278911374725867347L), tolerance
);
253 BOOST_AUTO_TEST_CASE( test_main
)
256 BOOST_MATH_CONTROL_FP
;
258 test_spots(0.0f
, "float");
259 test_spots(0.0, "double");
260 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
261 test_spots(0.0L, "long double");
262 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
263 test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
266 std::cout
<< "<note>The long double tests have been disabled on this platform "
267 "either because the long double overloads of the usual math functions are "
268 "not available at all, or because they are too inaccurate for these tests "
269 "to pass.</note>" << std::endl
;
272 test_inv_hyperbolics(0.1F
, "float");
273 test_inv_hyperbolics(0.1, "double");
274 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
275 test_inv_hyperbolics(0.1L, "long double");
276 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
277 test_inv_hyperbolics(boost::math::concepts::real_concept(0.1), "real_concept");
280 std::cout
<< "<note>The long double tests have been disabled on this platform "
281 "either because the long double overloads of the usual math functions are "
282 "not available at all, or because they are too inaccurate for these tests "
283 "to pass.</note>" << std::endl
;