projects / ceph.git / blame
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| 7c673cae FG |
1 | // test file for quaternion.hpp |
| 2 | ||
| 3 | // (C) Copyright Hubert Holin 2001. | |
| 4 | // Distributed under the Boost Software License, Version 1.0. (See | |
| 5 | // accompanying file LICENSE_1_0.txt or copy at | |
| 6 | // http://www.boost.org/LICENSE_1_0.txt) | |
| 7 | ||
| 8 | ||
| 9 | #include <iomanip> | |
| 10 | ||
| 11 | ||
| 12 | #include <boost/mpl/list.hpp> | |
| 13 | ||
| b32b8144 | 14 | #define BOOST_TEST_MAIN |
| 7c673cae FG |
15 | #include <boost/test/unit_test.hpp> |
| 16 | #include <boost/test/unit_test_log.hpp> | |
| b32b8144 FG |
17 | #include <boost/multiprecision/cpp_bin_float.hpp> |
| 18 | #include <boost/multiprecision/cpp_dec_float.hpp> | |
| 7c673cae FG |
19 | |
| 20 | #include <boost/math/quaternion.hpp> | |
| 21 | ||
| 1e59de90 | 22 | #ifdef _MSC_VER |
| b32b8144 FG |
23 | #pragma warning(disable:4127) // conditional expression is constant |
| 24 | #endif | |
| 25 | ||
| 7c673cae FG |
26 | template<typename T> |
| 27 | struct string_type_name; | |
| 28 | ||
| 29 | #define DEFINE_TYPE_NAME(Type) \ | |
| 30 | template<> struct string_type_name<Type> \ | |
| 31 | { \ | |
| 32 | static char const * _() \ | |
| 33 | { \ | |
| 34 | return #Type; \ | |
| 35 | } \ | |
| 36 | } | |
| 37 | ||
| 38 | DEFINE_TYPE_NAME(float); | |
| 39 | DEFINE_TYPE_NAME(double); | |
| 40 | DEFINE_TYPE_NAME(long double); | |
| b32b8144 FG |
41 | DEFINE_TYPE_NAME(boost::multiprecision::cpp_bin_float_quad); |
| 42 | DEFINE_TYPE_NAME(boost::multiprecision::number<boost::multiprecision::cpp_dec_float<25> >); | |
| 7c673cae | 43 | |
| b32b8144 FG |
44 | #if BOOST_WORKAROUND(BOOST_MSVC, < 1900) |
| 45 | # define CPP_DEC_FLOAT_TEST | |
| 46 | #else | |
| 47 | # define CPP_DEC_FLOAT_TEST , boost::multiprecision::number<boost::multiprecision::cpp_dec_float<25> > | |
| 48 | #endif | |
| 7c673cae | 49 | #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| b32b8144 | 50 | # define LD_TEST , long double |
| 7c673cae | 51 | #else |
| b32b8144 | 52 | # define LD_TEST |
| 7c673cae FG |
53 | #endif |
| 54 | ||
| b32b8144 FG |
55 | |
| 56 | typedef boost::mpl::list<float,double LD_TEST, boost::multiprecision::cpp_bin_float_quad CPP_DEC_FLOAT_TEST > test_types; | |
| 57 | ||
| 7c673cae FG |
58 | // Apple GCC 4.0 uses the "double double" format for its long double, |
| 59 | // which means that epsilon is VERY small but useless for | |
| 60 | // comparisons. So, don't do those comparisons. | |
| 61 | #if (defined(__APPLE_CC__) && defined(__GNUC__) && __GNUC__ == 4) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS) | |
| 62 | typedef boost::mpl::list<float,double> near_eps_test_types; | |
| 63 | #else | |
| 64 | typedef boost::mpl::list<float,double,long double> near_eps_test_types; | |
| 65 | #endif | |
| 66 | ||
| 67 | ||
| 68 | #if BOOST_WORKAROUND(__GNUC__, < 3) | |
| 69 | // gcc 2.x ignores function scope using declarations, | |
| 70 | // put them in the scope of the enclosing namespace instead: | |
| 71 | using ::std::sqrt; | |
| 72 | using ::std::atan; | |
| 73 | using ::std::log; | |
| 74 | using ::std::exp; | |
| 75 | using ::std::cos; | |
| 76 | using ::std::sin; | |
| 77 | using ::std::tan; | |
| 78 | using ::std::cosh; | |
| 79 | using ::std::sinh; | |
| 80 | using ::std::tanh; | |
| 81 | ||
| 82 | using ::std::numeric_limits; | |
| 83 | ||
| 84 | using ::boost::math::abs; | |
| 85 | #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 86 | ||
| 87 | #ifdef BOOST_NO_STDC_NAMESPACE | |
| 88 | using ::sqrt; | |
| 89 | using ::atan; | |
| 90 | using ::log; | |
| 91 | using ::exp; | |
| 92 | using ::cos; | |
| 93 | using ::sin; | |
| 94 | using ::tan; | |
| 95 | using ::cosh; | |
| 96 | using ::sinh; | |
| 97 | using ::tanh; | |
| 98 | #endif /* BOOST_NO_STDC_NAMESPACE */ | |
| 99 | ||
| 100 | #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP | |
| 101 | using ::boost::math::real; | |
| 102 | using ::boost::math::unreal; | |
| 103 | using ::boost::math::sup; | |
| 104 | using ::boost::math::l1; | |
| 105 | using ::boost::math::abs; | |
| 106 | using ::boost::math::norm; | |
| 107 | using ::boost::math::conj; | |
| 108 | using ::boost::math::exp; | |
| 109 | using ::boost::math::pow; | |
| 110 | using ::boost::math::cos; | |
| 111 | using ::boost::math::sin; | |
| 112 | using ::boost::math::tan; | |
| 113 | using ::boost::math::cosh; | |
| 114 | using ::boost::math::sinh; | |
| 115 | using ::boost::math::tanh; | |
| 116 | using ::boost::math::sinc_pi; | |
| 117 | using ::boost::math::sinhc_pi; | |
| 118 | #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ | |
| 119 | ||
| 120 | // Provide standard floating point abs() overloads if older Microsoft | |
| 121 | // library is used with _MSC_EXTENSIONS defined. This code also works | |
| 122 | // for the Intel compiler using the Microsoft library. | |
| 123 | #if defined(_MSC_EXTENSIONS) && BOOST_WORKAROUND(_MSC_VER, < 1310) | |
| 124 | #if !((__INTEL__ && _WIN32) && BOOST_WORKAROUND(__MWERKS__, >= 0x3201)) | |
| 125 | inline float abs(float v) | |
| 126 | { | |
| 127 | return(fabs(v)); | |
| 128 | } | |
| 129 | ||
| 130 | inline double abs(double v) | |
| 131 | { | |
| 132 | return(fabs(v)); | |
| 133 | } | |
| 134 | ||
| 135 | inline long double abs(long double v) | |
| 136 | { | |
| 137 | return(fabs(v)); | |
| 138 | } | |
| 139 | #endif /* !((__INTEL__ && _WIN32) && BOOST_WORKAROUND(__MWERKS__, >= 0x3201)) */ | |
| 140 | #endif /* defined(_MSC_EXTENSIONS) && BOOST_WORKAROUND(_MSC_VER, < 1310) */ | |
| 141 | ||
| 142 | ||
| 143 | // explicit (if ludicrous) instanciation | |
| 144 | #if !BOOST_WORKAROUND(__GNUC__, < 3) | |
| 145 | template class ::boost::math::quaternion<int>; | |
| 146 | #else | |
| 147 | // gcc doesn't like the absolutely-qualified namespace | |
| 148 | template class boost::math::quaternion<int>; | |
| 149 | #endif /* !BOOST_WORKAROUND(__GNUC__) */ | |
| 150 | ||
| b32b8144 FG |
151 | template <class T> |
| 152 | struct other_type | |
| 153 | { | |
| 154 | typedef double type; | |
| 155 | }; | |
| 156 | template<> | |
| 157 | struct other_type<double> | |
| 158 | { | |
| 159 | typedef float type; | |
| 160 | }; | |
| 161 | template<> | |
| 162 | struct other_type<float> | |
| 163 | { | |
| 164 | typedef short type; | |
| 165 | }; | |
| 7c673cae FG |
166 | |
| 167 | ||
| b32b8144 FG |
168 | template <class T, class U> |
| 169 | void test_compare(const T& a, const U& b, bool eq) | |
| 7c673cae | 170 | { |
| b32b8144 FG |
171 | if (eq) |
| 172 | { | |
| 173 | BOOST_CHECK_EQUAL(a, b); | |
| 174 | BOOST_CHECK((a != b) == false); | |
| 175 | BOOST_CHECK_EQUAL(b, a); | |
| 176 | BOOST_CHECK((b != a) == false); | |
| 177 | } | |
| 178 | else | |
| 179 | { | |
| 180 | BOOST_CHECK_NE(a, b); | |
| 181 | BOOST_CHECK((a == b) == false); | |
| 182 | BOOST_CHECK_NE(b, a); | |
| 183 | BOOST_CHECK((b == a) == false); | |
| 184 | } | |
| 185 | } | |
| 186 | ||
| 187 | template <class T, class R1, class R2, class R3, class R4> | |
| 188 | void check_exact_quaternion_result(const boost::math::quaternion<T>& q, R1 a, R2 b, R3 c, R4 d) | |
| 189 | { | |
| 190 | BOOST_CHECK_EQUAL(q.R_component_1(), a); | |
| 191 | BOOST_CHECK_EQUAL(q.R_component_2(), b); | |
| 192 | BOOST_CHECK_EQUAL(q.R_component_3(), c); | |
| 193 | BOOST_CHECK_EQUAL(q.R_component_4(), d); | |
| 194 | BOOST_CHECK_EQUAL(q.C_component_1(), std::complex<T>(T(a), T(b))); | |
| 195 | BOOST_CHECK_EQUAL(q.C_component_2(), std::complex<T>(T(c), T(d))); | |
| 196 | } | |
| 197 | ||
| 198 | template <class T, class R1, class R2, class R3, class R4> | |
| 199 | void check_approx_quaternion_result(const boost::math::quaternion<T>& q, R1 a, R2 b, R3 c, R4 d, int eps = 10) | |
| 200 | { | |
| f67539c2 | 201 | T tol = std::numeric_limits<T>::epsilon() * eps * 100; // epsilon as a percentage. |
| b32b8144 FG |
202 | using std::abs; |
| 203 | if (abs(a) > tol / 100) | |
| 204 | { | |
| 205 | BOOST_CHECK_CLOSE(q.R_component_1(), static_cast<T>(a), tol); | |
| 206 | } | |
| 207 | else | |
| 208 | { | |
| 209 | BOOST_CHECK_SMALL(q.R_component_1(), tol); | |
| 210 | } | |
| 211 | if (abs(b) > tol) | |
| 212 | { | |
| 213 | BOOST_CHECK_CLOSE(q.R_component_2(), static_cast<T>(b), tol); | |
| 214 | } | |
| 215 | else | |
| 216 | { | |
| 217 | BOOST_CHECK_SMALL(q.R_component_2(), tol); | |
| 218 | } | |
| 219 | if (abs(c) > tol) | |
| 220 | { | |
| 221 | BOOST_CHECK_CLOSE(q.R_component_3(), static_cast<T>(c), tol); | |
| 222 | } | |
| 223 | else | |
| 224 | { | |
| 225 | BOOST_CHECK_SMALL(q.R_component_3(), tol); | |
| 226 | } | |
| 227 | if (abs(d) > tol) | |
| 228 | { | |
| 229 | BOOST_CHECK_CLOSE(q.R_component_4(), static_cast<T>(d), tol); | |
| 230 | } | |
| 231 | else | |
| 232 | { | |
| 233 | BOOST_CHECK_SMALL(q.R_component_4(), tol); | |
| 234 | } | |
| 235 | } | |
| 236 | ||
| 237 | template <class T> | |
| 238 | void check_complex_ops_imp() | |
| 239 | { | |
| 240 | T tol = std::numeric_limits<T>::epsilon() * 200; | |
| 241 | ||
| 242 | ::std::complex<T> c0(5, 6); | |
| 243 | ||
| 244 | // using constructor "H seen as C^2" | |
| 245 | ::boost::math::quaternion<T> q2(c0), q1; | |
| 246 | check_exact_quaternion_result(q2, 5, 6, 0, 0); | |
| 247 | ||
| 248 | // using converting assignment operator | |
| 249 | q2 = 0; | |
| 250 | q2 = c0; | |
| 251 | check_exact_quaternion_result(q2, 5, 6, 0, 0); | |
| 252 | ||
| 253 | // using += (const ::std::complex<T> &) | |
| 254 | q2 = ::boost::math::quaternion<T>(5, 6, 7, 8); | |
| 255 | q2 += c0; | |
| 256 | check_exact_quaternion_result(q2, 10, 12, 7, 8); | |
| 257 | ||
| 258 | // using -= (const ::std::complex<T> &) | |
| 259 | q2 -= c0; | |
| 260 | check_exact_quaternion_result(q2, 5, 6, 7, 8); | |
| 261 | ||
| 262 | // using *= (const ::std::complex<T> &) | |
| 263 | q2 *= c0; | |
| 264 | check_exact_quaternion_result(q2, -11, 60, 83, -2); | |
| 265 | ||
| 266 | q2 /= c0; | |
| 267 | check_approx_quaternion_result(q2, 5, 6, 7, 8); | |
| 268 | ||
| 269 | q2 = ::boost::math::quaternion<T>(4, 5, 7, 8); | |
| 270 | // operator + | |
| 271 | q1 = c0 + q2; | |
| 272 | check_exact_quaternion_result(q1, 9, 11, 7, 8); | |
| 273 | q1 = q2 + c0; | |
| 274 | check_exact_quaternion_result(q1, 9, 11, 7, 8); | |
| 275 | ||
| 276 | // operator - | |
| 277 | q1 = c0 - q2; | |
| 278 | check_exact_quaternion_result(q1, 1, 1, -7, -8); | |
| 279 | q1 = q2 - c0; | |
| 280 | check_exact_quaternion_result(q1, -1, -1, 7, 8); | |
| 281 | ||
| 282 | // using * (const ::std::complex<T> &, const quaternion<T> &) | |
| 283 | q1 = c0 * q2; | |
| 284 | check_exact_quaternion_result(q1, -10, 49, -13, 82); | |
| 285 | ||
| 286 | // using * (const quaternion<T> &, const ::std::complex<T> &) | |
| 287 | q1 = q2 * c0; | |
| 288 | check_exact_quaternion_result(q1, -10, 49, 83, -2); | |
| 289 | ||
| 290 | // using / (const ::std::complex<T> &, const quaternion<T> &) | |
| 291 | q1 = c0 / q2; | |
| 292 | check_approx_quaternion_result(q1, T(25) / 77, -T(1) / 154, T(13) / 154, -T(41) / 77); | |
| 293 | q1 *= q2; | |
| 294 | BOOST_CHECK_CLOSE(q1.R_component_1(), T(5), tol); | |
| 295 | BOOST_CHECK_CLOSE(q1.R_component_2(), T(6), tol); | |
| 296 | BOOST_CHECK_SMALL(q1.R_component_3(), tol); | |
| 297 | BOOST_CHECK_SMALL(q1.R_component_4(), tol); | |
| 298 | ||
| 299 | // using / (const quaternion<T> &, const ::std::complex<T> &) | |
| 300 | q1 = q2 / c0; | |
| 301 | check_approx_quaternion_result(q1, T(50) / 61, T(1)/ 61, -T(13) / 61, T(82) / 61); | |
| 302 | q1 *= c0; | |
| 303 | check_approx_quaternion_result(q1, 4, 5, 7, 8); | |
| 304 | ||
| 305 | q1 = c0; | |
| 306 | test_compare(q1, c0, true); | |
| 307 | q1 += 1; | |
| 308 | test_compare(q1, c0, false); | |
| 309 | } | |
| 310 | ||
| 311 | template <class T> | |
| 312 | void check_complex_ops() {} | |
| 313 | ||
| 314 | template<> | |
| 315 | void check_complex_ops<float>() { check_complex_ops_imp<float>(); } | |
| 316 | template<> | |
| 317 | void check_complex_ops<double>() { check_complex_ops_imp<double>(); } | |
| 318 | template<> | |
| 319 | void check_complex_ops<long double>() { check_complex_ops_imp<long double>(); } | |
| 320 | ||
| 321 | BOOST_AUTO_TEST_CASE_TEMPLATE(arithmetic_test, T, test_types) | |
| 322 | { | |
| 323 | typedef typename other_type<T>::type other_type; | |
| 324 | check_complex_ops<T>(); | |
| 325 | ||
| 326 | T tol = std::numeric_limits<T>::epsilon() * 200; | |
| 327 | ||
| 328 | // using default constructor | |
| 329 | ::boost::math::quaternion<T> q0, q2; | |
| 330 | check_exact_quaternion_result(q0, 0, 0, 0, 0); | |
| 331 | BOOST_CHECK_EQUAL(q0, 0); | |
| 332 | ||
| 333 | ::boost::math::quaternion<T> qa[2]; | |
| 334 | check_exact_quaternion_result(qa[0], 0, 0, 0, 0); | |
| 335 | check_exact_quaternion_result(qa[1], 0, 0, 0, 0); | |
| 336 | BOOST_CHECK_EQUAL(qa[0], 0); | |
| 337 | BOOST_CHECK_EQUAL(qa[1], 0.f); | |
| 338 | ||
| 339 | // using constructor "H seen as R^4" | |
| 340 | ::boost::math::quaternion<T> q1(1, 2, 3, 4); | |
| 341 | check_exact_quaternion_result(q1, 1, 2, 3, 4); | |
| 342 | ||
| 343 | // using untemplated copy constructor | |
| 344 | ::boost::math::quaternion<T> q3(q1); | |
| 345 | check_exact_quaternion_result(q3, 1, 2, 3, 4); | |
| 346 | ||
| 347 | // using templated copy constructor | |
| 348 | ::boost::math::quaternion<other_type> qo(5, 6, 7, 8); | |
| 349 | boost::math::quaternion<T> q4(qo); | |
| 350 | check_exact_quaternion_result(q4, 5, 6, 7, 8); | |
| 351 | ||
| 352 | // using untemplated assignment operator | |
| 353 | q3 = q0; | |
| 354 | check_exact_quaternion_result(q0, 0, 0, 0, 0); | |
| 355 | //BOOST_CHECK_EQUAL(q3, 0.f); | |
| 356 | BOOST_CHECK_EQUAL(q3, q0); | |
| 357 | q3 = q4; | |
| 358 | check_exact_quaternion_result(q3, 5, 6, 7, 8); | |
| 359 | qa[0] = q4; | |
| 360 | check_exact_quaternion_result(qa[0], 5, 6, 7, 8); | |
| 361 | ||
| 362 | // using templated assignment operator | |
| 363 | q4 = qo; | |
| 364 | check_exact_quaternion_result(q4, 5, 6, 7, 8); | |
| 365 | ||
| 366 | other_type f0(7); | |
| 367 | T f1(7); | |
| 368 | ||
| 369 | // using converting assignment operator | |
| 370 | q2 = f0; | |
| 371 | check_exact_quaternion_result(q2, 7, 0, 0, 0); | |
| 372 | q2 = 33.; | |
| 373 | check_exact_quaternion_result(q2, 33, 0, 0, 0); | |
| 374 | ||
| 375 | // using += (const T &) | |
| 376 | q4 += f0; | |
| 377 | check_exact_quaternion_result(q4, 12, 6, 7, 8); | |
| 378 | ||
| 379 | // using += (const quaternion<X> &) | |
| 380 | q4 += q3; | |
| 381 | check_exact_quaternion_result(q4, 17, 12, 14, 16); | |
| 382 | ||
| 383 | // using -= (const T &) | |
| 384 | q4 -= f0; | |
| 385 | check_exact_quaternion_result(q4, 10, 12, 14, 16); | |
| 386 | ||
| 387 | // using -= (const quaternion<X> &) | |
| 388 | q4 -= q3; | |
| 389 | check_exact_quaternion_result(q4, 5, 6, 7, 8); | |
| 390 | ||
| 7c673cae | 391 | // using *= (const T &) |
| b32b8144 FG |
392 | q4 *= f0; |
| 393 | check_exact_quaternion_result(q4, 35, 42, 49, 56); | |
| 394 | // using *= (const quaternion<X> &) | |
| 395 | q4 *= q3; | |
| 396 | check_exact_quaternion_result(q4, -868, 420, 490, 560); | |
| 397 | ||
| 398 | // using /= (const T &) | |
| 399 | q4 /= f0; | |
| 1e59de90 TL |
400 | if(std::numeric_limits<T>::radix == 2) |
| 401 | check_exact_quaternion_result(q4, -T(868) / 7, T(420) / 7, T(490) / 7, T(560) / 7); | |
| 402 | else | |
| 403 | // cpp_dec_float division is still inextact / not rounded: | |
| 404 | check_approx_quaternion_result(q4, -T(868) / 7, T(420) / 7, T(490) / 7, T(560) / 7); | |
| b32b8144 FG |
405 | |
| 406 | q4 = q3; | |
| 407 | q4 /= boost::math::quaternion<T>(9, 4, 6, 2); | |
| 408 | check_approx_quaternion_result(q4, T(127) / 137, T(68) / 137, T(13) / 137, T(54) / 137); | |
| 409 | q4 *= boost::math::quaternion<T>(9, 4, 6, 2); | |
| 410 | check_approx_quaternion_result(q4, 5, 6, 7, 8); | |
| 411 | ||
| 412 | q4 = boost::math::quaternion<T>(34, 56, 20, 2); | |
| 413 | // using + (const T &, const quaternion<T> &) | |
| 414 | q1 = f1 + q4; | |
| 415 | check_exact_quaternion_result(q1, 41, 56, 20, 2); | |
| 416 | ||
| 417 | // using + (const quaternion<T> &, const T &) | |
| 418 | q1 = q4 + f1; | |
| 419 | check_exact_quaternion_result(q1, 41, 56, 20, 2); | |
| 420 | ||
| 421 | // using + (const T &, const quaternion<T> &) | |
| 422 | q1 = f0 + q4; | |
| 423 | check_exact_quaternion_result(q1, 41, 56, 20, 2); | |
| 424 | ||
| 425 | // using + (const quaternion<T> &, const T &) | |
| 426 | q1 = q4 + f0; | |
| 427 | check_exact_quaternion_result(q1, 41, 56, 20, 2); | |
| 428 | ||
| 429 | // using + (const quaternion<T> &,const quaternion<T> &) | |
| 430 | q1 = q3 + q4; | |
| 431 | check_exact_quaternion_result(q1, 39, 62, 27, 10); | |
| 432 | ||
| 433 | // using - (const T &, const quaternion<T> &) | |
| 434 | q1 = f1 - q4; | |
| 435 | check_exact_quaternion_result(q1, 7-34, -56, -20, -2); | |
| 436 | ||
| 437 | // using - (const quaternion<T> &, const T &) | |
| 438 | q1 = q4 - f1; | |
| 439 | check_exact_quaternion_result(q1, 34-7, 56, 20, 2); | |
| 440 | ||
| 441 | // using - (const T &, const quaternion<T> &) | |
| 442 | q1 = f0 - q4; | |
| 443 | check_exact_quaternion_result(q1, 7-34, -56, -20, -2); | |
| 444 | ||
| 445 | // using - (const quaternion<T> &, const T &) | |
| 446 | q1 = q4 - f0; | |
| 447 | check_exact_quaternion_result(q1, 34-7, 56, 20, 2); | |
| 448 | ||
| 449 | // using - (const quaternion<T> &,const quaternion<T> &) | |
| 450 | q1 = q3 - q4; | |
| 451 | check_exact_quaternion_result(q1, -29, -50, -13, 6); | |
| 452 | ||
| 453 | // using * (const T &, const quaternion<T> &) | |
| 454 | q1 = f0 * q4; | |
| 455 | check_exact_quaternion_result(q1, 238, 392, 140, 14); | |
| 456 | ||
| 457 | // using * (const quaternion<T> &, const T &) | |
| 458 | q1 = q4 * f0; | |
| 459 | check_exact_quaternion_result(q1, 238, 392, 140, 14); | |
| 460 | ||
| 461 | // using * (const quaternion<T> &,const quaternion<T> &) | |
| 462 | q1 = q4 * q3; | |
| 463 | check_exact_quaternion_result(q1, -322, 630, -98, 554); | |
| 464 | q1 = q3 * q4; | |
| 465 | check_exact_quaternion_result(q1, -322, 338, 774, 10); | |
| 466 | ||
| 467 | // using / (const T &, const quaternion<T> &) | |
| 468 | q1 = T(f0) / q4; | |
| 469 | check_approx_quaternion_result(q1, T(119) / 2348, -T(49) / 587, -T(35) / 1174, -T(7) / 2348); | |
| 470 | q1 *= q4; | |
| 471 | BOOST_CHECK_CLOSE(q1.R_component_1(), T(7), tol); | |
| 472 | BOOST_CHECK_SMALL(q1.R_component_2(), tol); | |
| 473 | BOOST_CHECK_SMALL(q1.R_component_3(), tol); | |
| 474 | BOOST_CHECK_SMALL(q1.R_component_3(), tol); | |
| 475 | ||
| 476 | // using / (const quaternion<T> &, const T &) | |
| 477 | q1 = q4 / T(f0); | |
| 478 | check_approx_quaternion_result(q1, T(34) / 7, T(56) / 7, T(20) / 7, T(2) / 7); | |
| 479 | ||
| 480 | // using / (const quaternion<T> &,const quaternion<T> &) | |
| 481 | q1 = q4 / q3; | |
| 482 | check_approx_quaternion_result(q1, T(331) / 87, -T(35) / 87, T(149) / 87, -T(89) / 29); | |
| 483 | q1 *= q3; | |
| 484 | check_approx_quaternion_result(q1, 34, 56, 20, 2); | |
| 485 | ||
| 486 | // using + (const quaternion<T> &) | |
| 487 | q1 = +q4; | |
| 488 | check_exact_quaternion_result(q1, 34, 56, 20, 2); | |
| 489 | ||
| 490 | // using - (const quaternion<T> &) | |
| 491 | q1 = -q4; | |
| 492 | check_exact_quaternion_result(q1, -34, -56, -20, -2); | |
| 493 | ||
| 494 | // comparisons: | |
| 495 | q1 = f0; | |
| 496 | test_compare(q1, f0, true); | |
| 497 | q1 += 1; | |
| 498 | test_compare(q1, f0, false); | |
| 499 | q1 = q3; | |
| 500 | test_compare(q1, q3, true); | |
| 501 | q1 += 1; | |
| 502 | test_compare(q1, q3, false); | |
| 503 | ||
| 1e59de90 | 504 | #ifndef BOOST_MATH_STANDALONE |
| b32b8144 FG |
505 | BOOST_CHECK_EQUAL(boost::lexical_cast<std::string>(q4), "(34,56,20,2)"); |
| 506 | q1 = boost::lexical_cast<boost::math::quaternion<T> >("(34,56,20,2)"); | |
| 507 | check_exact_quaternion_result(q1, 34, 56, 20, 2); | |
| 508 | ||
| 509 | q1 = q4 + 1; | |
| 510 | q1.swap(q4); | |
| 511 | check_exact_quaternion_result(q1, 34, 56, 20, 2); | |
| 512 | check_exact_quaternion_result(q4, 35, 56, 20, 2); | |
| 513 | swap(q1, q4); | |
| 514 | check_exact_quaternion_result(q1, 35, 56, 20, 2); | |
| 515 | check_exact_quaternion_result(q4, 34, 56, 20, 2); | |
| 516 | ||
| 517 | BOOST_CHECK_EQUAL(real(q4), 34); | |
| 518 | check_exact_quaternion_result(unreal(q1), 0, 56, 20, 2); | |
| 519 | BOOST_CHECK_EQUAL(sup(q4), 56); | |
| 520 | BOOST_CHECK_EQUAL(sup(-q4), 56); | |
| 521 | BOOST_CHECK_EQUAL(l1(q4), 34 + 56 + 20 + 2); | |
| 522 | BOOST_CHECK_EQUAL(l1(-q4), 34 + 56 + 20 + 2); | |
| 523 | BOOST_CHECK_CLOSE(abs(q4), boost::lexical_cast<T>("68.52736679604725626189080285032080446623"), tol); | |
| 524 | BOOST_CHECK_EQUAL(norm(q4), 4696); | |
| 525 | check_exact_quaternion_result(conj(q4), 34, -56, -20, -2); | |
| 526 | check_approx_quaternion_result(exp(q4), boost::lexical_cast<T>("-572700109350177.2871954597833265926769952"), boost::lexical_cast<T>("104986825963321.656891930274999993423955"), boost::lexical_cast<T>("37495294986900.59174711795535714050855537"), boost::lexical_cast<T>("3749529498690.059174711795535714050855537"), 300); | |
| 527 | check_approx_quaternion_result(pow(q4, 3), -321776, -4032, -1440, -144); | |
| 528 | check_approx_quaternion_result(sin(q4), boost::lexical_cast<T>("18285331065398556228976865.03309127394107"), boost::lexical_cast<T>("-27602822237164214909853379.68314411086089"), boost::lexical_cast<T>("-9858150798987219610661921.315408611021748"), boost::lexical_cast<T>("-985815079898721961066192.1315408611021748"), 40); | |
| 529 | check_approx_quaternion_result(cos(q4), boost::lexical_cast<T>("-29326963088663226843378365.81173441507358"), boost::lexical_cast<T>("-17210331032912252411431342.73890926302336"), boost::lexical_cast<T>("-6146546797468661575511193.835324736794056"), boost::lexical_cast<T>("-614654679746866157551119.3835324736794056"), 40); | |
| 530 | if(std::numeric_limits<T>::max_exponent >= std::numeric_limits<double>::max_exponent) | |
| 531 | check_approx_quaternion_result(tan(q4), boost::lexical_cast<T>("-3.758831069989140832054627039712718213887e-52"), boost::lexical_cast<T>("0.941209703633940052004990419391011076385"), boost::lexical_cast<T>("0.3361463227264071614303537212110753844232"), boost::lexical_cast<T>("0.03361463227264071614303537212110753844232"), 40); | |
| 532 | ||
| 533 | check_approx_quaternion_result(sinh(q4), boost::lexical_cast<T>("-286350054675088.6435977298916624551903343"), boost::lexical_cast<T>("52493412981660.82844596513750015091043914"), boost::lexical_cast<T>("18747647493450.29587355897767862532515683"), boost::lexical_cast<T>("1874764749345.029587355897767862532515683"), 200); | |
| 534 | check_approx_quaternion_result(cosh(q4), boost::lexical_cast<T>("-286350054675088.6435977298916641374866609"), boost::lexical_cast<T>("52493412981660.82844596513749984251351591"), boost::lexical_cast<T>("18747647493450.29587355897767851518339854"), boost::lexical_cast<T>("1874764749345.029587355897767851518339854"), 200); | |
| 535 | if(std::numeric_limits<T>::max_exponent >= std::numeric_limits<double>::max_exponent) | |
| 536 | check_approx_quaternion_result(tanh(q4), boost::lexical_cast<T>("0.9999999999999999999999999999945544805016"), boost::lexical_cast<T>("-2.075260044344318549117301019071435084233e-30"), boost::lexical_cast<T>("-7.411643015515423389704646496683696729404e-31"), boost::lexical_cast<T>("-7.411643015515423389704646496683696729404e-32"), 200); | |
| 537 | ||
| 538 | #ifndef BOOST_NO_TEMPLATE_TEMPLATES | |
| 539 | check_approx_quaternion_result(sinc_pi(q4), boost::lexical_cast<T>("-239180458943182912968898.352151239530846"), boost::lexical_cast<T>("-417903427539587405399855.0577257263862799"), boost::lexical_cast<T>("-149251224121281216214233.9491877594236714"), boost::lexical_cast<T>("-14925122412128121621423.39491877594236714"), 200); | |
| 540 | check_approx_quaternion_result(sinhc_pi(q4), boost::lexical_cast<T>("-1366603120232.604666248483234115586439226"), boost::lexical_cast<T>("3794799638667.255581055299959135992677524"), boost::lexical_cast<T>("1355285585238.305564662607128262854527687"), boost::lexical_cast<T>("135528558523.8305564662607128262854527687"), 200); | |
| 7c673cae | 541 | #endif |
| 1e59de90 | 542 | #endif // BOOST_MATH_STANDALONE |
| b32b8144 FG |
543 | // |
| 544 | // Construction variations: | |
| 545 | // | |
| 546 | T rho = boost::math::constants::root_two<T>() * 2; | |
| 547 | T theta = boost::math::constants::pi<T>() / 4; | |
| 548 | T phi1 = theta; | |
| 549 | T phi2 = theta; | |
| 550 | q1 = ::boost::math::spherical(rho, theta, phi1, phi2); | |
| 551 | check_approx_quaternion_result(q1, 1, 1, boost::math::constants::root_two<T>(), 2, 10); | |
| 552 | T alpha = theta; | |
| 553 | q1 = ::boost::math::semipolar(rho, alpha, phi1, phi2); | |
| 554 | check_approx_quaternion_result(q1, boost::math::constants::root_two<T>(), boost::math::constants::root_two<T>(), boost::math::constants::root_two<T>(), boost::math::constants::root_two<T>(), 10); | |
| 555 | T rho1 = 1; | |
| 556 | T rho2 = 2; | |
| 557 | T theta1 = 0; | |
| 558 | T theta2 = boost::math::constants::half_pi<T>(); | |
| 559 | q1 = ::boost::math::multipolar(rho1, theta1, rho2, theta2); | |
| 560 | check_approx_quaternion_result(q1, 1, 0, 0, 2, 10); | |
| 561 | T t = 5; | |
| 562 | T radius = boost::math::constants::root_two<T>(); | |
| 563 | T longitude = boost::math::constants::pi<T>() / 4; | |
| f67539c2 TL |
564 | T latitude = boost::math::constants::pi<T>() / 3; |
| 565 | q1 = ::boost::math::cylindrospherical(t, radius, longitude, latitude); | |
| 1e59de90 TL |
566 | |
| 567 | #ifndef BOOST_MATH_STANDALONE | |
| b32b8144 | 568 | check_approx_quaternion_result(q1, 5, 0.5, 0.5, boost::lexical_cast<T>("1.224744871391589049098642037352945695983"), 10); |
| 1e59de90 TL |
569 | #endif |
| 570 | ||
| b32b8144 FG |
571 | T r = boost::math::constants::root_two<T>(); |
| 572 | T angle = boost::math::constants::pi<T>() / 4; | |
| 573 | T h1 = 3; | |
| 574 | T h2 = 4; | |
| 575 | q1 = ::boost::math::cylindrical(r, angle, h1, h2); | |
| 576 | check_approx_quaternion_result(q1, 1, 1, 3, 4, 10); | |
| 577 | ||
| 578 | ::boost::math::quaternion<T> quaternion_1(1); | |
| 579 | ::boost::math::quaternion<T> quaternion_i(0, 1); | |
| 580 | ::boost::math::quaternion<T> quaternion_j(0, 0, 1); | |
| 581 | ::boost::math::quaternion<T> quaternion_k(0, 0, 0, 1); | |
| 582 | check_exact_quaternion_result(quaternion_1 * quaternion_1, 1, 0, 0, 0); | |
| 583 | check_exact_quaternion_result(quaternion_1 * quaternion_i, 0, 1, 0, 0); | |
| 584 | check_exact_quaternion_result(quaternion_1 * quaternion_j, 0, 0, 1, 0); | |
| 585 | check_exact_quaternion_result(quaternion_1 * quaternion_k, 0, 0, 0, 1); | |
| 586 | ||
| 587 | check_exact_quaternion_result(quaternion_i * quaternion_1, 0, 1, 0, 0); | |
| 588 | check_exact_quaternion_result(quaternion_i * quaternion_i, -1, 0, 0, 0); | |
| 589 | check_exact_quaternion_result(quaternion_i * quaternion_j, 0, 0, 0, 1); | |
| 590 | check_exact_quaternion_result(quaternion_i * quaternion_k, 0, 0, -1, 0); | |
| 591 | ||
| 592 | check_exact_quaternion_result(quaternion_j * quaternion_1, 0, 0, 1, 0); | |
| 593 | check_exact_quaternion_result(quaternion_j * quaternion_i, 0, 0, 0, -1); | |
| 594 | check_exact_quaternion_result(quaternion_j * quaternion_j, -1, 0, 0, 0); | |
| 595 | check_exact_quaternion_result(quaternion_j * quaternion_k, 0, 1, 0, 0); | |
| 596 | ||
| 597 | check_exact_quaternion_result(quaternion_k * quaternion_1, 0, 0, 0, 1); | |
| 598 | check_exact_quaternion_result(quaternion_k * quaternion_i, 0, 0, 1, 0); | |
| 599 | check_exact_quaternion_result(quaternion_k * quaternion_j, 0, -1, 0, 0); | |
| 600 | check_exact_quaternion_result(quaternion_k * quaternion_k, -1, 0, 0, 0); | |
| 7c673cae FG |
601 | } |
| 602 | ||
| b32b8144 | 603 | BOOST_AUTO_TEST_CASE_TEMPLATE(multiplication_test, T, test_types) |
| 7c673cae FG |
604 | { |
| 605 | #if BOOST_WORKAROUND(__GNUC__, < 3) | |
| 606 | #else /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 607 | using ::std::numeric_limits; | |
| 608 | ||
| 609 | using ::boost::math::abs; | |
| 610 | #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 611 | ||
| 612 | ||
| 613 | BOOST_TEST_MESSAGE("Testing multiplication for " | |
| 614 | << string_type_name<T>::_() << "."); | |
| 615 | ||
| 616 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 617 | (abs(::boost::math::quaternion<T>(1,0,0,0)* | |
| 618 | ::boost::math::quaternion<T>(1,0,0,0)-static_cast<T>(1))) | |
| 619 | (numeric_limits<T>::epsilon())); | |
| 620 | ||
| 621 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 622 | (abs(::boost::math::quaternion<T>(0,1,0,0)* | |
| 623 | ::boost::math::quaternion<T>(0,1,0,0)+static_cast<T>(1))) | |
| 624 | (numeric_limits<T>::epsilon())); | |
| 625 | ||
| 626 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 627 | (abs(::boost::math::quaternion<T>(0,0,1,0)* | |
| 628 | ::boost::math::quaternion<T>(0,0,1,0)+static_cast<T>(1))) | |
| 629 | (numeric_limits<T>::epsilon())); | |
| 630 | ||
| 631 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 632 | (abs(::boost::math::quaternion<T>(0,0,0,1)* | |
| 633 | ::boost::math::quaternion<T>(0,0,0,1)+static_cast<T>(1))) | |
| 634 | (numeric_limits<T>::epsilon())); | |
| 635 | ||
| 636 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 637 | (abs(::boost::math::quaternion<T>(0,1,0,0)* | |
| 638 | ::boost::math::quaternion<T>(0,0,1,0)- | |
| 639 | ::boost::math::quaternion<T>(0,0,0,1))) | |
| 640 | (numeric_limits<T>::epsilon())); | |
| 641 | ||
| 642 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 643 | (abs(::boost::math::quaternion<T>(0,0,1,0)* | |
| 644 | ::boost::math::quaternion<T>(0,1,0,0)+ | |
| 645 | ::boost::math::quaternion<T>(0,0,0,1))) | |
| 646 | (numeric_limits<T>::epsilon())); | |
| 647 | ||
| 648 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 649 | (abs(::boost::math::quaternion<T>(0,0,1,0)* | |
| 650 | ::boost::math::quaternion<T>(0,0,0,1)- | |
| 651 | ::boost::math::quaternion<T>(0,1,0,0))) | |
| 652 | (numeric_limits<T>::epsilon())); | |
| 653 | ||
| 654 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 655 | (abs(::boost::math::quaternion<T>(0,0,0,1)* | |
| 656 | ::boost::math::quaternion<T>(0,0,1,0)+ | |
| 657 | ::boost::math::quaternion<T>(0,1,0,0))) | |
| 658 | (numeric_limits<T>::epsilon())); | |
| 659 | ||
| 660 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 661 | (abs(::boost::math::quaternion<T>(0,0,0,1)* | |
| 662 | ::boost::math::quaternion<T>(0,1,0,0)- | |
| 663 | ::boost::math::quaternion<T>(0,0,1,0))) | |
| 664 | (numeric_limits<T>::epsilon())); | |
| 665 | ||
| 666 | BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(), | |
| 667 | (abs(::boost::math::quaternion<T>(0,1,0,0)* | |
| 668 | ::boost::math::quaternion<T>(0,0,0,1)+ | |
| 669 | ::boost::math::quaternion<T>(0,0,1,0))) | |
| 670 | (numeric_limits<T>::epsilon())); | |
| 671 | } | |
| 672 | ||
| 673 | ||
| b32b8144 | 674 | BOOST_AUTO_TEST_CASE_TEMPLATE(exp_test, T, test_types) |
| 7c673cae FG |
675 | { |
| 676 | #if BOOST_WORKAROUND(__GNUC__, < 3) | |
| 677 | #else /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 678 | using ::std::numeric_limits; | |
| 679 | ||
| 680 | using ::std::atan; | |
| 681 | ||
| 682 | using ::boost::math::abs; | |
| 683 | #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 684 | ||
| 685 | ||
| 686 | BOOST_TEST_MESSAGE("Testing exp for " | |
| 687 | << string_type_name<T>::_() << "."); | |
| 688 | ||
| 689 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 690 | (abs(exp(::boost::math::quaternion<T> | |
| 691 | (0,4*atan(static_cast<T>(1)),0,0))+static_cast<T>(1))) | |
| 692 | (2*numeric_limits<T>::epsilon())); | |
| 693 | ||
| 694 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 695 | (abs(exp(::boost::math::quaternion<T> | |
| 696 | (0,0,4*atan(static_cast<T>(1)),0))+static_cast<T>(1))) | |
| 697 | (2*numeric_limits<T>::epsilon())); | |
| 698 | ||
| 699 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 700 | (abs(exp(::boost::math::quaternion<T> | |
| 701 | (0,0,0,4*atan(static_cast<T>(1))))+static_cast<T>(1))) | |
| 702 | (2*numeric_limits<T>::epsilon())); | |
| 703 | } | |
| 704 | ||
| 705 | ||
| b32b8144 | 706 | BOOST_AUTO_TEST_CASE_TEMPLATE(cos_test, T, test_types) |
| 7c673cae FG |
707 | { |
| 708 | #if BOOST_WORKAROUND(__GNUC__, < 3) | |
| 709 | #else /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 710 | using ::std::numeric_limits; | |
| 711 | ||
| 712 | using ::std::log; | |
| 713 | ||
| 714 | using ::boost::math::abs; | |
| 715 | #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 716 | ||
| 717 | ||
| 718 | BOOST_TEST_MESSAGE("Testing cos for " | |
| 719 | << string_type_name<T>::_() << "."); | |
| 720 | ||
| 721 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 722 | (abs(static_cast<T>(4)*cos(::boost::math::quaternion<T> | |
| 723 | (0,log(static_cast<T>(2)),0,0))-static_cast<T>(5))) | |
| 724 | (4*numeric_limits<T>::epsilon())); | |
| 725 | ||
| 726 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 727 | (abs(static_cast<T>(4)*cos(::boost::math::quaternion<T> | |
| 728 | (0,0,log(static_cast<T>(2)),0))-static_cast<T>(5))) | |
| 729 | (4*numeric_limits<T>::epsilon())); | |
| 730 | ||
| 731 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 732 | (abs(static_cast<T>(4)*cos(::boost::math::quaternion<T> | |
| 733 | (0,0,0,log(static_cast<T>(2))))-static_cast<T>(5))) | |
| 734 | (4*numeric_limits<T>::epsilon())); | |
| 735 | } | |
| 736 | ||
| 737 | ||
| b32b8144 | 738 | BOOST_AUTO_TEST_CASE_TEMPLATE(sin_test, T, test_types) |
| 7c673cae FG |
739 | { |
| 740 | #if BOOST_WORKAROUND(__GNUC__, < 3) | |
| 741 | #else /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 742 | using ::std::numeric_limits; | |
| 743 | ||
| 744 | using ::std::log; | |
| 745 | ||
| 746 | using ::boost::math::abs; | |
| 747 | #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 748 | ||
| 749 | ||
| 750 | BOOST_TEST_MESSAGE("Testing sin for " | |
| 751 | << string_type_name<T>::_() << "."); | |
| 752 | ||
| 753 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 754 | (abs(static_cast<T>(4)*sin(::boost::math::quaternion<T> | |
| 755 | (0,log(static_cast<T>(2)),0,0)) | |
| 756 | -::boost::math::quaternion<T>(0,3,0,0))) | |
| 757 | (4*numeric_limits<T>::epsilon())); | |
| 758 | ||
| 759 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 760 | (abs(static_cast<T>(4)*sin(::boost::math::quaternion<T> | |
| 761 | (0,0,log(static_cast<T>(2)),0)) | |
| 762 | -::boost::math::quaternion<T>(0,0,3,0))) | |
| 763 | (4*numeric_limits<T>::epsilon())); | |
| 764 | ||
| 765 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 766 | (abs(static_cast<T>(4)*sin(::boost::math::quaternion<T> | |
| 767 | (0,0,0,log(static_cast<T>(2)))) | |
| 768 | -::boost::math::quaternion<T>(0,0,0,3))) | |
| 769 | (4*numeric_limits<T>::epsilon())); | |
| 770 | } | |
| 771 | ||
| 772 | ||
| b32b8144 | 773 | BOOST_AUTO_TEST_CASE_TEMPLATE(cosh_test, T, test_types) |
| 7c673cae FG |
774 | { |
| 775 | #if BOOST_WORKAROUND(__GNUC__, < 3) | |
| 776 | #else /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 777 | using ::std::numeric_limits; | |
| 778 | ||
| 779 | using ::std::atan; | |
| 780 | ||
| 781 | using ::boost::math::abs; | |
| 782 | #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 783 | ||
| 784 | ||
| 785 | BOOST_TEST_MESSAGE("Testing cosh for " | |
| 786 | << string_type_name<T>::_() << "."); | |
| 787 | ||
| 788 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 789 | (abs(cosh(::boost::math::quaternion<T> | |
| 790 | (0,4*atan(static_cast<T>(1)),0,0)) | |
| 791 | +static_cast<T>(1))) | |
| 792 | (4*numeric_limits<T>::epsilon())); | |
| 793 | ||
| 794 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 795 | (abs(cosh(::boost::math::quaternion<T> | |
| 796 | (0,0,4*atan(static_cast<T>(1)),0)) | |
| 797 | +static_cast<T>(1))) | |
| 798 | (4*numeric_limits<T>::epsilon())); | |
| 799 | ||
| 800 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 801 | (abs(cosh(::boost::math::quaternion<T> | |
| 802 | (0,0,0,4*atan(static_cast<T>(1)))) | |
| 803 | +static_cast<T>(1))) | |
| 804 | (4*numeric_limits<T>::epsilon())); | |
| 805 | } | |
| 806 | ||
| 807 | ||
| b32b8144 | 808 | BOOST_AUTO_TEST_CASE_TEMPLATE(sinh_test, T, test_types) |
| 7c673cae FG |
809 | { |
| 810 | #if BOOST_WORKAROUND(__GNUC__, < 3) | |
| 811 | #else /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 812 | using ::std::numeric_limits; | |
| 813 | ||
| 814 | using ::std::atan; | |
| 815 | ||
| 816 | using ::boost::math::abs; | |
| 817 | #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */ | |
| 818 | ||
| 819 | ||
| 820 | BOOST_TEST_MESSAGE("Testing sinh for " | |
| 821 | << string_type_name<T>::_() << "."); | |
| 822 | ||
| 823 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 824 | (abs(sinh(::boost::math::quaternion<T> | |
| 825 | (0,2*atan(static_cast<T>(1)),0,0)) | |
| 826 | -::boost::math::quaternion<T>(0,1,0,0))) | |
| 827 | (4*numeric_limits<T>::epsilon())); | |
| 828 | ||
| 829 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 830 | (abs(sinh(::boost::math::quaternion<T> | |
| 831 | (0,0,2*atan(static_cast<T>(1)),0)) | |
| 832 | -::boost::math::quaternion<T>(0,0,1,0))) | |
| 833 | (4*numeric_limits<T>::epsilon())); | |
| 834 | ||
| 835 | BOOST_CHECK_PREDICATE(::std::less_equal<T>(), | |
| 836 | (abs(sinh(::boost::math::quaternion<T> | |
| 837 | (0,0,0,2*atan(static_cast<T>(1)))) | |
| 838 | -::boost::math::quaternion<T>(0,0,0,1))) | |
| 839 | (4*numeric_limits<T>::epsilon())); | |
| 840 | } | |
| 841 |