boost/units/cmath.hpp

   1 // Boost.Units - A C++ library for zero-overhead dimensional analysis and
   2 // unit/quantity manipulation and conversion
   3 //
   4 // Copyright (C) 2003-2008 Matthias Christian Schabel
   5 // Copyright (C) 2007-2008 Steven Watanabe
   6 //
   7 // Distributed under the Boost Software License, Version 1.0. (See
   8 // accompanying file LICENSE_1_0.txt or copy at
   9 // http://www.boost.org/LICENSE_1_0.txt)
  10
  11 #ifndef BOOST_UNITS_CMATH_HPP
  12 #define BOOST_UNITS_CMATH_HPP
  13
  14 #include <boost/config/no_tr1/cmath.hpp>
  15 #include <cstdlib>
  16
  17 #include <boost/math/special_functions/fpclassify.hpp>
  18 #include <boost/math/special_functions/hypot.hpp>
  19 #include <boost/math/special_functions/next.hpp>
  20 #include <boost/math/special_functions/round.hpp>
  21 #include <boost/math/special_functions/sign.hpp>
  22
  23 #include <boost/units/dimensionless_quantity.hpp>
  24 #include <boost/units/pow.hpp>
  25 #include <boost/units/quantity.hpp>
  26 #include <boost/units/detail/cmath_impl.hpp>
  27
  28 #include <boost/units/systems/si/plane_angle.hpp>
  29
  30 /// \file
  31 /// \brief Overloads of functions in \<cmath\> for quantities
  32 ///
  33 /// \detailed Only functions for which a dimensionally-correct result type
  34 /// can be determined are overloaded. All functions work with dimensionless
  35 /// quantities.
  36
  37 // BOOST_PREVENT_MACRO_SUBSTITUTION is needed on certain compilers that define
  38 // some <cmath> functions as macros; it is used for all functions even though it
  39 // isn't necessary -- I didn't want to think :)
  40 //
  41 // the form using namespace detail; return(f(x)); is used
  42 // to enable ADL for UDTs
  43
  44 namespace boost {
  45
  46 namespace units {
  47
  48 template<class Unit,class Y>
  49 inline
  50 bool
  51 isfinite BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
  52 {
  53     using boost::math::isfinite;
  54     return isfinite BOOST_PREVENT_MACRO_SUBSTITUTION (q.value());
  55 }
  56
  57 template<class Unit,class Y>
  58 inline
  59 bool
  60 isinf BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
  61 {
  62     using boost::math::isinf;
  63     return isinf BOOST_PREVENT_MACRO_SUBSTITUTION (q.value());
  64 }
  65
  66 template<class Unit,class Y>
  67 inline
  68 bool
  69 isnan BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
  70 {
  71     using boost::math::isnan;
  72     return isnan BOOST_PREVENT_MACRO_SUBSTITUTION (q.value());
  73 }
  74
  75 template<class Unit,class Y>
  76 inline
  77 bool
  78 isnormal BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
  79 {
  80     using boost::math::isnormal;
  81     return isnormal BOOST_PREVENT_MACRO_SUBSTITUTION (q.value());
  82 }
  83
  84 template<class Unit,class Y>
  85 inline
  86 bool
  87 isgreater BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
  88                                             const quantity<Unit,Y>& q2)
  89 {
  90     using namespace detail;
  91     return isgreater BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value());
  92 }
  93
  94 template<class Unit,class Y>
  95 inline
  96 bool
  97 isgreaterequal BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
  98                                                  const quantity<Unit,Y>& q2)
  99 {
 100     using namespace detail;
 101     return isgreaterequal BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value());
 102 }
 103
 104 template<class Unit,class Y>
 105 inline
 106 bool
 107 isless BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 108                                          const quantity<Unit,Y>& q2)
 109 {
 110     using namespace detail;
 111     return isless BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value());
 112 }
 113
 114 template<class Unit,class Y>
 115 inline
 116 bool
 117 islessequal BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 118                                               const quantity<Unit,Y>& q2)
 119 {
 120     using namespace detail;
 121     return islessequal BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value());
 122 }
 123
 124 template<class Unit,class Y>
 125 inline
 126 bool
 127 islessgreater BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 128                                                 const quantity<Unit,Y>& q2)
 129 {
 130     using namespace detail;
 131     return islessgreater BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value());
 132 }
 133
 134 template<class Unit,class Y>
 135 inline
 136 bool
 137 isunordered BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 138                                               const quantity<Unit,Y>& q2)
 139 {
 140     using namespace detail;
 141     return isunordered BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value());
 142 }
 143
 144 template<class Unit,class Y>
 145 inline
 146 quantity<Unit,Y>
 147 abs BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 148 {
 149     using std::abs;
 150
 151     typedef quantity<Unit,Y>    quantity_type;
 152
 153     return quantity_type::from_value(abs BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 154 }
 155
 156 template<class Unit,class Y>
 157 inline
 158 quantity<Unit,Y>
 159 ceil BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 160 {
 161     using std::ceil;
 162
 163     typedef quantity<Unit,Y>    quantity_type;
 164
 165     return quantity_type::from_value(ceil BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 166 }
 167
 168 template<class Unit,class Y>
 169 inline
 170 quantity<Unit,Y>
 171 copysign BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 172          const quantity<Unit,Y>& q2)
 173 {
 174     using boost::math::copysign;
 175
 176     typedef quantity<Unit,Y>    quantity_type;
 177
 178     return quantity_type::from_value(copysign BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value()));
 179 }
 180
 181 template<class Unit,class Y>
 182 inline
 183 quantity<Unit,Y>
 184 fabs BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 185 {
 186     using std::fabs;
 187
 188     typedef quantity<Unit,Y>    quantity_type;
 189
 190     return quantity_type::from_value(fabs BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 191 }
 192
 193 template<class Unit,class Y>
 194 inline
 195 quantity<Unit,Y>
 196 floor BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 197 {
 198     using std::floor;
 199
 200     typedef quantity<Unit,Y>    quantity_type;
 201
 202     return quantity_type::from_value(floor BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 203 }
 204
 205 template<class Unit,class Y>
 206 inline
 207 quantity<Unit,Y>
 208 fdim BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 209                                        const quantity<Unit,Y>& q2)
 210 {
 211     using namespace detail;
 212
 213     typedef quantity<Unit,Y>    quantity_type;
 214
 215     return quantity_type::from_value(fdim BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value()));
 216 }
 217
 218 #if 0
 219
 220 template<class Unit1,class Unit2,class Unit3,class Y>
 221 inline
 222 typename add_typeof_helper<
 223     typename multiply_typeof_helper<quantity<Unit1,Y>,
 224                                     quantity<Unit2,Y> >::type,
 225     quantity<Unit3,Y> >::type
 226 fma BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit1,Y>& q1,
 227                                       const quantity<Unit2,Y>& q2,
 228                                       const quantity<Unit3,Y>& q3)
 229 {
 230     using namespace detail;
 231
 232     typedef quantity<Unit1,Y>   type1;
 233     typedef quantity<Unit2,Y>   type2;
 234     typedef quantity<Unit3,Y>   type3;
 235
 236     typedef typename multiply_typeof_helper<type1,type2>::type  prod_type;
 237     typedef typename add_typeof_helper<prod_type,type3>::type   quantity_type;
 238
 239     return quantity_type::from_value(fma BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value(),q3.value()));
 240 }
 241
 242 #endif
 243
 244 template<class Unit,class Y>
 245 inline
 246 quantity<Unit,Y>
 247 fmax BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 248                                        const quantity<Unit,Y>& q2)
 249 {
 250     using namespace detail;
 251
 252     typedef quantity<Unit,Y>    quantity_type;
 253
 254     return quantity_type::from_value(fmax BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value()));
 255 }
 256
 257 template<class Unit,class Y>
 258 inline
 259 quantity<Unit,Y>
 260 fmin BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 261                                        const quantity<Unit,Y>& q2)
 262 {
 263     using namespace detail;
 264
 265     typedef quantity<Unit,Y>    quantity_type;
 266
 267     return quantity_type::from_value(fmin BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value()));
 268 }
 269
 270 template<class Unit,class Y>
 271 inline
 272 int
 273 fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 274 {
 275     using boost::math::fpclassify;
 276
 277     return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION (q.value());
 278 }
 279
 280 template<class Unit,class Y>
 281 inline
 282 typename root_typeof_helper<
 283     typename add_typeof_helper<
 284         typename power_typeof_helper<quantity<Unit,Y>,
 285                                      static_rational<2> >::type,
 286         typename power_typeof_helper<quantity<Unit,Y>,
 287                                      static_rational<2> >::type>::type,
 288         static_rational<2> >::type
 289 hypot BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,const quantity<Unit,Y>& q2)
 290 {
 291     using boost::math::hypot;
 292
 293     typedef quantity<Unit,Y>    type1;
 294
 295     typedef typename power_typeof_helper<type1,static_rational<2> >::type   pow_type;
 296     typedef typename add_typeof_helper<pow_type,pow_type>::type             add_type;
 297     typedef typename root_typeof_helper<add_type,static_rational<2> >::type quantity_type;
 298
 299     return quantity_type::from_value(hypot BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value()));
 300 }
 301
 302 // does ISO C++ support long long? g++ claims not
 303 //template<class Unit,class Y>
 304 //inline
 305 //quantity<Unit,long long>
 306 //llrint BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 307 //{
 308 //    using namespace detail;
 309 //
 310 //    typedef quantity<Unit,long long>    quantity_type;
 311 //
 312 //    return quantity_type::from_value(llrint BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 313 //}
 314
 315 // does ISO C++ support long long? g++ claims not
 316 //template<class Unit,class Y>
 317 //inline
 318 //quantity<Unit,long long>
 319 //llround BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 320 //{
 321 //    using namespace detail;
 322 //
 323 //    typedef quantity<Unit,long long>    quantity_type;
 324 //
 325 //    return quantity_type::from_value(llround BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 326 //}
 327
 328 #if 0
 329
 330 template<class Unit,class Y>
 331 inline
 332 quantity<Unit,Y>
 333 nearbyint BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 334 {
 335     using namespace detail;
 336
 337     typedef quantity<Unit,Y>    quantity_type;
 338
 339     return quantity_type::from_value(nearbyint BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 340 }
 341
 342 #endif
 343
 344 template<class Unit,class Y>
 345 inline
 346 quantity<Unit,Y> nextafter BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 347                                                              const quantity<Unit,Y>& q2)
 348 {
 349     using boost::math::nextafter;
 350
 351     typedef quantity<Unit,Y>    quantity_type;
 352
 353     return quantity_type::from_value(nextafter BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value()));
 354 }
 355 template<class Unit,class Y>
 356 inline
 357 quantity<Unit,Y> nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q1,
 358                                                               const quantity<Unit,Y>& q2)
 359 {
 360     // the only difference between nextafter and nexttowards is
 361     // in the argument types.  Since we are requiring identical
 362     // argument types, there is no difference.
 363     using boost::math::nextafter;
 364
 365     typedef quantity<Unit,Y>    quantity_type;
 366
 367     return quantity_type::from_value(nextafter BOOST_PREVENT_MACRO_SUBSTITUTION (q1.value(),q2.value()));
 368 }
 369
 370 #if 0
 371
 372 template<class Unit,class Y>
 373 inline
 374 quantity<Unit,Y>
 375 rint BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 376 {
 377     using namespace detail;
 378
 379     typedef quantity<Unit,Y>    quantity_type;
 380
 381     return quantity_type::from_value(rint BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 382 }
 383
 384 #endif
 385
 386 template<class Unit,class Y>
 387 inline
 388 quantity<Unit,Y>
 389 round BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 390 {
 391     using boost::math::round;
 392
 393     typedef quantity<Unit,Y>    quantity_type;
 394
 395     return quantity_type::from_value(round BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 396 }
 397
 398 template<class Unit,class Y>
 399 inline
 400 int
 401 signbit BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 402 {
 403     using boost::math::signbit;
 404
 405     return signbit BOOST_PREVENT_MACRO_SUBSTITUTION (q.value());
 406 }
 407
 408 template<class Unit,class Y>
 409 inline
 410 quantity<Unit,Y>
 411 trunc BOOST_PREVENT_MACRO_SUBSTITUTION (const quantity<Unit,Y>& q)
 412 {
 413     using namespace detail;
 414
 415     typedef quantity<Unit,Y>    quantity_type;
 416
 417     return quantity_type::from_value(trunc BOOST_PREVENT_MACRO_SUBSTITUTION (q.value()));
 418 }
 419
 420 template<class Unit,class Y>
 421 inline
 422 quantity<Unit, Y>
 423 fmod(const quantity<Unit,Y>& q1, const quantity<Unit,Y>& q2)
 424 {
 425     using std::fmod;
 426
 427     typedef quantity<Unit,Y> quantity_type;
 428
 429     return quantity_type::from_value(fmod(q1.value(), q2.value()));
 430 }
 431
 432 template<class Unit, class Y>
 433 inline
 434 quantity<Unit, Y>
 435 modf(const quantity<Unit, Y>& q1, quantity<Unit, Y>* q2)
 436 {
 437     using std::modf;
 438
 439     typedef quantity<Unit,Y> quantity_type;
 440
 441     return quantity_type::from_value(modf(q1.value(), &quantity_cast<Y&>(*q2)));
 442 }
 443
 444 template<class Unit, class Y, class Int>
 445 inline
 446 quantity<Unit, Y>
 447 frexp(const quantity<Unit, Y>& q,Int* ex)
 448 {
 449     using std::frexp;
 450
 451     typedef quantity<Unit,Y> quantity_type;
 452
 453     return quantity_type::from_value(frexp(q.value(),ex));
 454 }
 455
 456 /// For non-dimensionless quantities, integral and rational powers
 457 /// and roots can be computed by @c pow<Ex> and @c root<Rt> respectively.
 458 template<class S, class Y>
 459 inline
 460 quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>
 461 pow(const quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>& q1,
 462     const quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>& q2)
 463 {
 464     using std::pow;
 465
 466     typedef quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S),Y> quantity_type;
 467
 468     return quantity_type::from_value(pow(q1.value(), q2.value()));
 469 }
 470
 471 template<class S, class Y>
 472 inline
 473 quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>
 474 exp(const quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>& q)
 475 {
 476     using std::exp;
 477
 478     typedef quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y> quantity_type;
 479
 480     return quantity_type::from_value(exp(q.value()));
 481 }
 482
 483 template<class Unit, class Y, class Int>
 484 inline
 485 quantity<Unit, Y>
 486 ldexp(const quantity<Unit, Y>& q,const Int& ex)
 487 {
 488     using std::ldexp;
 489
 490     typedef quantity<Unit,Y> quantity_type;
 491
 492     return quantity_type::from_value(ldexp(q.value(), ex));
 493 }
 494
 495 template<class S, class Y>
 496 inline
 497 quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>
 498 log(const quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>& q)
 499 {
 500     using std::log;
 501
 502     typedef quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y> quantity_type;
 503
 504     return quantity_type::from_value(log(q.value()));
 505 }
 506
 507 template<class S, class Y>
 508 inline
 509 quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>
 510 log10(const quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y>& q)
 511 {
 512     using std::log10;
 513
 514     typedef quantity<BOOST_UNITS_DIMENSIONLESS_UNIT(S), Y> quantity_type;
 515
 516     return quantity_type::from_value(log10(q.value()));
 517 }
 518
 519 template<class Unit,class Y>
 520 inline
 521 typename root_typeof_helper<
 522                             quantity<Unit,Y>,
 523                             static_rational<2>
 524                            >::type
 525 sqrt(const quantity<Unit,Y>& q)
 526 {
 527     using std::sqrt;
 528
 529     typedef typename root_typeof_helper<
 530                                         quantity<Unit,Y>,
 531                                         static_rational<2>
 532                                        >::type quantity_type;
 533
 534     return quantity_type::from_value(sqrt(q.value()));
 535 }
 536
 537 } // namespace units
 538
 539 } // namespace boost
 540
 541 namespace boost {
 542
 543 namespace units {
 544
 545 // trig functions with si argument/return types
 546
 547 /// cos of theta in radians
 548 template<class Y>
 549 typename dimensionless_quantity<si::system,Y>::type
 550 cos(const quantity<si::plane_angle,Y>& theta)
 551 {
 552     using std::cos;
 553     return cos(theta.value());
 554 }
 555
 556 /// sin of theta in radians
 557 template<class Y>
 558 typename dimensionless_quantity<si::system,Y>::type
 559 sin(const quantity<si::plane_angle,Y>& theta)
 560 {
 561     using std::sin;
 562     return sin(theta.value());
 563 }
 564
 565 /// tan of theta in radians
 566 template<class Y>
 567 typename dimensionless_quantity<si::system,Y>::type
 568 tan(const quantity<si::plane_angle,Y>& theta)
 569 {
 570     using std::tan;
 571     return tan(theta.value());
 572 }
 573
 574 /// cos of theta in other angular units
 575 template<class System,class Y>
 576 typename dimensionless_quantity<System,Y>::type
 577 cos(const quantity<unit<plane_angle_dimension,System>,Y>& theta)
 578 {
 579     return cos(quantity<si::plane_angle,Y>(theta));
 580 }
 581
 582 /// sin of theta in other angular units
 583 template<class System,class Y>
 584 typename dimensionless_quantity<System,Y>::type
 585 sin(const quantity<unit<plane_angle_dimension,System>,Y>& theta)
 586 {
 587     return sin(quantity<si::plane_angle,Y>(theta));
 588 }
 589
 590 /// tan of theta in other angular units
 591 template<class System,class Y>
 592 typename dimensionless_quantity<System,Y>::type
 593 tan(const quantity<unit<plane_angle_dimension,System>,Y>& theta)
 594 {
 595     return tan(quantity<si::plane_angle,Y>(theta));
 596 }
 597
 598 /// acos of dimensionless quantity returning angle in same system
 599 template<class Y,class System>
 600 quantity<unit<plane_angle_dimension, homogeneous_system<System> >,Y>
 601 acos(const quantity<unit<dimensionless_type, homogeneous_system<System> >,Y>& val)
 602 {
 603     using std::acos;
 604     return quantity<unit<plane_angle_dimension, homogeneous_system<System> >,Y>(acos(val.value())*si::radians);
 605 }
 606
 607 /// asin of dimensionless quantity returning angle in same system
 608 template<class Y,class System>
 609 quantity<unit<plane_angle_dimension, homogeneous_system<System> >,Y>
 610 asin(const quantity<unit<dimensionless_type, homogeneous_system<System> >,Y>& val)
 611 {
 612     using std::asin;
 613     return quantity<unit<plane_angle_dimension, homogeneous_system<System> >,Y>(asin(val.value())*si::radians);
 614 }
 615
 616 /// atan of dimensionless quantity returning angle in same system
 617 template<class Y,class System>
 618 quantity<unit<plane_angle_dimension, homogeneous_system<System> >,Y>
 619 atan(const quantity<unit<dimensionless_type, homogeneous_system<System> >, Y>& val)
 620 {
 621     using std::atan;
 622     return quantity<unit<plane_angle_dimension, homogeneous_system<System> >,Y>(atan(val.value())*si::radians);
 623 }
 624
 625 /// atan2 of @c value_type returning angle in radians
 626 template<class Y, class System>
 627 quantity<unit<plane_angle_dimension, homogeneous_system<System> >, Y>
 628 atan2(const quantity<unit<dimensionless_type, homogeneous_system<System> >, Y>& y,
 629       const quantity<unit<dimensionless_type, homogeneous_system<System> >, Y>& x)
 630 {
 631     using std::atan2;
 632     return quantity<unit<plane_angle_dimension, homogeneous_system<System> >, Y>(atan2(y.value(),x.value())*si::radians);
 633 }
 634
 635 } // namespace units
 636
 637 } // namespace boost
 638
 639 #endif // BOOST_UNITS_CMATH_HPP