1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/epoc32/include/stdapis/boost/math/octonion.hpp Tue Mar 16 16:12:26 2010 +0000
1.3 @@ -0,0 +1,4754 @@
1.4 +// boost octonion.hpp header file
1.5 +
1.6 +// (C) Copyright Hubert Holin 2001.
1.7 +// Distributed under the Boost Software License, Version 1.0. (See
1.8 +// accompanying file LICENSE_1_0.txt or copy at
1.9 +// http://www.boost.org/LICENSE_1_0.txt)
1.10 +
1.11 +// See http://www.boost.org for updates, documentation, and revision history.
1.12 +
1.13 +
1.14 +#ifndef BOOST_OCTONION_HPP
1.15 +#define BOOST_OCTONION_HPP
1.16 +
1.17 +#include <boost/math/quaternion.hpp>
1.18 +
1.19 +
1.20 +namespace boost
1.21 +{
1.22 + namespace math
1.23 + {
1.24 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.25 + // gcc 2.95.x uses expression templates for valarray calculations, but
1.26 + // the result is not conforming. We need BOOST_GET_VALARRAY to get an
1.27 + // actual valarray result when we need to call a member function
1.28 + #define BOOST_GET_VALARRAY(T,x) ::std::valarray<T>(x)
1.29 + // gcc 2.95.x has an "std::ios" class that is similar to
1.30 + // "std::ios_base", so we just use a #define
1.31 + #define BOOST_IOS_BASE ::std::ios
1.32 + // gcc 2.x ignores function scope using declarations,
1.33 + // put them in the scope of the enclosing namespace instead:
1.34 + using ::std::valarray;
1.35 + using ::std::sqrt;
1.36 + using ::std::cos;
1.37 + using ::std::sin;
1.38 + using ::std::exp;
1.39 + using ::std::cosh;
1.40 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.41 +
1.42 +#define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \
1.43 + type real() const \
1.44 + { \
1.45 + return(a); \
1.46 + } \
1.47 + \
1.48 + octonion<type> unreal() const \
1.49 + { \
1.50 + return( octonion<type>(static_cast<type>(0),b,c,d,e,f,g,h)); \
1.51 + } \
1.52 + \
1.53 + type R_component_1() const \
1.54 + { \
1.55 + return(a); \
1.56 + } \
1.57 + \
1.58 + type R_component_2() const \
1.59 + { \
1.60 + return(b); \
1.61 + } \
1.62 + \
1.63 + type R_component_3() const \
1.64 + { \
1.65 + return(c); \
1.66 + } \
1.67 + \
1.68 + type R_component_4() const \
1.69 + { \
1.70 + return(d); \
1.71 + } \
1.72 + \
1.73 + type R_component_5() const \
1.74 + { \
1.75 + return(e); \
1.76 + } \
1.77 + \
1.78 + type R_component_6() const \
1.79 + { \
1.80 + return(f); \
1.81 + } \
1.82 + \
1.83 + type R_component_7() const \
1.84 + { \
1.85 + return(g); \
1.86 + } \
1.87 + \
1.88 + type R_component_8() const \
1.89 + { \
1.90 + return(h); \
1.91 + } \
1.92 + \
1.93 + ::std::complex<type> C_component_1() const \
1.94 + { \
1.95 + return(::std::complex<type>(a,b)); \
1.96 + } \
1.97 + \
1.98 + ::std::complex<type> C_component_2() const \
1.99 + { \
1.100 + return(::std::complex<type>(c,d)); \
1.101 + } \
1.102 + \
1.103 + ::std::complex<type> C_component_3() const \
1.104 + { \
1.105 + return(::std::complex<type>(e,f)); \
1.106 + } \
1.107 + \
1.108 + ::std::complex<type> C_component_4() const \
1.109 + { \
1.110 + return(::std::complex<type>(g,h)); \
1.111 + } \
1.112 + \
1.113 + ::boost::math::quaternion<type> H_component_1() const \
1.114 + { \
1.115 + return(::boost::math::quaternion<type>(a,b,c,d)); \
1.116 + } \
1.117 + \
1.118 + ::boost::math::quaternion<type> H_component_2() const \
1.119 + { \
1.120 + return(::boost::math::quaternion<type>(e,f,g,h)); \
1.121 + }
1.122 +
1.123 +
1.124 +#define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \
1.125 + template<typename X> \
1.126 + octonion<type> & operator = (octonion<X> const & a_affecter) \
1.127 + { \
1.128 + a = static_cast<type>(a_affecter.R_component_1()); \
1.129 + b = static_cast<type>(a_affecter.R_component_2()); \
1.130 + c = static_cast<type>(a_affecter.R_component_3()); \
1.131 + d = static_cast<type>(a_affecter.R_component_4()); \
1.132 + e = static_cast<type>(a_affecter.R_component_5()); \
1.133 + f = static_cast<type>(a_affecter.R_component_6()); \
1.134 + g = static_cast<type>(a_affecter.R_component_7()); \
1.135 + h = static_cast<type>(a_affecter.R_component_8()); \
1.136 + \
1.137 + return(*this); \
1.138 + } \
1.139 + \
1.140 + octonion<type> & operator = (octonion<type> const & a_affecter) \
1.141 + { \
1.142 + a = a_affecter.a; \
1.143 + b = a_affecter.b; \
1.144 + c = a_affecter.c; \
1.145 + d = a_affecter.d; \
1.146 + e = a_affecter.e; \
1.147 + f = a_affecter.f; \
1.148 + g = a_affecter.g; \
1.149 + h = a_affecter.h; \
1.150 + \
1.151 + return(*this); \
1.152 + } \
1.153 + \
1.154 + octonion<type> & operator = (type const & a_affecter) \
1.155 + { \
1.156 + a = a_affecter; \
1.157 + \
1.158 + b = c = d = e = f= g = h = static_cast<type>(0); \
1.159 + \
1.160 + return(*this); \
1.161 + } \
1.162 + \
1.163 + octonion<type> & operator = (::std::complex<type> const & a_affecter) \
1.164 + { \
1.165 + a = a_affecter.real(); \
1.166 + b = a_affecter.imag(); \
1.167 + \
1.168 + c = d = e = f = g = h = static_cast<type>(0); \
1.169 + \
1.170 + return(*this); \
1.171 + } \
1.172 + \
1.173 + octonion<type> & operator = (::boost::math::quaternion<type> const & a_affecter) \
1.174 + { \
1.175 + a = a_affecter.R_component_1(); \
1.176 + b = a_affecter.R_component_2(); \
1.177 + c = a_affecter.R_component_3(); \
1.178 + d = a_affecter.R_component_4(); \
1.179 + \
1.180 + e = f = g = h = static_cast<type>(0); \
1.181 + \
1.182 + return(*this); \
1.183 + }
1.184 +
1.185 +
1.186 +#define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \
1.187 + type a; \
1.188 + type b; \
1.189 + type c; \
1.190 + type d; \
1.191 + type e; \
1.192 + type f; \
1.193 + type g; \
1.194 + type h; \
1.195 +
1.196 +
1.197 + template<typename T>
1.198 + class octonion
1.199 + {
1.200 + public:
1.201 +
1.202 + typedef T value_type;
1.203 +
1.204 + // constructor for O seen as R^8
1.205 + // (also default constructor)
1.206 +
1.207 + explicit octonion( T const & requested_a = T(),
1.208 + T const & requested_b = T(),
1.209 + T const & requested_c = T(),
1.210 + T const & requested_d = T(),
1.211 + T const & requested_e = T(),
1.212 + T const & requested_f = T(),
1.213 + T const & requested_g = T(),
1.214 + T const & requested_h = T())
1.215 + : a(requested_a),
1.216 + b(requested_b),
1.217 + c(requested_c),
1.218 + d(requested_d),
1.219 + e(requested_e),
1.220 + f(requested_f),
1.221 + g(requested_g),
1.222 + h(requested_h)
1.223 + {
1.224 + // nothing to do!
1.225 + }
1.226 +
1.227 +
1.228 + // constructor for H seen as C^4
1.229 +
1.230 + explicit octonion( ::std::complex<T> const & z0,
1.231 + ::std::complex<T> const & z1 = ::std::complex<T>(),
1.232 + ::std::complex<T> const & z2 = ::std::complex<T>(),
1.233 + ::std::complex<T> const & z3 = ::std::complex<T>())
1.234 + : a(z0.real()),
1.235 + b(z0.imag()),
1.236 + c(z1.real()),
1.237 + d(z1.imag()),
1.238 + e(z2.real()),
1.239 + f(z2.imag()),
1.240 + g(z3.real()),
1.241 + h(z3.imag())
1.242 + {
1.243 + // nothing to do!
1.244 + }
1.245 +
1.246 +
1.247 + // constructor for O seen as H^2
1.248 +
1.249 + explicit octonion( ::boost::math::quaternion<T> const & q0,
1.250 + ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>())
1.251 + : a(q0.R_component_1()),
1.252 + b(q0.R_component_2()),
1.253 + c(q0.R_component_3()),
1.254 + d(q0.R_component_4()),
1.255 + e(q1.R_component_1()),
1.256 + f(q1.R_component_2()),
1.257 + g(q1.R_component_3()),
1.258 + h(q1.R_component_4())
1.259 + {
1.260 + // nothing to do!
1.261 + }
1.262 +
1.263 +
1.264 + // UNtemplated copy constructor
1.265 + // (this is taken care of by the compiler itself)
1.266 +
1.267 +
1.268 + // templated copy constructor
1.269 +
1.270 + template<typename X>
1.271 + explicit octonion(octonion<X> const & a_recopier)
1.272 + : a(static_cast<T>(a_recopier.R_component_1())),
1.273 + b(static_cast<T>(a_recopier.R_component_2())),
1.274 + c(static_cast<T>(a_recopier.R_component_3())),
1.275 + d(static_cast<T>(a_recopier.R_component_4())),
1.276 + e(static_cast<T>(a_recopier.R_component_5())),
1.277 + f(static_cast<T>(a_recopier.R_component_6())),
1.278 + g(static_cast<T>(a_recopier.R_component_7())),
1.279 + h(static_cast<T>(a_recopier.R_component_8()))
1.280 + {
1.281 + // nothing to do!
1.282 + }
1.283 +
1.284 +
1.285 + // destructor
1.286 + // (this is taken care of by the compiler itself)
1.287 +
1.288 +
1.289 + // accessors
1.290 + //
1.291 + // Note: Like complex number, octonions do have a meaningful notion of "real part",
1.292 + // but unlike them there is no meaningful notion of "imaginary part".
1.293 + // Instead there is an "unreal part" which itself is an octonion, and usually
1.294 + // nothing simpler (as opposed to the complex number case).
1.295 + // However, for practicallity, there are accessors for the other components
1.296 + // (these are necessary for the templated copy constructor, for instance).
1.297 +
1.298 + BOOST_OCTONION_ACCESSOR_GENERATOR(T)
1.299 +
1.300 + // assignment operators
1.301 +
1.302 + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T)
1.303 +
1.304 + // other assignment-related operators
1.305 + //
1.306 + // NOTE: Octonion multiplication is *NOT* commutative;
1.307 + // symbolically, "q *= rhs;" means "q = q * rhs;"
1.308 + // and "q /= rhs;" means "q = q * inverse_of(rhs);";
1.309 + // octonion multiplication is also *NOT* associative
1.310 +
1.311 + octonion<T> & operator += (T const & rhs)
1.312 + {
1.313 + T at = a + rhs; // exception guard
1.314 +
1.315 + a = at;
1.316 +
1.317 + return(*this);
1.318 + }
1.319 +
1.320 +
1.321 + octonion<T> & operator += (::std::complex<T> const & rhs)
1.322 + {
1.323 + T at = a + rhs.real(); // exception guard
1.324 + T bt = b + rhs.imag(); // exception guard
1.325 +
1.326 + a = at;
1.327 + b = bt;
1.328 +
1.329 + return(*this);
1.330 + }
1.331 +
1.332 +
1.333 + octonion<T> & operator += (::boost::math::quaternion<T> const & rhs)
1.334 + {
1.335 + T at = a + rhs.R_component_1(); // exception guard
1.336 + T bt = b + rhs.R_component_2(); // exception guard
1.337 + T ct = c + rhs.R_component_3(); // exception guard
1.338 + T dt = d + rhs.R_component_4(); // exception guard
1.339 +
1.340 + a = at;
1.341 + b = bt;
1.342 + c = ct;
1.343 + d = dt;
1.344 +
1.345 + return(*this);
1.346 + }
1.347 +
1.348 +
1.349 + template<typename X>
1.350 + octonion<T> & operator += (octonion<X> const & rhs)
1.351 + {
1.352 + T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
1.353 + T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
1.354 + T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
1.355 + T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
1.356 + T et = e + static_cast<T>(rhs.R_component_5()); // exception guard
1.357 + T ft = f + static_cast<T>(rhs.R_component_6()); // exception guard
1.358 + T gt = g + static_cast<T>(rhs.R_component_7()); // exception guard
1.359 + T ht = h + static_cast<T>(rhs.R_component_8()); // exception guard
1.360 +
1.361 + a = at;
1.362 + b = bt;
1.363 + c = ct;
1.364 + d = dt;
1.365 + e = et;
1.366 + f = ft;
1.367 + g = gt;
1.368 + h = ht;
1.369 +
1.370 + return(*this);
1.371 + }
1.372 +
1.373 +
1.374 +
1.375 + octonion<T> & operator -= (T const & rhs)
1.376 + {
1.377 + T at = a - rhs; // exception guard
1.378 +
1.379 + a = at;
1.380 +
1.381 + return(*this);
1.382 + }
1.383 +
1.384 +
1.385 + octonion<T> & operator -= (::std::complex<T> const & rhs)
1.386 + {
1.387 + T at = a - rhs.real(); // exception guard
1.388 + T bt = b - rhs.imag(); // exception guard
1.389 +
1.390 + a = at;
1.391 + b = bt;
1.392 +
1.393 + return(*this);
1.394 + }
1.395 +
1.396 +
1.397 + octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs)
1.398 + {
1.399 + T at = a - rhs.R_component_1(); // exception guard
1.400 + T bt = b - rhs.R_component_2(); // exception guard
1.401 + T ct = c - rhs.R_component_3(); // exception guard
1.402 + T dt = d - rhs.R_component_4(); // exception guard
1.403 +
1.404 + a = at;
1.405 + b = bt;
1.406 + c = ct;
1.407 + d = dt;
1.408 +
1.409 + return(*this);
1.410 + }
1.411 +
1.412 +
1.413 + template<typename X>
1.414 + octonion<T> & operator -= (octonion<X> const & rhs)
1.415 + {
1.416 + T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
1.417 + T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
1.418 + T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
1.419 + T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
1.420 + T et = e - static_cast<T>(rhs.R_component_5()); // exception guard
1.421 + T ft = f - static_cast<T>(rhs.R_component_6()); // exception guard
1.422 + T gt = g - static_cast<T>(rhs.R_component_7()); // exception guard
1.423 + T ht = h - static_cast<T>(rhs.R_component_8()); // exception guard
1.424 +
1.425 + a = at;
1.426 + b = bt;
1.427 + c = ct;
1.428 + d = dt;
1.429 + e = et;
1.430 + f = ft;
1.431 + g = gt;
1.432 + h = ht;
1.433 +
1.434 + return(*this);
1.435 + }
1.436 +
1.437 +
1.438 + octonion<T> & operator *= (T const & rhs)
1.439 + {
1.440 + T at = a * rhs; // exception guard
1.441 + T bt = b * rhs; // exception guard
1.442 + T ct = c * rhs; // exception guard
1.443 + T dt = d * rhs; // exception guard
1.444 + T et = e * rhs; // exception guard
1.445 + T ft = f * rhs; // exception guard
1.446 + T gt = g * rhs; // exception guard
1.447 + T ht = h * rhs; // exception guard
1.448 +
1.449 + a = at;
1.450 + b = bt;
1.451 + c = ct;
1.452 + d = dt;
1.453 + e = et;
1.454 + f = ft;
1.455 + g = gt;
1.456 + h = ht;
1.457 +
1.458 + return(*this);
1.459 + }
1.460 +
1.461 +
1.462 + octonion<T> & operator *= (::std::complex<T> const & rhs)
1.463 + {
1.464 + T ar = rhs.real();
1.465 + T br = rhs.imag();
1.466 +
1.467 + T at = +a*ar-b*br;
1.468 + T bt = +a*br+b*ar;
1.469 + T ct = +c*ar+d*br;
1.470 + T dt = -c*br+d*ar;
1.471 + T et = +e*ar+f*br;
1.472 + T ft = -e*br+f*ar;
1.473 + T gt = +g*ar-h*br;
1.474 + T ht = +g*br+h*ar;
1.475 +
1.476 + a = at;
1.477 + b = bt;
1.478 + c = ct;
1.479 + d = dt;
1.480 + e = et;
1.481 + f = ft;
1.482 + g = gt;
1.483 + h = ht;
1.484 +
1.485 + return(*this);
1.486 + }
1.487 +
1.488 +
1.489 + octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs)
1.490 + {
1.491 + T ar = rhs.R_component_1();
1.492 + T br = rhs.R_component_2();
1.493 + T cr = rhs.R_component_2();
1.494 + T dr = rhs.R_component_2();
1.495 +
1.496 + T at = +a*ar-b*br-c*cr-d*dr;
1.497 + T bt = +a*br+b*ar+c*dr-d*cr;
1.498 + T ct = +a*cr-b*dr+c*ar+d*br;
1.499 + T dt = +a*dr+b*cr-c*br+d*ar;
1.500 + T et = +e*ar+f*br+g*cr+h*dr;
1.501 + T ft = -e*br+f*ar-g*dr+h*cr;
1.502 + T gt = -e*cr+f*dr+g*ar-h*br;
1.503 + T ht = -e*dr-f*cr+g*br+h*ar;
1.504 +
1.505 + a = at;
1.506 + b = bt;
1.507 + c = ct;
1.508 + d = dt;
1.509 + e = et;
1.510 + f = ft;
1.511 + g = gt;
1.512 + h = ht;
1.513 +
1.514 + return(*this);
1.515 + }
1.516 +
1.517 +
1.518 + template<typename X>
1.519 + octonion<T> & operator *= (octonion<X> const & rhs)
1.520 + {
1.521 + T ar = static_cast<T>(rhs.R_component_1());
1.522 + T br = static_cast<T>(rhs.R_component_2());
1.523 + T cr = static_cast<T>(rhs.R_component_3());
1.524 + T dr = static_cast<T>(rhs.R_component_4());
1.525 + T er = static_cast<T>(rhs.R_component_5());
1.526 + T fr = static_cast<T>(rhs.R_component_6());
1.527 + T gr = static_cast<T>(rhs.R_component_7());
1.528 + T hr = static_cast<T>(rhs.R_component_8());
1.529 +
1.530 + T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr;
1.531 + T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr;
1.532 + T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr;
1.533 + T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er;
1.534 + T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr;
1.535 + T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr;
1.536 + T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br;
1.537 + T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar;
1.538 +
1.539 + a = at;
1.540 + b = bt;
1.541 + c = ct;
1.542 + d = dt;
1.543 + e = et;
1.544 + f = ft;
1.545 + g = gt;
1.546 + h = ht;
1.547 +
1.548 + return(*this);
1.549 + }
1.550 +
1.551 +
1.552 + octonion<T> & operator /= (T const & rhs)
1.553 + {
1.554 + T at = a / rhs; // exception guard
1.555 + T bt = b / rhs; // exception guard
1.556 + T ct = c / rhs; // exception guard
1.557 + T dt = d / rhs; // exception guard
1.558 + T et = e / rhs; // exception guard
1.559 + T ft = f / rhs; // exception guard
1.560 + T gt = g / rhs; // exception guard
1.561 + T ht = h / rhs; // exception guard
1.562 +
1.563 + a = at;
1.564 + b = bt;
1.565 + c = ct;
1.566 + d = dt;
1.567 + e = et;
1.568 + f = ft;
1.569 + g = gt;
1.570 + h = ht;
1.571 +
1.572 + return(*this);
1.573 + }
1.574 +
1.575 +
1.576 + octonion<T> & operator /= (::std::complex<T> const & rhs)
1.577 + {
1.578 + T ar = rhs.real();
1.579 + T br = rhs.imag();
1.580 +
1.581 + T denominator = ar*ar+br*br;
1.582 +
1.583 + T at = (+a*ar-b*br)/denominator;
1.584 + T bt = (-a*br+b*ar)/denominator;
1.585 + T ct = (+c*ar-d*br)/denominator;
1.586 + T dt = (+c*br+d*ar)/denominator;
1.587 + T et = (+e*ar-f*br)/denominator;
1.588 + T ft = (+e*br+f*ar)/denominator;
1.589 + T gt = (+g*ar+h*br)/denominator;
1.590 + T ht = (+g*br+h*ar)/denominator;
1.591 +
1.592 + a = at;
1.593 + b = bt;
1.594 + c = ct;
1.595 + d = dt;
1.596 + e = et;
1.597 + f = ft;
1.598 + g = gt;
1.599 + h = ht;
1.600 +
1.601 + return(*this);
1.602 + }
1.603 +
1.604 +
1.605 + octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs)
1.606 + {
1.607 + T ar = rhs.R_component_1();
1.608 + T br = rhs.R_component_2();
1.609 + T cr = rhs.R_component_2();
1.610 + T dr = rhs.R_component_2();
1.611 +
1.612 + T denominator = ar*ar+br*br+cr*cr+dr*dr;
1.613 +
1.614 + T at = (+a*ar+b*br+c*cr+d*dr)/denominator;
1.615 + T bt = (-a*br+b*ar-c*dr+d*cr)/denominator;
1.616 + T ct = (-a*cr+b*dr+c*ar-d*br)/denominator;
1.617 + T dt = (-a*dr-b*cr+c*br+d*ar)/denominator;
1.618 + T et = (+e*ar-f*br-g*cr-h*dr)/denominator;
1.619 + T ft = (+e*br+f*ar+g*dr-h*cr)/denominator;
1.620 + T gt = (+e*cr-f*dr+g*ar+h*br)/denominator;
1.621 + T ht = (+e*dr+f*cr-g*br+h*ar)/denominator;
1.622 +
1.623 + a = at;
1.624 + b = bt;
1.625 + c = ct;
1.626 + d = dt;
1.627 + e = et;
1.628 + f = ft;
1.629 + g = gt;
1.630 + h = ht;
1.631 +
1.632 + return(*this);
1.633 + }
1.634 +
1.635 +
1.636 + template<typename X>
1.637 + octonion<T> & operator /= (octonion<X> const & rhs)
1.638 + {
1.639 + T ar = static_cast<T>(rhs.R_component_1());
1.640 + T br = static_cast<T>(rhs.R_component_2());
1.641 + T cr = static_cast<T>(rhs.R_component_3());
1.642 + T dr = static_cast<T>(rhs.R_component_4());
1.643 + T er = static_cast<T>(rhs.R_component_5());
1.644 + T fr = static_cast<T>(rhs.R_component_6());
1.645 + T gr = static_cast<T>(rhs.R_component_7());
1.646 + T hr = static_cast<T>(rhs.R_component_8());
1.647 +
1.648 + T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr;
1.649 +
1.650 + T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator;
1.651 + T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator;
1.652 + T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator;
1.653 + T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator;
1.654 + T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator;
1.655 + T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator;
1.656 + T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator;
1.657 + T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator;
1.658 +
1.659 + a = at;
1.660 + b = bt;
1.661 + c = ct;
1.662 + d = dt;
1.663 + e = et;
1.664 + f = ft;
1.665 + g = gt;
1.666 + h = ht;
1.667 +
1.668 + return(*this);
1.669 + }
1.670 +
1.671 +
1.672 + protected:
1.673 +
1.674 + BOOST_OCTONION_MEMBER_DATA_GENERATOR(T)
1.675 +
1.676 +
1.677 + private:
1.678 +
1.679 + };
1.680 +
1.681 +
1.682 + // declaration of octonion specialization
1.683 +
1.684 + template<> class octonion<float>;
1.685 + template<> class octonion<double>;
1.686 + template<> class octonion<long double>;
1.687 +
1.688 +
1.689 + // helper templates for converting copy constructors (declaration)
1.690 +
1.691 + namespace detail
1.692 + {
1.693 +
1.694 + template< typename T,
1.695 + typename U
1.696 + >
1.697 + octonion<T> octonion_type_converter(octonion<U> const & rhs);
1.698 + }
1.699 +
1.700 +
1.701 + // implementation of octonion specialization
1.702 +
1.703 +
1.704 +#define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \
1.705 + explicit octonion( type const & requested_a = static_cast<type>(0), \
1.706 + type const & requested_b = static_cast<type>(0), \
1.707 + type const & requested_c = static_cast<type>(0), \
1.708 + type const & requested_d = static_cast<type>(0), \
1.709 + type const & requested_e = static_cast<type>(0), \
1.710 + type const & requested_f = static_cast<type>(0), \
1.711 + type const & requested_g = static_cast<type>(0), \
1.712 + type const & requested_h = static_cast<type>(0)) \
1.713 + : a(requested_a), \
1.714 + b(requested_b), \
1.715 + c(requested_c), \
1.716 + d(requested_d), \
1.717 + e(requested_e), \
1.718 + f(requested_f), \
1.719 + g(requested_g), \
1.720 + h(requested_h) \
1.721 + { \
1.722 + } \
1.723 + \
1.724 + explicit octonion( ::std::complex<type> const & z0, \
1.725 + ::std::complex<type> const & z1 = ::std::complex<type>(), \
1.726 + ::std::complex<type> const & z2 = ::std::complex<type>(), \
1.727 + ::std::complex<type> const & z3 = ::std::complex<type>()) \
1.728 + : a(z0.real()), \
1.729 + b(z0.imag()), \
1.730 + c(z1.real()), \
1.731 + d(z1.imag()), \
1.732 + e(z2.real()), \
1.733 + f(z2.imag()), \
1.734 + g(z3.real()), \
1.735 + h(z3.imag()) \
1.736 + { \
1.737 + } \
1.738 + \
1.739 + explicit octonion( ::boost::math::quaternion<type> const & q0, \
1.740 + ::boost::math::quaternion<type> const & q1 = ::boost::math::quaternion<type>()) \
1.741 + : a(q0.R_component_1()), \
1.742 + b(q0.R_component_2()), \
1.743 + c(q0.R_component_3()), \
1.744 + d(q0.R_component_4()), \
1.745 + e(q1.R_component_1()), \
1.746 + f(q1.R_component_2()), \
1.747 + g(q1.R_component_3()), \
1.748 + h(q1.R_component_4()) \
1.749 + { \
1.750 + }
1.751 +
1.752 +
1.753 +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
1.754 + octonion<type> & operator += (type const & rhs) \
1.755 + { \
1.756 + a += rhs; \
1.757 + \
1.758 + return(*this); \
1.759 + }
1.760 +
1.761 +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
1.762 + octonion<type> & operator += (::std::complex<type> const & rhs) \
1.763 + { \
1.764 + a += rhs.real(); \
1.765 + b += rhs.imag(); \
1.766 + \
1.767 + return(*this); \
1.768 + }
1.769 +
1.770 +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
1.771 + octonion<type> & operator += (::boost::math::quaternion<type> const & rhs) \
1.772 + { \
1.773 + a += rhs.R_component_1(); \
1.774 + b += rhs.R_component_2(); \
1.775 + c += rhs.R_component_3(); \
1.776 + d += rhs.R_component_4(); \
1.777 + \
1.778 + return(*this); \
1.779 + }
1.780 +
1.781 +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \
1.782 + template<typename X> \
1.783 + octonion<type> & operator += (octonion<X> const & rhs) \
1.784 + { \
1.785 + a += static_cast<type>(rhs.R_component_1()); \
1.786 + b += static_cast<type>(rhs.R_component_2()); \
1.787 + c += static_cast<type>(rhs.R_component_3()); \
1.788 + d += static_cast<type>(rhs.R_component_4()); \
1.789 + e += static_cast<type>(rhs.R_component_5()); \
1.790 + f += static_cast<type>(rhs.R_component_6()); \
1.791 + g += static_cast<type>(rhs.R_component_7()); \
1.792 + h += static_cast<type>(rhs.R_component_8()); \
1.793 + \
1.794 + return(*this); \
1.795 + }
1.796 +
1.797 +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
1.798 + octonion<type> & operator -= (type const & rhs) \
1.799 + { \
1.800 + a -= rhs; \
1.801 + \
1.802 + return(*this); \
1.803 + }
1.804 +
1.805 +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
1.806 + octonion<type> & operator -= (::std::complex<type> const & rhs) \
1.807 + { \
1.808 + a -= rhs.real(); \
1.809 + b -= rhs.imag(); \
1.810 + \
1.811 + return(*this); \
1.812 + }
1.813 +
1.814 +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
1.815 + octonion<type> & operator -= (::boost::math::quaternion<type> const & rhs) \
1.816 + { \
1.817 + a -= rhs.R_component_1(); \
1.818 + b -= rhs.R_component_2(); \
1.819 + c -= rhs.R_component_3(); \
1.820 + d -= rhs.R_component_4(); \
1.821 + \
1.822 + return(*this); \
1.823 + }
1.824 +
1.825 +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \
1.826 + template<typename X> \
1.827 + octonion<type> & operator -= (octonion<X> const & rhs) \
1.828 + { \
1.829 + a -= static_cast<type>(rhs.R_component_1()); \
1.830 + b -= static_cast<type>(rhs.R_component_2()); \
1.831 + c -= static_cast<type>(rhs.R_component_3()); \
1.832 + d -= static_cast<type>(rhs.R_component_4()); \
1.833 + e -= static_cast<type>(rhs.R_component_5()); \
1.834 + f -= static_cast<type>(rhs.R_component_6()); \
1.835 + g -= static_cast<type>(rhs.R_component_7()); \
1.836 + h -= static_cast<type>(rhs.R_component_8()); \
1.837 + \
1.838 + return(*this); \
1.839 + }
1.840 +
1.841 +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
1.842 + octonion<type> & operator *= (type const & rhs) \
1.843 + { \
1.844 + a *= rhs; \
1.845 + b *= rhs; \
1.846 + c *= rhs; \
1.847 + d *= rhs; \
1.848 + e *= rhs; \
1.849 + f *= rhs; \
1.850 + g *= rhs; \
1.851 + h *= rhs; \
1.852 + \
1.853 + return(*this); \
1.854 + }
1.855 +
1.856 +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
1.857 + octonion<type> & operator *= (::std::complex<type> const & rhs) \
1.858 + { \
1.859 + type ar = rhs.real(); \
1.860 + type br = rhs.imag(); \
1.861 + \
1.862 + type at = +a*ar-b*br; \
1.863 + type bt = +a*br+b*ar; \
1.864 + type ct = +c*ar+d*br; \
1.865 + type dt = -c*br+d*ar; \
1.866 + type et = +e*ar+f*br; \
1.867 + type ft = -e*br+f*ar; \
1.868 + type gt = +g*ar-h*br; \
1.869 + type ht = +g*br+h*ar; \
1.870 + \
1.871 + a = at; \
1.872 + b = bt; \
1.873 + c = ct; \
1.874 + d = dt; \
1.875 + e = et; \
1.876 + f = ft; \
1.877 + g = gt; \
1.878 + h = ht; \
1.879 + \
1.880 + return(*this); \
1.881 + }
1.882 +
1.883 +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
1.884 + octonion<type> & operator *= (::boost::math::quaternion<type> const & rhs) \
1.885 + { \
1.886 + type ar = rhs.R_component_1(); \
1.887 + type br = rhs.R_component_2(); \
1.888 + type cr = rhs.R_component_2(); \
1.889 + type dr = rhs.R_component_2(); \
1.890 + \
1.891 + type at = +a*ar-b*br-c*cr-d*dr; \
1.892 + type bt = +a*br+b*ar+c*dr-d*cr; \
1.893 + type ct = +a*cr-b*dr+c*ar+d*br; \
1.894 + type dt = +a*dr+b*cr-c*br+d*ar; \
1.895 + type et = +e*ar+f*br+g*cr+h*dr; \
1.896 + type ft = -e*br+f*ar-g*dr+h*cr; \
1.897 + type gt = -e*cr+f*dr+g*ar-h*br; \
1.898 + type ht = -e*dr-f*cr+g*br+h*ar; \
1.899 + \
1.900 + a = at; \
1.901 + b = bt; \
1.902 + c = ct; \
1.903 + d = dt; \
1.904 + e = et; \
1.905 + f = ft; \
1.906 + g = gt; \
1.907 + h = ht; \
1.908 + \
1.909 + return(*this); \
1.910 + }
1.911 +
1.912 +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \
1.913 + template<typename X> \
1.914 + octonion<type> & operator *= (octonion<X> const & rhs) \
1.915 + { \
1.916 + type ar = static_cast<type>(rhs.R_component_1()); \
1.917 + type br = static_cast<type>(rhs.R_component_2()); \
1.918 + type cr = static_cast<type>(rhs.R_component_3()); \
1.919 + type dr = static_cast<type>(rhs.R_component_4()); \
1.920 + type er = static_cast<type>(rhs.R_component_5()); \
1.921 + type fr = static_cast<type>(rhs.R_component_6()); \
1.922 + type gr = static_cast<type>(rhs.R_component_7()); \
1.923 + type hr = static_cast<type>(rhs.R_component_8()); \
1.924 + \
1.925 + type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \
1.926 + type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \
1.927 + type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \
1.928 + type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \
1.929 + type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \
1.930 + type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \
1.931 + type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \
1.932 + type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \
1.933 + \
1.934 + a = at; \
1.935 + b = bt; \
1.936 + c = ct; \
1.937 + d = dt; \
1.938 + e = et; \
1.939 + f = ft; \
1.940 + g = gt; \
1.941 + h = ht; \
1.942 + \
1.943 + return(*this); \
1.944 + }
1.945 +
1.946 +// There is quite a lot of repetition in the code below. This is intentional.
1.947 +// The last conditional block is the normal form, and the others merely
1.948 +// consist of workarounds for various compiler deficiencies. Hopefuly, when
1.949 +// more compilers are conformant and we can retire support for those that are
1.950 +// not, we will be able to remove the clutter. This is makes the situation
1.951 +// (painfully) explicit.
1.952 +
1.953 +#define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
1.954 + octonion<type> & operator /= (type const & rhs) \
1.955 + { \
1.956 + a /= rhs; \
1.957 + b /= rhs; \
1.958 + c /= rhs; \
1.959 + d /= rhs; \
1.960 + \
1.961 + return(*this); \
1.962 + }
1.963 +
1.964 +#if defined(__GNUC__) && (__GNUC__ < 3)
1.965 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1.966 + octonion<type> & operator /= (::std::complex<type> const & rhs) \
1.967 + { \
1.968 + using ::std::valarray; \
1.969 + \
1.970 + valarray<type> tr(2); \
1.971 + \
1.972 + tr[0] = rhs.real(); \
1.973 + tr[1] = rhs.imag(); \
1.974 + \
1.975 + type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)(); \
1.976 + \
1.977 + tr *= mixam; \
1.978 + \
1.979 + valarray<type> tt(8); \
1.980 + \
1.981 + tt[0] = +a*tr[0]-b*tr[1]; \
1.982 + tt[1] = -a*tr[1]+b*tr[0]; \
1.983 + tt[2] = +c*tr[0]-d*tr[1]; \
1.984 + tt[3] = +c*tr[1]+d*tr[0]; \
1.985 + tt[4] = +e*tr[0]-f*tr[1]; \
1.986 + tt[5] = +e*tr[1]+f*tr[0]; \
1.987 + tt[6] = +g*tr[0]+h*tr[1]; \
1.988 + tt[7] = +g*tr[1]+h*tr[0]; \
1.989 + \
1.990 + tr *= tr; \
1.991 + \
1.992 + tt *= (mixam/tr.sum()); \
1.993 + \
1.994 + a = tt[0]; \
1.995 + b = tt[1]; \
1.996 + c = tt[2]; \
1.997 + d = tt[3]; \
1.998 + e = tt[4]; \
1.999 + f = tt[5]; \
1.1000 + g = tt[6]; \
1.1001 + h = tt[7]; \
1.1002 + \
1.1003 + return(*this); \
1.1004 + }
1.1005 +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1.1006 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1.1007 + octonion<type> & operator /= (::std::complex<type> const & rhs) \
1.1008 + { \
1.1009 + using ::std::valarray; \
1.1010 + using ::std::abs; \
1.1011 + \
1.1012 + valarray<type> tr(2); \
1.1013 + \
1.1014 + tr[0] = rhs.real(); \
1.1015 + tr[1] = rhs.imag(); \
1.1016 + \
1.1017 + type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1.1018 + \
1.1019 + tr *= mixam; \
1.1020 + \
1.1021 + valarray<type> tt(8); \
1.1022 + \
1.1023 + tt[0] = +a*tr[0]-b*tr[1]; \
1.1024 + tt[1] = -a*tr[1]+b*tr[0]; \
1.1025 + tt[2] = +c*tr[0]-d*tr[1]; \
1.1026 + tt[3] = +c*tr[1]+d*tr[0]; \
1.1027 + tt[4] = +e*tr[0]-f*tr[1]; \
1.1028 + tt[5] = +e*tr[1]+f*tr[0]; \
1.1029 + tt[6] = +g*tr[0]+h*tr[1]; \
1.1030 + tt[7] = +g*tr[1]+h*tr[0]; \
1.1031 + \
1.1032 + tr *= tr; \
1.1033 + \
1.1034 + tt *= (mixam/tr.sum()); \
1.1035 + \
1.1036 + a = tt[0]; \
1.1037 + b = tt[1]; \
1.1038 + c = tt[2]; \
1.1039 + d = tt[3]; \
1.1040 + e = tt[4]; \
1.1041 + f = tt[5]; \
1.1042 + g = tt[6]; \
1.1043 + h = tt[7]; \
1.1044 + \
1.1045 + return(*this); \
1.1046 + }
1.1047 +#else
1.1048 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1.1049 + octonion<type> & operator /= (::std::complex<type> const & rhs) \
1.1050 + { \
1.1051 + using ::std::valarray; \
1.1052 + \
1.1053 + valarray<type> tr(2); \
1.1054 + \
1.1055 + tr[0] = rhs.real(); \
1.1056 + tr[1] = rhs.imag(); \
1.1057 + \
1.1058 + type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1.1059 + \
1.1060 + tr *= mixam; \
1.1061 + \
1.1062 + valarray<type> tt(8); \
1.1063 + \
1.1064 + tt[0] = +a*tr[0]-b*tr[1]; \
1.1065 + tt[1] = -a*tr[1]+b*tr[0]; \
1.1066 + tt[2] = +c*tr[0]-d*tr[1]; \
1.1067 + tt[3] = +c*tr[1]+d*tr[0]; \
1.1068 + tt[4] = +e*tr[0]-f*tr[1]; \
1.1069 + tt[5] = +e*tr[1]+f*tr[0]; \
1.1070 + tt[6] = +g*tr[0]+h*tr[1]; \
1.1071 + tt[7] = +g*tr[1]+h*tr[0]; \
1.1072 + \
1.1073 + tr *= tr; \
1.1074 + \
1.1075 + tt *= (mixam/tr.sum()); \
1.1076 + \
1.1077 + a = tt[0]; \
1.1078 + b = tt[1]; \
1.1079 + c = tt[2]; \
1.1080 + d = tt[3]; \
1.1081 + e = tt[4]; \
1.1082 + f = tt[5]; \
1.1083 + g = tt[6]; \
1.1084 + h = tt[7]; \
1.1085 + \
1.1086 + return(*this); \
1.1087 + }
1.1088 +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1.1089 +
1.1090 +#if defined(__GNUC__) && (__GNUC__ < 3)
1.1091 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1.1092 + octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1.1093 + { \
1.1094 + using ::std::valarray; \
1.1095 + \
1.1096 + valarray<type> tr(4); \
1.1097 + \
1.1098 + tr[0] = static_cast<type>(rhs.R_component_1()); \
1.1099 + tr[1] = static_cast<type>(rhs.R_component_2()); \
1.1100 + tr[2] = static_cast<type>(rhs.R_component_3()); \
1.1101 + tr[3] = static_cast<type>(rhs.R_component_4()); \
1.1102 + \
1.1103 + type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
1.1104 + \
1.1105 + tr *= mixam; \
1.1106 + \
1.1107 + valarray<type> tt(8); \
1.1108 + \
1.1109 + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
1.1110 + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
1.1111 + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
1.1112 + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
1.1113 + tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1.1114 + tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1.1115 + tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1.1116 + tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1.1117 + \
1.1118 + tr *= tr; \
1.1119 + \
1.1120 + tt *= (mixam/tr.sum()); \
1.1121 + \
1.1122 + a = tt[0]; \
1.1123 + b = tt[1]; \
1.1124 + c = tt[2]; \
1.1125 + d = tt[3]; \
1.1126 + e = tt[4]; \
1.1127 + f = tt[5]; \
1.1128 + g = tt[6]; \
1.1129 + h = tt[7]; \
1.1130 + \
1.1131 + return(*this); \
1.1132 + }
1.1133 +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1.1134 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1.1135 + octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1.1136 + { \
1.1137 + using ::std::valarray; \
1.1138 + using ::std::abs; \
1.1139 + \
1.1140 + valarray<type> tr(4); \
1.1141 + \
1.1142 + tr[0] = static_cast<type>(rhs.R_component_1()); \
1.1143 + tr[1] = static_cast<type>(rhs.R_component_2()); \
1.1144 + tr[2] = static_cast<type>(rhs.R_component_3()); \
1.1145 + tr[3] = static_cast<type>(rhs.R_component_4()); \
1.1146 + \
1.1147 + type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1.1148 + \
1.1149 + tr *= mixam; \
1.1150 + \
1.1151 + valarray<type> tt(8); \
1.1152 + \
1.1153 + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
1.1154 + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
1.1155 + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
1.1156 + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
1.1157 + tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1.1158 + tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1.1159 + tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1.1160 + tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1.1161 + \
1.1162 + tr *= tr; \
1.1163 + \
1.1164 + tt *= (mixam/tr.sum()); \
1.1165 + \
1.1166 + a = tt[0]; \
1.1167 + b = tt[1]; \
1.1168 + c = tt[2]; \
1.1169 + d = tt[3]; \
1.1170 + e = tt[4]; \
1.1171 + f = tt[5]; \
1.1172 + g = tt[6]; \
1.1173 + h = tt[7]; \
1.1174 + \
1.1175 + return(*this); \
1.1176 + }
1.1177 +#else
1.1178 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1.1179 + octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1.1180 + { \
1.1181 + using ::std::valarray; \
1.1182 + \
1.1183 + valarray<type> tr(4); \
1.1184 + \
1.1185 + tr[0] = static_cast<type>(rhs.R_component_1()); \
1.1186 + tr[1] = static_cast<type>(rhs.R_component_2()); \
1.1187 + tr[2] = static_cast<type>(rhs.R_component_3()); \
1.1188 + tr[3] = static_cast<type>(rhs.R_component_4()); \
1.1189 + \
1.1190 + type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1.1191 + \
1.1192 + tr *= mixam; \
1.1193 + \
1.1194 + valarray<type> tt(8); \
1.1195 + \
1.1196 + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
1.1197 + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
1.1198 + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
1.1199 + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
1.1200 + tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1.1201 + tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1.1202 + tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1.1203 + tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1.1204 + \
1.1205 + tr *= tr; \
1.1206 + \
1.1207 + tt *= (mixam/tr.sum()); \
1.1208 + \
1.1209 + a = tt[0]; \
1.1210 + b = tt[1]; \
1.1211 + c = tt[2]; \
1.1212 + d = tt[3]; \
1.1213 + e = tt[4]; \
1.1214 + f = tt[5]; \
1.1215 + g = tt[6]; \
1.1216 + h = tt[7]; \
1.1217 + \
1.1218 + return(*this); \
1.1219 + }
1.1220 +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1.1221 +
1.1222 +#if defined(__GNUC__) && (__GNUC__ < 3)
1.1223 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1.1224 + template<typename X> \
1.1225 + octonion<type> & operator /= (octonion<X> const & rhs) \
1.1226 + { \
1.1227 + using ::std::valarray; \
1.1228 + \
1.1229 + valarray<type> tr(8); \
1.1230 + \
1.1231 + tr[0] = static_cast<type>(rhs.R_component_1()); \
1.1232 + tr[1] = static_cast<type>(rhs.R_component_2()); \
1.1233 + tr[2] = static_cast<type>(rhs.R_component_3()); \
1.1234 + tr[3] = static_cast<type>(rhs.R_component_4()); \
1.1235 + tr[4] = static_cast<type>(rhs.R_component_5()); \
1.1236 + tr[5] = static_cast<type>(rhs.R_component_6()); \
1.1237 + tr[6] = static_cast<type>(rhs.R_component_7()); \
1.1238 + tr[7] = static_cast<type>(rhs.R_component_8()); \
1.1239 + \
1.1240 + type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
1.1241 + \
1.1242 + tr *= mixam; \
1.1243 + \
1.1244 + valarray<type> tt(8); \
1.1245 + \
1.1246 + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
1.1247 + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
1.1248 + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
1.1249 + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
1.1250 + tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1.1251 + tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1.1252 + tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1.1253 + tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1.1254 + \
1.1255 + tr *= tr; \
1.1256 + \
1.1257 + tt *= (mixam/tr.sum()); \
1.1258 + \
1.1259 + a = tt[0]; \
1.1260 + b = tt[1]; \
1.1261 + c = tt[2]; \
1.1262 + d = tt[3]; \
1.1263 + e = tt[4]; \
1.1264 + f = tt[5]; \
1.1265 + g = tt[6]; \
1.1266 + h = tt[7]; \
1.1267 + \
1.1268 + return(*this); \
1.1269 + }
1.1270 +#elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1.1271 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1.1272 + template<typename X> \
1.1273 + octonion<type> & operator /= (octonion<X> const & rhs) \
1.1274 + { \
1.1275 + using ::std::valarray; \
1.1276 + using ::std::abs; \
1.1277 + \
1.1278 + valarray<type> tr(8); \
1.1279 + \
1.1280 + tr[0] = static_cast<type>(rhs.R_component_1()); \
1.1281 + tr[1] = static_cast<type>(rhs.R_component_2()); \
1.1282 + tr[2] = static_cast<type>(rhs.R_component_3()); \
1.1283 + tr[3] = static_cast<type>(rhs.R_component_4()); \
1.1284 + tr[4] = static_cast<type>(rhs.R_component_5()); \
1.1285 + tr[5] = static_cast<type>(rhs.R_component_6()); \
1.1286 + tr[6] = static_cast<type>(rhs.R_component_7()); \
1.1287 + tr[7] = static_cast<type>(rhs.R_component_8()); \
1.1288 + \
1.1289 + type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1.1290 + \
1.1291 + tr *= mixam; \
1.1292 + \
1.1293 + valarray<type> tt(8); \
1.1294 + \
1.1295 + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
1.1296 + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
1.1297 + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
1.1298 + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
1.1299 + tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1.1300 + tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1.1301 + tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1.1302 + tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1.1303 + \
1.1304 + tr *= tr; \
1.1305 + \
1.1306 + tt *= (mixam/tr.sum()); \
1.1307 + \
1.1308 + a = tt[0]; \
1.1309 + b = tt[1]; \
1.1310 + c = tt[2]; \
1.1311 + d = tt[3]; \
1.1312 + e = tt[4]; \
1.1313 + f = tt[5]; \
1.1314 + g = tt[6]; \
1.1315 + h = tt[7]; \
1.1316 + \
1.1317 + return(*this); \
1.1318 + }
1.1319 +#else
1.1320 + #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1.1321 + template<typename X> \
1.1322 + octonion<type> & operator /= (octonion<X> const & rhs) \
1.1323 + { \
1.1324 + using ::std::valarray; \
1.1325 + \
1.1326 + valarray<type> tr(8); \
1.1327 + \
1.1328 + tr[0] = static_cast<type>(rhs.R_component_1()); \
1.1329 + tr[1] = static_cast<type>(rhs.R_component_2()); \
1.1330 + tr[2] = static_cast<type>(rhs.R_component_3()); \
1.1331 + tr[3] = static_cast<type>(rhs.R_component_4()); \
1.1332 + tr[4] = static_cast<type>(rhs.R_component_5()); \
1.1333 + tr[5] = static_cast<type>(rhs.R_component_6()); \
1.1334 + tr[6] = static_cast<type>(rhs.R_component_7()); \
1.1335 + tr[7] = static_cast<type>(rhs.R_component_8()); \
1.1336 + \
1.1337 + type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1.1338 + \
1.1339 + tr *= mixam; \
1.1340 + \
1.1341 + valarray<type> tt(8); \
1.1342 + \
1.1343 + tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]+e*tr[4]+f*tr[5]+g*tr[6]+h*tr[7]; \
1.1344 + tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]-e*tr[5]+f*tr[4]+g*tr[7]-h*tr[6]; \
1.1345 + tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]-e*tr[6]-f*tr[7]+g*tr[4]+h*tr[5]; \
1.1346 + tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]-e*tr[7]+f*tr[6]-g*tr[5]+h*tr[4]; \
1.1347 + tt[4] = -a*tr[4]+b*tr[5]+c*tr[6]+d*tr[7]+e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1.1348 + tt[5] = -a*tr[5]-b*tr[4]+c*tr[7]-d*tr[6]+e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1.1349 + tt[6] = -a*tr[6]-b*tr[7]-c*tr[4]+d*tr[5]+e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1.1350 + tt[7] = -a*tr[7]+b*tr[6]-c*tr[5]-d*tr[4]+e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1.1351 + \
1.1352 + tr *= tr; \
1.1353 + \
1.1354 + tt *= (mixam/tr.sum()); \
1.1355 + \
1.1356 + a = tt[0]; \
1.1357 + b = tt[1]; \
1.1358 + c = tt[2]; \
1.1359 + d = tt[3]; \
1.1360 + e = tt[4]; \
1.1361 + f = tt[5]; \
1.1362 + g = tt[6]; \
1.1363 + h = tt[7]; \
1.1364 + \
1.1365 + return(*this); \
1.1366 + }
1.1367 +#endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1.1368 +
1.1369 +
1.1370 +#define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
1.1371 + BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
1.1372 + BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
1.1373 + BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
1.1374 + BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type)
1.1375 +
1.1376 +#define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
1.1377 + BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
1.1378 + BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
1.1379 + BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
1.1380 + BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type)
1.1381 +
1.1382 +#define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
1.1383 + BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
1.1384 + BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
1.1385 + BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
1.1386 + BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)
1.1387 +
1.1388 +#define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \
1.1389 + BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
1.1390 + BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1.1391 + BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1.1392 + BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type)
1.1393 +
1.1394 +#define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \
1.1395 + BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
1.1396 + BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
1.1397 + BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
1.1398 + BOOST_OCTONION_MEMBER_DIV_GENERATOR(type)
1.1399 +
1.1400 +
1.1401 + template<>
1.1402 + class octonion<float>
1.1403 + {
1.1404 + public:
1.1405 +
1.1406 + typedef float value_type;
1.1407 +
1.1408 + BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
1.1409 +
1.1410 + // UNtemplated copy constructor
1.1411 + // (this is taken care of by the compiler itself)
1.1412 +
1.1413 + // explicit copy constructors (precision-loosing converters)
1.1414 +
1.1415 + explicit octonion(octonion<double> const & a_recopier)
1.1416 + {
1.1417 + *this = detail::octonion_type_converter<float, double>(a_recopier);
1.1418 + }
1.1419 +
1.1420 + explicit octonion(octonion<long double> const & a_recopier)
1.1421 + {
1.1422 + *this = detail::octonion_type_converter<float, long double>(a_recopier);
1.1423 + }
1.1424 +
1.1425 + // destructor
1.1426 + // (this is taken care of by the compiler itself)
1.1427 +
1.1428 + // accessors
1.1429 + //
1.1430 + // Note: Like complex number, octonions do have a meaningful notion of "real part",
1.1431 + // but unlike them there is no meaningful notion of "imaginary part".
1.1432 + // Instead there is an "unreal part" which itself is an octonion, and usually
1.1433 + // nothing simpler (as opposed to the complex number case).
1.1434 + // However, for practicallity, there are accessors for the other components
1.1435 + // (these are necessary for the templated copy constructor, for instance).
1.1436 +
1.1437 + BOOST_OCTONION_ACCESSOR_GENERATOR(float)
1.1438 +
1.1439 + // assignment operators
1.1440 +
1.1441 + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float)
1.1442 +
1.1443 + // other assignment-related operators
1.1444 + //
1.1445 + // NOTE: Octonion multiplication is *NOT* commutative;
1.1446 + // symbolically, "q *= rhs;" means "q = q * rhs;"
1.1447 + // and "q /= rhs;" means "q = q * inverse_of(rhs);";
1.1448 + // octonion multiplication is also *NOT* associative
1.1449 +
1.1450 + BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float)
1.1451 +
1.1452 +
1.1453 + protected:
1.1454 +
1.1455 + BOOST_OCTONION_MEMBER_DATA_GENERATOR(float)
1.1456 +
1.1457 +
1.1458 + private:
1.1459 +
1.1460 + };
1.1461 +
1.1462 +
1.1463 + template<>
1.1464 + class octonion<double>
1.1465 + {
1.1466 + public:
1.1467 +
1.1468 + typedef double value_type;
1.1469 +
1.1470 + BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double)
1.1471 +
1.1472 + // UNtemplated copy constructor
1.1473 + // (this is taken care of by the compiler itself)
1.1474 +
1.1475 + // converting copy constructor
1.1476 +
1.1477 + explicit octonion(octonion<float> const & a_recopier)
1.1478 + {
1.1479 + *this = detail::octonion_type_converter<double, float>(a_recopier);
1.1480 + }
1.1481 +
1.1482 + // explicit copy constructors (precision-loosing converters)
1.1483 +
1.1484 + explicit octonion(octonion<long double> const & a_recopier)
1.1485 + {
1.1486 + *this = detail::octonion_type_converter<double, long double>(a_recopier);
1.1487 + }
1.1488 +
1.1489 + // destructor
1.1490 + // (this is taken care of by the compiler itself)
1.1491 +
1.1492 + // accessors
1.1493 + //
1.1494 + // Note: Like complex number, octonions do have a meaningful notion of "real part",
1.1495 + // but unlike them there is no meaningful notion of "imaginary part".
1.1496 + // Instead there is an "unreal part" which itself is an octonion, and usually
1.1497 + // nothing simpler (as opposed to the complex number case).
1.1498 + // However, for practicallity, there are accessors for the other components
1.1499 + // (these are necessary for the templated copy constructor, for instance).
1.1500 +
1.1501 + BOOST_OCTONION_ACCESSOR_GENERATOR(double)
1.1502 +
1.1503 + // assignment operators
1.1504 +
1.1505 + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double)
1.1506 +
1.1507 + // other assignment-related operators
1.1508 + //
1.1509 + // NOTE: Octonion multiplication is *NOT* commutative;
1.1510 + // symbolically, "q *= rhs;" means "q = q * rhs;"
1.1511 + // and "q /= rhs;" means "q = q * inverse_of(rhs);";
1.1512 + // octonion multiplication is also *NOT* associative
1.1513 +
1.1514 + BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double)
1.1515 +
1.1516 +
1.1517 + protected:
1.1518 +
1.1519 + BOOST_OCTONION_MEMBER_DATA_GENERATOR(double)
1.1520 +
1.1521 +
1.1522 + private:
1.1523 +
1.1524 + };
1.1525 +
1.1526 +
1.1527 + template<>
1.1528 + class octonion<long double>
1.1529 + {
1.1530 + public:
1.1531 +
1.1532 + typedef long double value_type;
1.1533 +
1.1534 + BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double)
1.1535 +
1.1536 + // UNtemplated copy constructor
1.1537 + // (this is taken care of by the compiler itself)
1.1538 +
1.1539 + // converting copy constructor
1.1540 +
1.1541 + explicit octonion(octonion<float> const & a_recopier)
1.1542 + {
1.1543 + *this = detail::octonion_type_converter<long double, float>(a_recopier);
1.1544 + }
1.1545 +
1.1546 +
1.1547 + explicit octonion(octonion<double> const & a_recopier)
1.1548 + {
1.1549 + *this = detail::octonion_type_converter<long double, double>(a_recopier);
1.1550 + }
1.1551 +
1.1552 +
1.1553 + // destructor
1.1554 + // (this is taken care of by the compiler itself)
1.1555 +
1.1556 + // accessors
1.1557 + //
1.1558 + // Note: Like complex number, octonions do have a meaningful notion of "real part",
1.1559 + // but unlike them there is no meaningful notion of "imaginary part".
1.1560 + // Instead there is an "unreal part" which itself is an octonion, and usually
1.1561 + // nothing simpler (as opposed to the complex number case).
1.1562 + // However, for practicallity, there are accessors for the other components
1.1563 + // (these are necessary for the templated copy constructor, for instance).
1.1564 +
1.1565 + BOOST_OCTONION_ACCESSOR_GENERATOR(long double)
1.1566 +
1.1567 + // assignment operators
1.1568 +
1.1569 + BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double)
1.1570 +
1.1571 + // other assignment-related operators
1.1572 + //
1.1573 + // NOTE: Octonion multiplication is *NOT* commutative;
1.1574 + // symbolically, "q *= rhs;" means "q = q * rhs;"
1.1575 + // and "q /= rhs;" means "q = q * inverse_of(rhs);";
1.1576 + // octonion multiplication is also *NOT* associative
1.1577 +
1.1578 + BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double)
1.1579 +
1.1580 +
1.1581 + protected:
1.1582 +
1.1583 + BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double)
1.1584 +
1.1585 +
1.1586 + private:
1.1587 +
1.1588 + };
1.1589 +
1.1590 +
1.1591 +#undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR
1.1592 +
1.1593 +#undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR
1.1594 +
1.1595 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR
1.1596 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR
1.1597 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR
1.1598 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR
1.1599 +
1.1600 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1
1.1601 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2
1.1602 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3
1.1603 +#undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4
1.1604 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1
1.1605 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2
1.1606 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3
1.1607 +#undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4
1.1608 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1
1.1609 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2
1.1610 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3
1.1611 +#undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4
1.1612 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1
1.1613 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2
1.1614 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3
1.1615 +#undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4
1.1616 +
1.1617 +
1.1618 +#undef BOOST_OCTONION_MEMBER_DATA_GENERATOR
1.1619 +
1.1620 +#undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR
1.1621 +
1.1622 +#undef BOOST_OCTONION_ACCESSOR_GENERATOR
1.1623 +
1.1624 +
1.1625 + // operators
1.1626 +
1.1627 +#define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \
1.1628 + { \
1.1629 + octonion<T> res(lhs); \
1.1630 + res op##= rhs; \
1.1631 + return(res); \
1.1632 + }
1.1633 +
1.1634 +#define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
1.1635 + template<typename T> \
1.1636 + inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \
1.1637 + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1.1638 +
1.1639 +#define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
1.1640 + template<typename T> \
1.1641 + inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \
1.1642 + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1.1643 +
1.1644 +#define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
1.1645 + template<typename T> \
1.1646 + inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \
1.1647 + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1.1648 +
1.1649 +#define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
1.1650 + template<typename T> \
1.1651 + inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \
1.1652 + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1.1653 +
1.1654 +#define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
1.1655 + template<typename T> \
1.1656 + inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \
1.1657 + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1.1658 +
1.1659 +#define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
1.1660 + template<typename T> \
1.1661 + inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \
1.1662 + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1.1663 +
1.1664 +#define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \
1.1665 + template<typename T> \
1.1666 + inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \
1.1667 + BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1.1668 +
1.1669 +#define BOOST_OCTONION_OPERATOR_GENERATOR(op) \
1.1670 + BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
1.1671 + BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
1.1672 + BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
1.1673 + BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
1.1674 + BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
1.1675 + BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
1.1676 + BOOST_OCTONION_OPERATOR_GENERATOR_4(op)
1.1677 +
1.1678 +
1.1679 + BOOST_OCTONION_OPERATOR_GENERATOR(+)
1.1680 + BOOST_OCTONION_OPERATOR_GENERATOR(-)
1.1681 + BOOST_OCTONION_OPERATOR_GENERATOR(*)
1.1682 + BOOST_OCTONION_OPERATOR_GENERATOR(/)
1.1683 +
1.1684 +
1.1685 +#undef BOOST_OCTONION_OPERATOR_GENERATOR
1.1686 +
1.1687 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L
1.1688 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R
1.1689 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L
1.1690 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R
1.1691 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L
1.1692 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R
1.1693 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_4
1.1694 +
1.1695 +#undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY
1.1696 +
1.1697 +
1.1698 + template<typename T>
1.1699 + inline octonion<T> operator + (octonion<T> const & o)
1.1700 + {
1.1701 + return(o);
1.1702 + }
1.1703 +
1.1704 +
1.1705 + template<typename T>
1.1706 + inline octonion<T> operator - (octonion<T> const & o)
1.1707 + {
1.1708 + return(octonion<T>(-o.R_component_1(),-o.R_component_2(),-o.R_component_3(),-o.R_component_4(),-o.R_component_5(),-o.R_component_6(),-o.R_component_7(),-o.R_component_8()));
1.1709 + }
1.1710 +
1.1711 +
1.1712 + template<typename T>
1.1713 + inline bool operator == (T const & lhs, octonion<T> const & rhs)
1.1714 + {
1.1715 + return(
1.1716 + (rhs.R_component_1() == lhs)&&
1.1717 + (rhs.R_component_2() == static_cast<T>(0))&&
1.1718 + (rhs.R_component_3() == static_cast<T>(0))&&
1.1719 + (rhs.R_component_4() == static_cast<T>(0))&&
1.1720 + (rhs.R_component_5() == static_cast<T>(0))&&
1.1721 + (rhs.R_component_6() == static_cast<T>(0))&&
1.1722 + (rhs.R_component_7() == static_cast<T>(0))&&
1.1723 + (rhs.R_component_8() == static_cast<T>(0))
1.1724 + );
1.1725 + }
1.1726 +
1.1727 +
1.1728 + template<typename T>
1.1729 + inline bool operator == (octonion<T> const & lhs, T const & rhs)
1.1730 + {
1.1731 + return(
1.1732 + (lhs.R_component_1() == rhs)&&
1.1733 + (lhs.R_component_2() == static_cast<T>(0))&&
1.1734 + (lhs.R_component_3() == static_cast<T>(0))&&
1.1735 + (lhs.R_component_4() == static_cast<T>(0))&&
1.1736 + (lhs.R_component_5() == static_cast<T>(0))&&
1.1737 + (lhs.R_component_6() == static_cast<T>(0))&&
1.1738 + (lhs.R_component_7() == static_cast<T>(0))&&
1.1739 + (lhs.R_component_8() == static_cast<T>(0))
1.1740 + );
1.1741 + }
1.1742 +
1.1743 +
1.1744 + template<typename T>
1.1745 + inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs)
1.1746 + {
1.1747 + return(
1.1748 + (rhs.R_component_1() == lhs.real())&&
1.1749 + (rhs.R_component_2() == lhs.imag())&&
1.1750 + (rhs.R_component_3() == static_cast<T>(0))&&
1.1751 + (rhs.R_component_4() == static_cast<T>(0))&&
1.1752 + (rhs.R_component_5() == static_cast<T>(0))&&
1.1753 + (rhs.R_component_6() == static_cast<T>(0))&&
1.1754 + (rhs.R_component_7() == static_cast<T>(0))&&
1.1755 + (rhs.R_component_8() == static_cast<T>(0))
1.1756 + );
1.1757 + }
1.1758 +
1.1759 +
1.1760 + template<typename T>
1.1761 + inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs)
1.1762 + {
1.1763 + return(
1.1764 + (lhs.R_component_1() == rhs.real())&&
1.1765 + (lhs.R_component_2() == rhs.imag())&&
1.1766 + (lhs.R_component_3() == static_cast<T>(0))&&
1.1767 + (lhs.R_component_4() == static_cast<T>(0))&&
1.1768 + (lhs.R_component_5() == static_cast<T>(0))&&
1.1769 + (lhs.R_component_6() == static_cast<T>(0))&&
1.1770 + (lhs.R_component_7() == static_cast<T>(0))&&
1.1771 + (lhs.R_component_8() == static_cast<T>(0))
1.1772 + );
1.1773 + }
1.1774 +
1.1775 +
1.1776 + template<typename T>
1.1777 + inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
1.1778 + {
1.1779 + return(
1.1780 + (rhs.R_component_1() == lhs.R_component_1())&&
1.1781 + (rhs.R_component_2() == lhs.R_component_2())&&
1.1782 + (rhs.R_component_3() == lhs.R_component_3())&&
1.1783 + (rhs.R_component_4() == lhs.R_component_4())&&
1.1784 + (rhs.R_component_5() == static_cast<T>(0))&&
1.1785 + (rhs.R_component_6() == static_cast<T>(0))&&
1.1786 + (rhs.R_component_7() == static_cast<T>(0))&&
1.1787 + (rhs.R_component_8() == static_cast<T>(0))
1.1788 + );
1.1789 + }
1.1790 +
1.1791 +
1.1792 + template<typename T>
1.1793 + inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
1.1794 + {
1.1795 + return(
1.1796 + (lhs.R_component_1() == rhs.R_component_1())&&
1.1797 + (lhs.R_component_2() == rhs.R_component_2())&&
1.1798 + (lhs.R_component_3() == rhs.R_component_3())&&
1.1799 + (lhs.R_component_4() == rhs.R_component_4())&&
1.1800 + (lhs.R_component_5() == static_cast<T>(0))&&
1.1801 + (lhs.R_component_6() == static_cast<T>(0))&&
1.1802 + (lhs.R_component_7() == static_cast<T>(0))&&
1.1803 + (lhs.R_component_8() == static_cast<T>(0))
1.1804 + );
1.1805 + }
1.1806 +
1.1807 +
1.1808 + template<typename T>
1.1809 + inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs)
1.1810 + {
1.1811 + return(
1.1812 + (rhs.R_component_1() == lhs.R_component_1())&&
1.1813 + (rhs.R_component_2() == lhs.R_component_2())&&
1.1814 + (rhs.R_component_3() == lhs.R_component_3())&&
1.1815 + (rhs.R_component_4() == lhs.R_component_4())&&
1.1816 + (rhs.R_component_5() == lhs.R_component_5())&&
1.1817 + (rhs.R_component_6() == lhs.R_component_6())&&
1.1818 + (rhs.R_component_7() == lhs.R_component_7())&&
1.1819 + (rhs.R_component_8() == lhs.R_component_8())
1.1820 + );
1.1821 + }
1.1822 +
1.1823 +
1.1824 +#define BOOST_OCTONION_NOT_EQUAL_GENERATOR \
1.1825 + { \
1.1826 + return(!(lhs == rhs)); \
1.1827 + }
1.1828 +
1.1829 + template<typename T>
1.1830 + inline bool operator != (T const & lhs, octonion<T> const & rhs)
1.1831 + BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1832 +
1.1833 + template<typename T>
1.1834 + inline bool operator != (octonion<T> const & lhs, T const & rhs)
1.1835 + BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1836 +
1.1837 + template<typename T>
1.1838 + inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs)
1.1839 + BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1840 +
1.1841 + template<typename T>
1.1842 + inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs)
1.1843 + BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1844 +
1.1845 + template<typename T>
1.1846 + inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
1.1847 + BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1848 +
1.1849 + template<typename T>
1.1850 + inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
1.1851 + BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1852 +
1.1853 + template<typename T>
1.1854 + inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs)
1.1855 + BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1856 +
1.1857 + #undef BOOST_OCTONION_NOT_EQUAL_GENERATOR
1.1858 +
1.1859 +
1.1860 + // Note: the default values in the constructors of the complex and quaternions make for
1.1861 + // a very complex and ambiguous situation; we have made choices to disambiguate.
1.1862 +
1.1863 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.1864 + template<typename T>
1.1865 + ::std::istream & operator >> ( ::std::istream & is,
1.1866 + octonion<T>& o)
1.1867 +#else
1.1868 + template<typename T, typename charT, class traits>
1.1869 + ::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
1.1870 + octonion<T> & o)
1.1871 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.1872 + {
1.1873 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.1874 + typedef char charT;
1.1875 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.1876 +
1.1877 +#ifdef BOOST_NO_STD_LOCALE
1.1878 +#else
1.1879 + const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
1.1880 +#endif /* BOOST_NO_STD_LOCALE */
1.1881 +
1.1882 + T a = T();
1.1883 + T b = T();
1.1884 + T c = T();
1.1885 + T d = T();
1.1886 + T e = T();
1.1887 + T f = T();
1.1888 + T g = T();
1.1889 + T h = T();
1.1890 +
1.1891 + ::std::complex<T> u = ::std::complex<T>();
1.1892 + ::std::complex<T> v = ::std::complex<T>();
1.1893 + ::std::complex<T> x = ::std::complex<T>();
1.1894 + ::std::complex<T> y = ::std::complex<T>();
1.1895 +
1.1896 + ::boost::math::quaternion<T> p = ::boost::math::quaternion<T>();
1.1897 + ::boost::math::quaternion<T> q = ::boost::math::quaternion<T>();
1.1898 +
1.1899 + charT ch = charT();
1.1900 + char cc;
1.1901 +
1.1902 + is >> ch; // get the first lexeme
1.1903 +
1.1904 + if (!is.good()) goto finish;
1.1905 +
1.1906 +#ifdef BOOST_NO_STD_LOCALE
1.1907 + cc = ch;
1.1908 +#else
1.1909 + cc = ct.narrow(ch, char());
1.1910 +#endif /* BOOST_NO_STD_LOCALE */
1.1911 +
1.1912 + if (cc == '(') // read "("
1.1913 + {
1.1914 + is >> ch; // get the second lexeme
1.1915 +
1.1916 + if (!is.good()) goto finish;
1.1917 +
1.1918 +#ifdef BOOST_NO_STD_LOCALE
1.1919 + cc = ch;
1.1920 +#else
1.1921 + cc = ct.narrow(ch, char());
1.1922 +#endif /* BOOST_NO_STD_LOCALE */
1.1923 +
1.1924 + if (cc == '(') // read "(("
1.1925 + {
1.1926 + is >> ch; // get the third lexeme
1.1927 +
1.1928 + if (!is.good()) goto finish;
1.1929 +
1.1930 +#ifdef BOOST_NO_STD_LOCALE
1.1931 + cc = ch;
1.1932 +#else
1.1933 + cc = ct.narrow(ch, char());
1.1934 +#endif /* BOOST_NO_STD_LOCALE */
1.1935 +
1.1936 + if (cc == '(') // read "((("
1.1937 + {
1.1938 + is.putback(ch);
1.1939 +
1.1940 + is >> u; // read "((u"
1.1941 +
1.1942 + if (!is.good()) goto finish;
1.1943 +
1.1944 + is >> ch; // get the next lexeme
1.1945 +
1.1946 + if (!is.good()) goto finish;
1.1947 +
1.1948 +#ifdef BOOST_NO_STD_LOCALE
1.1949 + cc = ch;
1.1950 +#else
1.1951 + cc = ct.narrow(ch, char());
1.1952 +#endif /* BOOST_NO_STD_LOCALE */
1.1953 +
1.1954 + if (cc == ')') // read "((u)"
1.1955 + {
1.1956 + is >> ch; // get the next lexeme
1.1957 +
1.1958 + if (!is.good()) goto finish;
1.1959 +
1.1960 +#ifdef BOOST_NO_STD_LOCALE
1.1961 + cc = ch;
1.1962 +#else
1.1963 + cc = ct.narrow(ch, char());
1.1964 +#endif /* BOOST_NO_STD_LOCALE */
1.1965 +
1.1966 + if (cc == ')') // format: (((a))), (((a,b)))
1.1967 + {
1.1968 + o = octonion<T>(u);
1.1969 + }
1.1970 + else if (cc == ',') // read "((u),"
1.1971 + {
1.1972 + p = ::boost::math::quaternion<T>(u);
1.1973 +
1.1974 + is >> q; // read "((u),q"
1.1975 +
1.1976 + if (!is.good()) goto finish;
1.1977 +
1.1978 + is >> ch; // get the next lexeme
1.1979 +
1.1980 + if (!is.good()) goto finish;
1.1981 +
1.1982 +#ifdef BOOST_NO_STD_LOCALE
1.1983 + cc = ch;
1.1984 +#else
1.1985 + cc = ct.narrow(ch, char());
1.1986 +#endif /* BOOST_NO_STD_LOCALE */
1.1987 +
1.1988 + if (cc == ')') // format: (((a)),q), (((a,b)),q)
1.1989 + {
1.1990 + o = octonion<T>(p,q);
1.1991 + }
1.1992 + else // error
1.1993 + {
1.1994 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.1995 + is.setstate(::std::ios::failbit);
1.1996 +#else
1.1997 + is.setstate(::std::ios_base::failbit);
1.1998 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.1999 + }
1.2000 + }
1.2001 + else // error
1.2002 + {
1.2003 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2004 + is.setstate(::std::ios::failbit);
1.2005 +#else
1.2006 + is.setstate(::std::ios_base::failbit);
1.2007 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2008 + }
1.2009 + }
1.2010 + else if (cc ==',') // read "((u,"
1.2011 + {
1.2012 + is >> v; // read "((u,v"
1.2013 +
1.2014 + if (!is.good()) goto finish;
1.2015 +
1.2016 + is >> ch; // get the next lexeme
1.2017 +
1.2018 + if (!is.good()) goto finish;
1.2019 +
1.2020 +#ifdef BOOST_NO_STD_LOCALE
1.2021 + cc = ch;
1.2022 +#else
1.2023 + cc = ct.narrow(ch, char());
1.2024 +#endif /* BOOST_NO_STD_LOCALE */
1.2025 +
1.2026 + if (cc == ')') // read "((u,v)"
1.2027 + {
1.2028 + p = ::boost::math::quaternion<T>(u,v);
1.2029 +
1.2030 + is >> ch; // get the next lexeme
1.2031 +
1.2032 + if (!is.good()) goto finish;
1.2033 +
1.2034 +#ifdef BOOST_NO_STD_LOCALE
1.2035 + cc = ch;
1.2036 +#else
1.2037 + cc = ct.narrow(ch, char());
1.2038 +#endif /* BOOST_NO_STD_LOCALE */
1.2039 +
1.2040 + if (cc == ')') // format: (((a),v)), (((a,b),v))
1.2041 + {
1.2042 + o = octonion<T>(p);
1.2043 + }
1.2044 + else if (cc == ',') // read "((u,v),"
1.2045 + {
1.2046 + is >> q; // read "(p,q"
1.2047 +
1.2048 + if (!is.good()) goto finish;
1.2049 +
1.2050 + is >> ch; // get the next lexeme
1.2051 +
1.2052 + if (!is.good()) goto finish;
1.2053 +
1.2054 +#ifdef BOOST_NO_STD_LOCALE
1.2055 + cc = ch;
1.2056 +#else
1.2057 + cc = ct.narrow(ch, char());
1.2058 +#endif /* BOOST_NO_STD_LOCALE */
1.2059 +
1.2060 + if (cc == ')') // format: (((a),v),q), (((a,b),v),q)
1.2061 + {
1.2062 + o = octonion<T>(p,q);
1.2063 + }
1.2064 + else // error
1.2065 + {
1.2066 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2067 + is.setstate(::std::ios::failbit);
1.2068 +#else
1.2069 + is.setstate(::std::ios_base::failbit);
1.2070 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2071 + }
1.2072 + }
1.2073 + else // error
1.2074 + {
1.2075 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2076 + is.setstate(::std::ios::failbit);
1.2077 +#else
1.2078 + is.setstate(::std::ios_base::failbit);
1.2079 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2080 + }
1.2081 + }
1.2082 + else // error
1.2083 + {
1.2084 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2085 + is.setstate(::std::ios::failbit);
1.2086 +#else
1.2087 + is.setstate(::std::ios_base::failbit);
1.2088 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2089 + }
1.2090 + }
1.2091 + else // error
1.2092 + {
1.2093 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2094 + is.setstate(::std::ios::failbit);
1.2095 +#else
1.2096 + is.setstate(::std::ios_base::failbit);
1.2097 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2098 + }
1.2099 + }
1.2100 + else // read "((a"
1.2101 + {
1.2102 + is.putback(ch);
1.2103 +
1.2104 + is >> a; // we extract the first component
1.2105 +
1.2106 + if (!is.good()) goto finish;
1.2107 +
1.2108 + is >> ch; // get the next lexeme
1.2109 +
1.2110 + if (!is.good()) goto finish;
1.2111 +
1.2112 +#ifdef BOOST_NO_STD_LOCALE
1.2113 + cc = ch;
1.2114 +#else
1.2115 + cc = ct.narrow(ch, char());
1.2116 +#endif /* BOOST_NO_STD_LOCALE */
1.2117 +
1.2118 + if (cc == ')') // read "((a)"
1.2119 + {
1.2120 + is >> ch; // get the next lexeme
1.2121 +
1.2122 + if (!is.good()) goto finish;
1.2123 +
1.2124 +#ifdef BOOST_NO_STD_LOCALE
1.2125 + cc = ch;
1.2126 +#else
1.2127 + cc = ct.narrow(ch, char());
1.2128 +#endif /* BOOST_NO_STD_LOCALE */
1.2129 +
1.2130 + if (cc == ')') // read "((a))"
1.2131 + {
1.2132 + o = octonion<T>(a);
1.2133 + }
1.2134 + else if (cc == ',') // read "((a),"
1.2135 + {
1.2136 + is >> ch; // get the next lexeme
1.2137 +
1.2138 + if (!is.good()) goto finish;
1.2139 +
1.2140 +#ifdef BOOST_NO_STD_LOCALE
1.2141 + cc = ch;
1.2142 +#else
1.2143 + cc = ct.narrow(ch, char());
1.2144 +#endif /* BOOST_NO_STD_LOCALE */
1.2145 +
1.2146 + if (cc == '(') // read "((a),("
1.2147 + {
1.2148 + is >> ch; // get the next lexeme
1.2149 +
1.2150 + if (!is.good()) goto finish;
1.2151 +
1.2152 +#ifdef BOOST_NO_STD_LOCALE
1.2153 + cc = ch;
1.2154 +#else
1.2155 + cc = ct.narrow(ch, char());
1.2156 +#endif /* BOOST_NO_STD_LOCALE */
1.2157 +
1.2158 + if (cc == '(') // read "((a),(("
1.2159 + {
1.2160 + is.putback(ch);
1.2161 +
1.2162 + is.putback(ch); // we backtrack twice, with the same value!
1.2163 +
1.2164 + is >> q; // read "((a),q"
1.2165 +
1.2166 + if (!is.good()) goto finish;
1.2167 +
1.2168 + is >> ch; // get the next lexeme
1.2169 +
1.2170 + if (!is.good()) goto finish;
1.2171 +
1.2172 +#ifdef BOOST_NO_STD_LOCALE
1.2173 + cc = ch;
1.2174 +#else
1.2175 + cc = ct.narrow(ch, char());
1.2176 +#endif /* BOOST_NO_STD_LOCALE */
1.2177 +
1.2178 + if (cc == ')') // read "((a),q)"
1.2179 + {
1.2180 + p = ::boost::math::quaternion<T>(a);
1.2181 +
1.2182 + o = octonion<T>(p,q);
1.2183 + }
1.2184 + else // error
1.2185 + {
1.2186 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2187 + is.setstate(::std::ios::failbit);
1.2188 +#else
1.2189 + is.setstate(::std::ios_base::failbit);
1.2190 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2191 + }
1.2192 + }
1.2193 + else // read "((a),(c" or "((a),(e"
1.2194 + {
1.2195 + is.putback(ch);
1.2196 +
1.2197 + is >> c;
1.2198 +
1.2199 + if (!is.good()) goto finish;
1.2200 +
1.2201 + is >> ch; // get the next lexeme
1.2202 +
1.2203 + if (!is.good()) goto finish;
1.2204 +
1.2205 +#ifdef BOOST_NO_STD_LOCALE
1.2206 + cc = ch;
1.2207 +#else
1.2208 + cc = ct.narrow(ch, char());
1.2209 +#endif /* BOOST_NO_STD_LOCALE */
1.2210 +
1.2211 + if (cc == ')') // read "((a),(c)" (ambiguity resolution)
1.2212 + {
1.2213 + is >> ch; // get the next lexeme
1.2214 +
1.2215 + if (!is.good()) goto finish;
1.2216 +
1.2217 +#ifdef BOOST_NO_STD_LOCALE
1.2218 + cc = ch;
1.2219 +#else
1.2220 + cc = ct.narrow(ch, char());
1.2221 +#endif /* BOOST_NO_STD_LOCALE */
1.2222 +
1.2223 + if (cc == ')') // read "((a),(c))"
1.2224 + {
1.2225 + o = octonion<T>(a,b,c);
1.2226 + }
1.2227 + else if (cc == ',') // read "((a),(c),"
1.2228 + {
1.2229 + u = ::std::complex<T>(a);
1.2230 +
1.2231 + v = ::std::complex<T>(c);
1.2232 +
1.2233 + is >> x; // read "((a),(c),x"
1.2234 +
1.2235 + if (!is.good()) goto finish;
1.2236 +
1.2237 + is >> ch; // get the next lexeme
1.2238 +
1.2239 + if (!is.good()) goto finish;
1.2240 +
1.2241 +#ifdef BOOST_NO_STD_LOCALE
1.2242 + cc = ch;
1.2243 +#else
1.2244 + cc = ct.narrow(ch, char());
1.2245 +#endif /* BOOST_NO_STD_LOCALE */
1.2246 +
1.2247 + if (cc == ')') // read "((a),(c),x)"
1.2248 + {
1.2249 + o = octonion<T>(u,v,x);
1.2250 + }
1.2251 + else if (cc == ',') // read "((a),(c),x,"
1.2252 + {
1.2253 + is >> y; // read "((a),(c),x,y"
1.2254 +
1.2255 + if (!is.good()) goto finish;
1.2256 +
1.2257 + is >> ch; // get the next lexeme
1.2258 +
1.2259 + if (!is.good()) goto finish;
1.2260 +
1.2261 +#ifdef BOOST_NO_STD_LOCALE
1.2262 + cc = ch;
1.2263 +#else
1.2264 + cc = ct.narrow(ch, char());
1.2265 +#endif /* BOOST_NO_STD_LOCALE */
1.2266 +
1.2267 + if (cc == ')') // read "((a),(c),x,y)"
1.2268 + {
1.2269 + o = octonion<T>(u,v,x,y);
1.2270 + }
1.2271 + else // error
1.2272 + {
1.2273 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2274 + is.setstate(::std::ios::failbit);
1.2275 +#else
1.2276 + is.setstate(::std::ios_base::failbit);
1.2277 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2278 + }
1.2279 + }
1.2280 + else // error
1.2281 + {
1.2282 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2283 + is.setstate(::std::ios::failbit);
1.2284 +#else
1.2285 + is.setstate(::std::ios_base::failbit);
1.2286 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2287 + }
1.2288 + }
1.2289 + else // error
1.2290 + {
1.2291 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2292 + is.setstate(::std::ios::failbit);
1.2293 +#else
1.2294 + is.setstate(::std::ios_base::failbit);
1.2295 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2296 + }
1.2297 + }
1.2298 + else if (cc == ',') // read "((a),(c," or "((a),(e,"
1.2299 + {
1.2300 + is >> ch; // get the next lexeme
1.2301 +
1.2302 + if (!is.good()) goto finish;
1.2303 +
1.2304 +#ifdef BOOST_NO_STD_LOCALE
1.2305 + cc = ch;
1.2306 +#else
1.2307 + cc = ct.narrow(ch, char());
1.2308 +#endif /* BOOST_NO_STD_LOCALE */
1.2309 +
1.2310 + if (cc == '(') // read "((a),(e,(" (ambiguity resolution)
1.2311 + {
1.2312 + p = ::boost::math::quaternion<T>(a);
1.2313 +
1.2314 + x = ::std::complex<T>(c); // "c" was actually "e"
1.2315 +
1.2316 + is.putback(ch); // we can only backtrace once
1.2317 +
1.2318 + is >> y; // read "((a),(e,y"
1.2319 +
1.2320 + if (!is.good()) goto finish;
1.2321 +
1.2322 + is >> ch; // get the next lexeme
1.2323 +
1.2324 +#ifdef BOOST_NO_STD_LOCALE
1.2325 + cc = ch;
1.2326 +#else
1.2327 + cc = ct.narrow(ch, char());
1.2328 +#endif /* BOOST_NO_STD_LOCALE */
1.2329 +
1.2330 + if (cc == ')') // read "((a),(e,y)"
1.2331 + {
1.2332 + q = ::boost::math::quaternion<T>(x,y);
1.2333 +
1.2334 + is >> ch; // get the next lexeme
1.2335 +
1.2336 +#ifdef BOOST_NO_STD_LOCALE
1.2337 + cc = ch;
1.2338 +#else
1.2339 + cc = ct.narrow(ch, char());
1.2340 +#endif /* BOOST_NO_STD_LOCALE */
1.2341 +
1.2342 + if (cc == ')') // read "((a),(e,y))"
1.2343 + {
1.2344 + o = octonion<T>(p,q);
1.2345 + }
1.2346 + else // error
1.2347 + {
1.2348 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2349 + is.setstate(::std::ios::failbit);
1.2350 +#else
1.2351 + is.setstate(::std::ios_base::failbit);
1.2352 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2353 + }
1.2354 + }
1.2355 + else // error
1.2356 + {
1.2357 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2358 + is.setstate(::std::ios::failbit);
1.2359 +#else
1.2360 + is.setstate(::std::ios_base::failbit);
1.2361 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2362 + }
1.2363 + }
1.2364 + else // read "((a),(c,d" or "((a),(e,f"
1.2365 + {
1.2366 + is.putback(ch);
1.2367 +
1.2368 + is >> d;
1.2369 +
1.2370 + if (!is.good()) goto finish;
1.2371 +
1.2372 + is >> ch; // get the next lexeme
1.2373 +
1.2374 + if (!is.good()) goto finish;
1.2375 +
1.2376 +#ifdef BOOST_NO_STD_LOCALE
1.2377 + cc = ch;
1.2378 +#else
1.2379 + cc = ct.narrow(ch, char());
1.2380 +#endif /* BOOST_NO_STD_LOCALE */
1.2381 +
1.2382 + if (cc == ')') // read "((a),(c,d)" (ambiguity resolution)
1.2383 + {
1.2384 + is >> ch; // get the next lexeme
1.2385 +
1.2386 + if (!is.good()) goto finish;
1.2387 +
1.2388 +#ifdef BOOST_NO_STD_LOCALE
1.2389 + cc = ch;
1.2390 +#else
1.2391 + cc = ct.narrow(ch, char());
1.2392 +#endif /* BOOST_NO_STD_LOCALE */
1.2393 +
1.2394 + if (cc == ')') // read "((a),(c,d))"
1.2395 + {
1.2396 + o = octonion<T>(a,b,c,d);
1.2397 + }
1.2398 + else if (cc == ',') // read "((a),(c,d),"
1.2399 + {
1.2400 + u = ::std::complex<T>(a);
1.2401 +
1.2402 + v = ::std::complex<T>(c,d);
1.2403 +
1.2404 + is >> x; // read "((a),(c,d),x"
1.2405 +
1.2406 + if (!is.good()) goto finish;
1.2407 +
1.2408 + is >> ch; // get the next lexeme
1.2409 +
1.2410 + if (!is.good()) goto finish;
1.2411 +
1.2412 +#ifdef BOOST_NO_STD_LOCALE
1.2413 + cc = ch;
1.2414 +#else
1.2415 + cc = ct.narrow(ch, char());
1.2416 +#endif /* BOOST_NO_STD_LOCALE */
1.2417 +
1.2418 + if (cc == ')') // read "((a),(c,d),x)"
1.2419 + {
1.2420 + o = octonion<T>(u,v,x);
1.2421 + }
1.2422 + else if (cc == ',') // read "((a),(c,d),x,"
1.2423 + {
1.2424 + is >> y; // read "((a),(c,d),x,y"
1.2425 +
1.2426 + if (!is.good()) goto finish;
1.2427 +
1.2428 + is >> ch; // get the next lexeme
1.2429 +
1.2430 + if (!is.good()) goto finish;
1.2431 +
1.2432 +#ifdef BOOST_NO_STD_LOCALE
1.2433 + cc = ch;
1.2434 +#else
1.2435 + cc = ct.narrow(ch, char());
1.2436 +#endif /* BOOST_NO_STD_LOCALE */
1.2437 +
1.2438 + if (cc == ')') // read "((a),(c,d),x,y)"
1.2439 + {
1.2440 + o = octonion<T>(u,v,x,y);
1.2441 + }
1.2442 + else // error
1.2443 + {
1.2444 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2445 + is.setstate(::std::ios::failbit);
1.2446 +#else
1.2447 + is.setstate(::std::ios_base::failbit);
1.2448 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2449 + }
1.2450 + }
1.2451 + else // error
1.2452 + {
1.2453 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2454 + is.setstate(::std::ios::failbit);
1.2455 +#else
1.2456 + is.setstate(::std::ios_base::failbit);
1.2457 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2458 + }
1.2459 + }
1.2460 + else // error
1.2461 + {
1.2462 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2463 + is.setstate(::std::ios::failbit);
1.2464 +#else
1.2465 + is.setstate(::std::ios_base::failbit);
1.2466 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2467 + }
1.2468 + }
1.2469 + else if (cc == ',') // read "((a),(e,f," (ambiguity resolution)
1.2470 + {
1.2471 + p = ::boost::math::quaternion<T>(a);
1.2472 +
1.2473 + is >> g; // read "((a),(e,f,g" (too late to backtrack)
1.2474 +
1.2475 + if (!is.good()) goto finish;
1.2476 +
1.2477 + is >> ch; // get the next lexeme
1.2478 +
1.2479 + if (!is.good()) goto finish;
1.2480 +
1.2481 +#ifdef BOOST_NO_STD_LOCALE
1.2482 + cc = ch;
1.2483 +#else
1.2484 + cc = ct.narrow(ch, char());
1.2485 +#endif /* BOOST_NO_STD_LOCALE */
1.2486 +
1.2487 + if (cc == ')') // read "((a),(e,f,g)"
1.2488 + {
1.2489 + q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f"
1.2490 +
1.2491 + is >> ch; // get the next lexeme
1.2492 +
1.2493 + if (!is.good()) goto finish;
1.2494 +
1.2495 +#ifdef BOOST_NO_STD_LOCALE
1.2496 + cc = ch;
1.2497 +#else
1.2498 + cc = ct.narrow(ch, char());
1.2499 +#endif /* BOOST_NO_STD_LOCALE */
1.2500 +
1.2501 + if (cc == ')') // read "((a),(e,f,g))"
1.2502 + {
1.2503 + o = octonion<T>(p,q);
1.2504 + }
1.2505 + else // error
1.2506 + {
1.2507 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2508 + is.setstate(::std::ios::failbit);
1.2509 +#else
1.2510 + is.setstate(::std::ios_base::failbit);
1.2511 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2512 + }
1.2513 + }
1.2514 + else if (cc == ',') // read "((a),(e,f,g,"
1.2515 + {
1.2516 + is >> h; // read "((a),(e,f,g,h"
1.2517 +
1.2518 + if (!is.good()) goto finish;
1.2519 +
1.2520 + is >> ch; // get the next lexeme
1.2521 +
1.2522 + if (!is.good()) goto finish;
1.2523 +
1.2524 +#ifdef BOOST_NO_STD_LOCALE
1.2525 + cc = ch;
1.2526 +#else
1.2527 + cc = ct.narrow(ch, char());
1.2528 +#endif /* BOOST_NO_STD_LOCALE */
1.2529 +
1.2530 + if (cc == ')') // read "((a),(e,f,g,h)"
1.2531 + {
1.2532 + q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f"
1.2533 +
1.2534 + is >> ch; // get the next lexeme
1.2535 +
1.2536 + if (!is.good()) goto finish;
1.2537 +
1.2538 +#ifdef BOOST_NO_STD_LOCALE
1.2539 + cc = ch;
1.2540 +#else
1.2541 + cc = ct.narrow(ch, char());
1.2542 +#endif /* BOOST_NO_STD_LOCALE */
1.2543 +
1.2544 + if (cc == ')') // read "((a),(e,f,g,h))"
1.2545 + {
1.2546 + o = octonion<T>(p,q);
1.2547 + }
1.2548 + else // error
1.2549 + {
1.2550 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2551 + is.setstate(::std::ios::failbit);
1.2552 +#else
1.2553 + is.setstate(::std::ios_base::failbit);
1.2554 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2555 + }
1.2556 + }
1.2557 + else // error
1.2558 + {
1.2559 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2560 + is.setstate(::std::ios::failbit);
1.2561 +#else
1.2562 + is.setstate(::std::ios_base::failbit);
1.2563 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2564 + }
1.2565 + }
1.2566 + else // error
1.2567 + {
1.2568 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2569 + is.setstate(::std::ios::failbit);
1.2570 +#else
1.2571 + is.setstate(::std::ios_base::failbit);
1.2572 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2573 + }
1.2574 + }
1.2575 + else // error
1.2576 + {
1.2577 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2578 + is.setstate(::std::ios::failbit);
1.2579 +#else
1.2580 + is.setstate(::std::ios_base::failbit);
1.2581 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2582 + }
1.2583 + }
1.2584 + }
1.2585 + else // error
1.2586 + {
1.2587 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2588 + is.setstate(::std::ios::failbit);
1.2589 +#else
1.2590 + is.setstate(::std::ios_base::failbit);
1.2591 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2592 + }
1.2593 + }
1.2594 + }
1.2595 + else // read "((a),c" (ambiguity resolution)
1.2596 + {
1.2597 + is.putback(ch);
1.2598 +
1.2599 + is >> c; // we extract the third component
1.2600 +
1.2601 + if (!is.good()) goto finish;
1.2602 +
1.2603 + is >> ch; // get the next lexeme
1.2604 +
1.2605 + if (!is.good()) goto finish;
1.2606 +
1.2607 +#ifdef BOOST_NO_STD_LOCALE
1.2608 + cc = ch;
1.2609 +#else
1.2610 + cc = ct.narrow(ch, char());
1.2611 +#endif /* BOOST_NO_STD_LOCALE */
1.2612 +
1.2613 + if (cc == ')') // read "((a),c)"
1.2614 + {
1.2615 + o = octonion<T>(a,b,c);
1.2616 + }
1.2617 + else if (cc == ',') // read "((a),c,"
1.2618 + {
1.2619 + is >> x; // read "((a),c,x"
1.2620 +
1.2621 + if (!is.good()) goto finish;
1.2622 +
1.2623 + is >> ch; // get the next lexeme
1.2624 +
1.2625 + if (!is.good()) goto finish;
1.2626 +
1.2627 +#ifdef BOOST_NO_STD_LOCALE
1.2628 + cc = ch;
1.2629 +#else
1.2630 + cc = ct.narrow(ch, char());
1.2631 +#endif /* BOOST_NO_STD_LOCALE */
1.2632 +
1.2633 + if (cc == ')') // read "((a),c,x)"
1.2634 + {
1.2635 + o = octonion<T>(a,b,c,d,x.real(),x.imag());
1.2636 + }
1.2637 + else if (cc == ',') // read "((a),c,x,"
1.2638 + {
1.2639 + is >> y;if (!is.good()) goto finish; // read "((a),c,x,y"
1.2640 +
1.2641 + is >> ch; // get the next lexeme
1.2642 +
1.2643 + if (!is.good()) goto finish;
1.2644 +
1.2645 +#ifdef BOOST_NO_STD_LOCALE
1.2646 + cc = ch;
1.2647 +#else
1.2648 + cc = ct.narrow(ch, char());
1.2649 +#endif /* BOOST_NO_STD_LOCALE */
1.2650 +
1.2651 + if (cc == ')') // read "((a),c,x,y)"
1.2652 + {
1.2653 + o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag());
1.2654 + }
1.2655 + else // error
1.2656 + {
1.2657 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2658 + is.setstate(::std::ios::failbit);
1.2659 +#else
1.2660 + is.setstate(::std::ios_base::failbit);
1.2661 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2662 + }
1.2663 + }
1.2664 + else // error
1.2665 + {
1.2666 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2667 + is.setstate(::std::ios::failbit);
1.2668 +#else
1.2669 + is.setstate(::std::ios_base::failbit);
1.2670 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2671 + }
1.2672 + }
1.2673 + else // error
1.2674 + {
1.2675 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2676 + is.setstate(::std::ios::failbit);
1.2677 +#else
1.2678 + is.setstate(::std::ios_base::failbit);
1.2679 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2680 + }
1.2681 + }
1.2682 + }
1.2683 + else // error
1.2684 + {
1.2685 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2686 + is.setstate(::std::ios::failbit);
1.2687 +#else
1.2688 + is.setstate(::std::ios_base::failbit);
1.2689 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2690 + }
1.2691 + }
1.2692 + else if (cc ==',') // read "((a,"
1.2693 + {
1.2694 + is >> ch; // get the next lexeme
1.2695 +
1.2696 + if (!is.good()) goto finish;
1.2697 +
1.2698 +#ifdef BOOST_NO_STD_LOCALE
1.2699 + cc = ch;
1.2700 +#else
1.2701 + cc = ct.narrow(ch, char());
1.2702 +#endif /* BOOST_NO_STD_LOCALE */
1.2703 +
1.2704 + if (cc == '(') // read "((a,("
1.2705 + {
1.2706 + u = ::std::complex<T>(a);
1.2707 +
1.2708 + is.putback(ch); // can only backtrack so much
1.2709 +
1.2710 + is >> v; // read "((a,v"
1.2711 +
1.2712 + if (!is.good()) goto finish;
1.2713 +
1.2714 + is >> ch; // get the next lexeme
1.2715 +
1.2716 + if (!is.good()) goto finish;
1.2717 +
1.2718 +#ifdef BOOST_NO_STD_LOCALE
1.2719 + cc = ch;
1.2720 +#else
1.2721 + cc = ct.narrow(ch, char());
1.2722 +#endif /* BOOST_NO_STD_LOCALE */
1.2723 +
1.2724 + if (cc == ')') // read "((a,v)"
1.2725 + {
1.2726 + is >> ch; // get the next lexeme
1.2727 +
1.2728 + if (!is.good()) goto finish;
1.2729 +
1.2730 +#ifdef BOOST_NO_STD_LOCALE
1.2731 + cc = ch;
1.2732 +#else
1.2733 + cc = ct.narrow(ch, char());
1.2734 +#endif /* BOOST_NO_STD_LOCALE */
1.2735 +
1.2736 + if (cc == ')') // read "((a,v))"
1.2737 + {
1.2738 + o = octonion<T>(u,v);
1.2739 + }
1.2740 + else if (cc == ',') // read "((a,v),"
1.2741 + {
1.2742 + p = ::boost::math::quaternion<T>(u,v);
1.2743 +
1.2744 + is >> q; // read "((a,v),q"
1.2745 +
1.2746 + if (!is.good()) goto finish;
1.2747 +
1.2748 + is >> ch; // get the next lexeme
1.2749 +
1.2750 + if (!is.good()) goto finish;
1.2751 +
1.2752 +#ifdef BOOST_NO_STD_LOCALE
1.2753 + cc = ch;
1.2754 +#else
1.2755 + cc = ct.narrow(ch, char());
1.2756 +#endif /* BOOST_NO_STD_LOCALE */
1.2757 +
1.2758 + if (cc == ')') // read "((a,v),q)"
1.2759 + {
1.2760 + o = octonion<T>(p,q);
1.2761 + }
1.2762 + else // error
1.2763 + {
1.2764 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2765 + is.setstate(::std::ios::failbit);
1.2766 +#else
1.2767 + is.setstate(::std::ios_base::failbit);
1.2768 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2769 + }
1.2770 + }
1.2771 + else // error
1.2772 + {
1.2773 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2774 + is.setstate(::std::ios::failbit);
1.2775 +#else
1.2776 + is.setstate(::std::ios_base::failbit);
1.2777 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2778 + }
1.2779 + }
1.2780 + else // error
1.2781 + {
1.2782 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2783 + is.setstate(::std::ios::failbit);
1.2784 +#else
1.2785 + is.setstate(::std::ios_base::failbit);
1.2786 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2787 + }
1.2788 + }
1.2789 + else
1.2790 + {
1.2791 + is.putback(ch);
1.2792 +
1.2793 + is >> b; // read "((a,b"
1.2794 +
1.2795 + if (!is.good()) goto finish;
1.2796 +
1.2797 + is >> ch; // get the next lexeme
1.2798 +
1.2799 + if (!is.good()) goto finish;
1.2800 +
1.2801 +#ifdef BOOST_NO_STD_LOCALE
1.2802 + cc = ch;
1.2803 +#else
1.2804 + cc = ct.narrow(ch, char());
1.2805 +#endif /* BOOST_NO_STD_LOCALE */
1.2806 +
1.2807 + if (cc == ')') // read "((a,b)"
1.2808 + {
1.2809 + is >> ch; // get the next lexeme
1.2810 +
1.2811 + if (!is.good()) goto finish;
1.2812 +
1.2813 +#ifdef BOOST_NO_STD_LOCALE
1.2814 + cc = ch;
1.2815 +#else
1.2816 + cc = ct.narrow(ch, char());
1.2817 +#endif /* BOOST_NO_STD_LOCALE */
1.2818 +
1.2819 + if (cc == ')') // read "((a,b))"
1.2820 + {
1.2821 + o = octonion<T>(a,b);
1.2822 + }
1.2823 + else if (cc == ',') // read "((a,b),"
1.2824 + {
1.2825 + is >> ch; // get the next lexeme
1.2826 +
1.2827 + if (!is.good()) goto finish;
1.2828 +
1.2829 +#ifdef BOOST_NO_STD_LOCALE
1.2830 + cc = ch;
1.2831 +#else
1.2832 + cc = ct.narrow(ch, char());
1.2833 +#endif /* BOOST_NO_STD_LOCALE */
1.2834 +
1.2835 + if (cc == '(') // read "((a,b),("
1.2836 + {
1.2837 + is >> ch; // get the next lexeme
1.2838 +
1.2839 + if (!is.good()) goto finish;
1.2840 +
1.2841 +#ifdef BOOST_NO_STD_LOCALE
1.2842 + cc = ch;
1.2843 +#else
1.2844 + cc = ct.narrow(ch, char());
1.2845 +#endif /* BOOST_NO_STD_LOCALE */
1.2846 +
1.2847 + if (cc == '(') // read "((a,b),(("
1.2848 + {
1.2849 + p = ::boost::math::quaternion<T>(a,b);
1.2850 +
1.2851 + is.putback(ch);
1.2852 +
1.2853 + is.putback(ch); // we backtrack twice, with the same value
1.2854 +
1.2855 + is >> q; // read "((a,b),q"
1.2856 +
1.2857 + if (!is.good()) goto finish;
1.2858 +
1.2859 + is >> ch; // get the next lexeme
1.2860 +
1.2861 + if (!is.good()) goto finish;
1.2862 +
1.2863 +#ifdef BOOST_NO_STD_LOCALE
1.2864 + cc = ch;
1.2865 +#else
1.2866 + cc = ct.narrow(ch, char());
1.2867 +#endif /* BOOST_NO_STD_LOCALE */
1.2868 +
1.2869 + if (cc == ')') // read "((a,b),q)"
1.2870 + {
1.2871 + o = octonion<T>(p,q);
1.2872 + }
1.2873 + else // error
1.2874 + {
1.2875 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2876 + is.setstate(::std::ios::failbit);
1.2877 +#else
1.2878 + is.setstate(::std::ios_base::failbit);
1.2879 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2880 + }
1.2881 + }
1.2882 + else // read "((a,b),(c" or "((a,b),(e"
1.2883 + {
1.2884 + is.putback(ch);
1.2885 +
1.2886 + is >> c;
1.2887 +
1.2888 + if (!is.good()) goto finish;
1.2889 +
1.2890 + is >> ch; // get the next lexeme
1.2891 +
1.2892 + if (!is.good()) goto finish;
1.2893 +
1.2894 +#ifdef BOOST_NO_STD_LOCALE
1.2895 + cc = ch;
1.2896 +#else
1.2897 + cc = ct.narrow(ch, char());
1.2898 +#endif /* BOOST_NO_STD_LOCALE */
1.2899 +
1.2900 + if (cc == ')') // read "((a,b),(c)" (ambiguity resolution)
1.2901 + {
1.2902 + is >> ch; // get the next lexeme
1.2903 +
1.2904 + if (!is.good()) goto finish;
1.2905 +
1.2906 +#ifdef BOOST_NO_STD_LOCALE
1.2907 + cc = ch;
1.2908 +#else
1.2909 + cc = ct.narrow(ch, char());
1.2910 +#endif /* BOOST_NO_STD_LOCALE */
1.2911 +
1.2912 + if (cc == ')') // read "((a,b),(c))"
1.2913 + {
1.2914 + o = octonion<T>(a,b,c);
1.2915 + }
1.2916 + else if (cc == ',') // read "((a,b),(c),"
1.2917 + {
1.2918 + u = ::std::complex<T>(a,b);
1.2919 +
1.2920 + v = ::std::complex<T>(c);
1.2921 +
1.2922 + is >> x; // read "((a,b),(c),x"
1.2923 +
1.2924 + if (!is.good()) goto finish;
1.2925 +
1.2926 + is >> ch; // get the next lexeme
1.2927 +
1.2928 + if (!is.good()) goto finish;
1.2929 +
1.2930 +#ifdef BOOST_NO_STD_LOCALE
1.2931 + cc = ch;
1.2932 +#else
1.2933 + cc = ct.narrow(ch, char());
1.2934 +#endif /* BOOST_NO_STD_LOCALE */
1.2935 +
1.2936 + if (cc == ')') // read "((a,b),(c),x)"
1.2937 + {
1.2938 + o = octonion<T>(u,v,x);
1.2939 + }
1.2940 + else if (cc == ',') // read "((a,b),(c),x,"
1.2941 + {
1.2942 + is >> y; // read "((a,b),(c),x,y"
1.2943 +
1.2944 + if (!is.good()) goto finish;
1.2945 +
1.2946 + is >> ch; // get the next lexeme
1.2947 +
1.2948 + if (!is.good()) goto finish;
1.2949 +
1.2950 +#ifdef BOOST_NO_STD_LOCALE
1.2951 + cc = ch;
1.2952 +#else
1.2953 + cc = ct.narrow(ch, char());
1.2954 +#endif /* BOOST_NO_STD_LOCALE */
1.2955 +
1.2956 + if (cc == ')') // read "((a,b),(c),x,y)"
1.2957 + {
1.2958 + o = octonion<T>(u,v,x,y);
1.2959 + }
1.2960 + else // error
1.2961 + {
1.2962 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2963 + is.setstate(::std::ios::failbit);
1.2964 +#else
1.2965 + is.setstate(::std::ios_base::failbit);
1.2966 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2967 + }
1.2968 + }
1.2969 + else // error
1.2970 + {
1.2971 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2972 + is.setstate(::std::ios::failbit);
1.2973 +#else
1.2974 + is.setstate(::std::ios_base::failbit);
1.2975 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2976 + }
1.2977 + }
1.2978 + else // error
1.2979 + {
1.2980 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.2981 + is.setstate(::std::ios::failbit);
1.2982 +#else
1.2983 + is.setstate(::std::ios_base::failbit);
1.2984 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.2985 + }
1.2986 + }
1.2987 + else if (cc == ',') // read "((a,b),(c," or "((a,b),(e,"
1.2988 + {
1.2989 + is >> ch; // get the next lexeme
1.2990 +
1.2991 + if (!is.good()) goto finish;
1.2992 +
1.2993 +#ifdef BOOST_NO_STD_LOCALE
1.2994 + cc = ch;
1.2995 +#else
1.2996 + cc = ct.narrow(ch, char());
1.2997 +#endif /* BOOST_NO_STD_LOCALE */
1.2998 +
1.2999 + if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution)
1.3000 + {
1.3001 + u = ::std::complex<T>(a,b);
1.3002 +
1.3003 + x = ::std::complex<T>(c); // "c" is actually "e"
1.3004 +
1.3005 + is.putback(ch);
1.3006 +
1.3007 + is >> y; // read "((a,b),(e,y"
1.3008 +
1.3009 + if (!is.good()) goto finish;
1.3010 +
1.3011 + is >> ch; // get the next lexeme
1.3012 +
1.3013 + if (!is.good()) goto finish;
1.3014 +
1.3015 +#ifdef BOOST_NO_STD_LOCALE
1.3016 + cc = ch;
1.3017 +#else
1.3018 + cc = ct.narrow(ch, char());
1.3019 +#endif /* BOOST_NO_STD_LOCALE */
1.3020 +
1.3021 + if (cc == ')') // read "((a,b),(e,y)"
1.3022 + {
1.3023 + is >> ch; // get the next lexeme
1.3024 +
1.3025 + if (!is.good()) goto finish;
1.3026 +
1.3027 +#ifdef BOOST_NO_STD_LOCALE
1.3028 + cc = ch;
1.3029 +#else
1.3030 + cc = ct.narrow(ch, char());
1.3031 +#endif /* BOOST_NO_STD_LOCALE */
1.3032 +
1.3033 + if (cc == ')') // read "((a,b),(e,y))"
1.3034 + {
1.3035 + o = octonion<T>(u,v,x,y);
1.3036 + }
1.3037 + else // error
1.3038 + {
1.3039 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3040 + is.setstate(::std::ios::failbit);
1.3041 +#else
1.3042 + is.setstate(::std::ios_base::failbit);
1.3043 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3044 + }
1.3045 + }
1.3046 + else // error
1.3047 + {
1.3048 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3049 + is.setstate(::std::ios::failbit);
1.3050 +#else
1.3051 + is.setstate(::std::ios_base::failbit);
1.3052 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3053 + }
1.3054 + }
1.3055 + else // read "((a,b),(c,d" or "((a,b),(e,f"
1.3056 + {
1.3057 + is.putback(ch);
1.3058 +
1.3059 + is >> d;
1.3060 +
1.3061 + if (!is.good()) goto finish;
1.3062 +
1.3063 + is >> ch; // get the next lexeme
1.3064 +
1.3065 + if (!is.good()) goto finish;
1.3066 +
1.3067 +#ifdef BOOST_NO_STD_LOCALE
1.3068 + cc = ch;
1.3069 +#else
1.3070 + cc = ct.narrow(ch, char());
1.3071 +#endif /* BOOST_NO_STD_LOCALE */
1.3072 +
1.3073 + if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution)
1.3074 + {
1.3075 + u = ::std::complex<T>(a,b);
1.3076 +
1.3077 + v = ::std::complex<T>(c,d);
1.3078 +
1.3079 + is >> ch; // get the next lexeme
1.3080 +
1.3081 + if (!is.good()) goto finish;
1.3082 +
1.3083 +#ifdef BOOST_NO_STD_LOCALE
1.3084 + cc = ch;
1.3085 +#else
1.3086 + cc = ct.narrow(ch, char());
1.3087 +#endif /* BOOST_NO_STD_LOCALE */
1.3088 +
1.3089 + if (cc == ')') // read "((a,b),(c,d))"
1.3090 + {
1.3091 + o = octonion<T>(u,v);
1.3092 + }
1.3093 + else if (cc == ',') // read "((a,b),(c,d),"
1.3094 + {
1.3095 + is >> x; // read "((a,b),(c,d),x
1.3096 +
1.3097 + if (!is.good()) goto finish;
1.3098 +
1.3099 + is >> ch; // get the next lexeme
1.3100 +
1.3101 + if (!is.good()) goto finish;
1.3102 +
1.3103 +#ifdef BOOST_NO_STD_LOCALE
1.3104 + cc = ch;
1.3105 +#else
1.3106 + cc = ct.narrow(ch, char());
1.3107 +#endif /* BOOST_NO_STD_LOCALE */
1.3108 +
1.3109 + if (cc == ')') // read "((a,b),(c,d),x)"
1.3110 + {
1.3111 + o = octonion<T>(u,v,x);
1.3112 + }
1.3113 + else if (cc == ',') // read "((a,b),(c,d),x,"
1.3114 + {
1.3115 + is >> y; // read "((a,b),(c,d),x,y"
1.3116 +
1.3117 + if (!is.good()) goto finish;
1.3118 +
1.3119 + is >> ch; // get the next lexeme
1.3120 +
1.3121 + if (!is.good()) goto finish;
1.3122 +
1.3123 +#ifdef BOOST_NO_STD_LOCALE
1.3124 + cc = ch;
1.3125 +#else
1.3126 + cc = ct.narrow(ch, char());
1.3127 +#endif /* BOOST_NO_STD_LOCALE */
1.3128 +
1.3129 + if (cc == ')') // read "((a,b),(c,d),x,y)"
1.3130 + {
1.3131 + o = octonion<T>(u,v,x,y);
1.3132 + }
1.3133 + else // error
1.3134 + {
1.3135 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3136 + is.setstate(::std::ios::failbit);
1.3137 +#else
1.3138 + is.setstate(::std::ios_base::failbit);
1.3139 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3140 + }
1.3141 + }
1.3142 + else // error
1.3143 + {
1.3144 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3145 + is.setstate(::std::ios::failbit);
1.3146 +#else
1.3147 + is.setstate(::std::ios_base::failbit);
1.3148 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3149 + }
1.3150 + }
1.3151 + else // error
1.3152 + {
1.3153 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3154 + is.setstate(::std::ios::failbit);
1.3155 +#else
1.3156 + is.setstate(::std::ios_base::failbit);
1.3157 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3158 + }
1.3159 + }
1.3160 + else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution)
1.3161 + {
1.3162 + p = ::boost::math::quaternion<T>(a,b); // too late to backtrack
1.3163 +
1.3164 + is >> g; // read "((a,b),(e,f,g"
1.3165 +
1.3166 + if (!is.good()) goto finish;
1.3167 +
1.3168 + is >> ch; // get the next lexeme
1.3169 +
1.3170 + if (!is.good()) goto finish;
1.3171 +
1.3172 +#ifdef BOOST_NO_STD_LOCALE
1.3173 + cc = ch;
1.3174 +#else
1.3175 + cc = ct.narrow(ch, char());
1.3176 +#endif /* BOOST_NO_STD_LOCALE */
1.3177 +
1.3178 + if (cc == ')') // read "((a,b),(e,f,g)"
1.3179 + {
1.3180 + is >> ch; // get the next lexeme
1.3181 +
1.3182 + if (!is.good()) goto finish;
1.3183 +
1.3184 +#ifdef BOOST_NO_STD_LOCALE
1.3185 + cc = ch;
1.3186 +#else
1.3187 + cc = ct.narrow(ch, char());
1.3188 +#endif /* BOOST_NO_STD_LOCALE */
1.3189 +
1.3190 + if (cc == ')') // read "((a,b),(e,f,g))"
1.3191 + {
1.3192 + q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
1.3193 +
1.3194 + o = octonion<T>(p,q);
1.3195 + }
1.3196 + else // error
1.3197 + {
1.3198 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3199 + is.setstate(::std::ios::failbit);
1.3200 +#else
1.3201 + is.setstate(::std::ios_base::failbit);
1.3202 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3203 + }
1.3204 + }
1.3205 + else if (cc == ',') // read "((a,b),(e,f,g,"
1.3206 + {
1.3207 + is >> h; // read "((a,b),(e,f,g,h"
1.3208 +
1.3209 + if (!is.good()) goto finish;
1.3210 +
1.3211 + is >> ch; // get the next lexeme
1.3212 +
1.3213 + if (!is.good()) goto finish;
1.3214 +
1.3215 +#ifdef BOOST_NO_STD_LOCALE
1.3216 + cc = ch;
1.3217 +#else
1.3218 + cc = ct.narrow(ch, char());
1.3219 +#endif /* BOOST_NO_STD_LOCALE */
1.3220 +
1.3221 + if (cc == ')') // read "((a,b),(e,f,g,h)"
1.3222 + {
1.3223 + is >> ch; // get the next lexeme
1.3224 +
1.3225 + if (!is.good()) goto finish;
1.3226 +
1.3227 +#ifdef BOOST_NO_STD_LOCALE
1.3228 + cc = ch;
1.3229 +#else
1.3230 + cc = ct.narrow(ch, char());
1.3231 +#endif /* BOOST_NO_STD_LOCALE */
1.3232 +
1.3233 + if (cc == ')') // read ((a,b),(e,f,g,h))"
1.3234 + {
1.3235 + q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
1.3236 +
1.3237 + o = octonion<T>(p,q);
1.3238 + }
1.3239 + else // error
1.3240 + {
1.3241 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3242 + is.setstate(::std::ios::failbit);
1.3243 +#else
1.3244 + is.setstate(::std::ios_base::failbit);
1.3245 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3246 + }
1.3247 + }
1.3248 + else // error
1.3249 + {
1.3250 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3251 + is.setstate(::std::ios::failbit);
1.3252 +#else
1.3253 + is.setstate(::std::ios_base::failbit);
1.3254 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3255 + }
1.3256 + }
1.3257 + else // error
1.3258 + {
1.3259 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3260 + is.setstate(::std::ios::failbit);
1.3261 +#else
1.3262 + is.setstate(::std::ios_base::failbit);
1.3263 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3264 + }
1.3265 + }
1.3266 + else // error
1.3267 + {
1.3268 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3269 + is.setstate(::std::ios::failbit);
1.3270 +#else
1.3271 + is.setstate(::std::ios_base::failbit);
1.3272 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3273 + }
1.3274 + }
1.3275 + }
1.3276 + else // error
1.3277 + {
1.3278 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3279 + is.setstate(::std::ios::failbit);
1.3280 +#else
1.3281 + is.setstate(::std::ios_base::failbit);
1.3282 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3283 + }
1.3284 + }
1.3285 + }
1.3286 + else // error
1.3287 + {
1.3288 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3289 + is.setstate(::std::ios::failbit);
1.3290 +#else
1.3291 + is.setstate(::std::ios_base::failbit);
1.3292 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3293 + }
1.3294 + }
1.3295 + else // error
1.3296 + {
1.3297 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3298 + is.setstate(::std::ios::failbit);
1.3299 +#else
1.3300 + is.setstate(::std::ios_base::failbit);
1.3301 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3302 + }
1.3303 + }
1.3304 + else if (cc == ',') // read "((a,b,"
1.3305 + {
1.3306 + is >> c; // read "((a,b,c"
1.3307 +
1.3308 + if (!is.good()) goto finish;
1.3309 +
1.3310 + is >> ch; // get the next lexeme
1.3311 +
1.3312 + if (!is.good()) goto finish;
1.3313 +
1.3314 +#ifdef BOOST_NO_STD_LOCALE
1.3315 + cc = ch;
1.3316 +#else
1.3317 + cc = ct.narrow(ch, char());
1.3318 +#endif /* BOOST_NO_STD_LOCALE */
1.3319 +
1.3320 + if (cc == ')') // read "((a,b,c)"
1.3321 + {
1.3322 + is >> ch; // get the next lexeme
1.3323 +
1.3324 + if (!is.good()) goto finish;
1.3325 +
1.3326 +#ifdef BOOST_NO_STD_LOCALE
1.3327 + cc = ch;
1.3328 +#else
1.3329 + cc = ct.narrow(ch, char());
1.3330 +#endif /* BOOST_NO_STD_LOCALE */
1.3331 +
1.3332 + if (cc == ')') // read "((a,b,c))"
1.3333 + {
1.3334 + o = octonion<T>(a,b,c);
1.3335 + }
1.3336 + else if (cc == ',') // read "((a,b,c),"
1.3337 + {
1.3338 + p = ::boost::math::quaternion<T>(a,b,c);
1.3339 +
1.3340 + is >> q; // read "((a,b,c),q"
1.3341 +
1.3342 + if (!is.good()) goto finish;
1.3343 +
1.3344 + is >> ch; // get the next lexeme
1.3345 +
1.3346 + if (!is.good()) goto finish;
1.3347 +
1.3348 +#ifdef BOOST_NO_STD_LOCALE
1.3349 + cc = ch;
1.3350 +#else
1.3351 + cc = ct.narrow(ch, char());
1.3352 +#endif /* BOOST_NO_STD_LOCALE */
1.3353 +
1.3354 + if (cc == ')') // read "((a,b,c),q)"
1.3355 + {
1.3356 + o = octonion<T>(p,q);
1.3357 + }
1.3358 + else // error
1.3359 + {
1.3360 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3361 + is.setstate(::std::ios::failbit);
1.3362 +#else
1.3363 + is.setstate(::std::ios_base::failbit);
1.3364 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3365 + }
1.3366 + }
1.3367 + else // error
1.3368 + {
1.3369 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3370 + is.setstate(::std::ios::failbit);
1.3371 +#else
1.3372 + is.setstate(::std::ios_base::failbit);
1.3373 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3374 + }
1.3375 + }
1.3376 + else if (cc == ',') // read "((a,b,c,"
1.3377 + {
1.3378 + is >> d; // read "((a,b,c,d"
1.3379 +
1.3380 + if (!is.good()) goto finish;
1.3381 +
1.3382 + is >> ch; // get the next lexeme
1.3383 +
1.3384 + if (!is.good()) goto finish;
1.3385 +
1.3386 +#ifdef BOOST_NO_STD_LOCALE
1.3387 + cc = ch;
1.3388 +#else
1.3389 + cc = ct.narrow(ch, char());
1.3390 +#endif /* BOOST_NO_STD_LOCALE */
1.3391 +
1.3392 + if (cc == ')') // read "((a,b,c,d)"
1.3393 + {
1.3394 + is >> ch; // get the next lexeme
1.3395 +
1.3396 + if (!is.good()) goto finish;
1.3397 +
1.3398 +#ifdef BOOST_NO_STD_LOCALE
1.3399 + cc = ch;
1.3400 +#else
1.3401 + cc = ct.narrow(ch, char());
1.3402 +#endif /* BOOST_NO_STD_LOCALE */
1.3403 +
1.3404 + if (cc == ')') // read "((a,b,c,d))"
1.3405 + {
1.3406 + o = octonion<T>(a,b,c,d);
1.3407 + }
1.3408 + else if (cc == ',') // read "((a,b,c,d),"
1.3409 + {
1.3410 + p = ::boost::math::quaternion<T>(a,b,c,d);
1.3411 +
1.3412 + is >> q; // read "((a,b,c,d),q"
1.3413 +
1.3414 + if (!is.good()) goto finish;
1.3415 +
1.3416 + is >> ch; // get the next lexeme
1.3417 +
1.3418 + if (!is.good()) goto finish;
1.3419 +
1.3420 +#ifdef BOOST_NO_STD_LOCALE
1.3421 + cc = ch;
1.3422 +#else
1.3423 + cc = ct.narrow(ch, char());
1.3424 +#endif /* BOOST_NO_STD_LOCALE */
1.3425 +
1.3426 + if (cc == ')') // read "((a,b,c,d),q)"
1.3427 + {
1.3428 + o = octonion<T>(p,q);
1.3429 + }
1.3430 + else // error
1.3431 + {
1.3432 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3433 + is.setstate(::std::ios::failbit);
1.3434 +#else
1.3435 + is.setstate(::std::ios_base::failbit);
1.3436 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3437 + }
1.3438 + }
1.3439 + else // error
1.3440 + {
1.3441 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3442 + is.setstate(::std::ios::failbit);
1.3443 +#else
1.3444 + is.setstate(::std::ios_base::failbit);
1.3445 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3446 + }
1.3447 + }
1.3448 + else // error
1.3449 + {
1.3450 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3451 + is.setstate(::std::ios::failbit);
1.3452 +#else
1.3453 + is.setstate(::std::ios_base::failbit);
1.3454 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3455 + }
1.3456 + }
1.3457 + else // error
1.3458 + {
1.3459 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3460 + is.setstate(::std::ios::failbit);
1.3461 +#else
1.3462 + is.setstate(::std::ios_base::failbit);
1.3463 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3464 + }
1.3465 + }
1.3466 + else // error
1.3467 + {
1.3468 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3469 + is.setstate(::std::ios::failbit);
1.3470 +#else
1.3471 + is.setstate(::std::ios_base::failbit);
1.3472 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3473 + }
1.3474 + }
1.3475 + }
1.3476 + else // error
1.3477 + {
1.3478 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3479 + is.setstate(::std::ios::failbit);
1.3480 +#else
1.3481 + is.setstate(::std::ios_base::failbit);
1.3482 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3483 + }
1.3484 + }
1.3485 + }
1.3486 + else // read "(a"
1.3487 + {
1.3488 + is.putback(ch);
1.3489 +
1.3490 + is >> a; // we extract the first component
1.3491 +
1.3492 + if (!is.good()) goto finish;
1.3493 +
1.3494 + is >> ch; // get the next lexeme
1.3495 +
1.3496 + if (!is.good()) goto finish;
1.3497 +
1.3498 +#ifdef BOOST_NO_STD_LOCALE
1.3499 + cc = ch;
1.3500 +#else
1.3501 + cc = ct.narrow(ch, char());
1.3502 +#endif /* BOOST_NO_STD_LOCALE */
1.3503 +
1.3504 + if (cc == ')') // read "(a)"
1.3505 + {
1.3506 + o = octonion<T>(a);
1.3507 + }
1.3508 + else if (cc == ',') // read "(a,"
1.3509 + {
1.3510 + is >> ch; // get the next lexeme
1.3511 +
1.3512 + if (!is.good()) goto finish;
1.3513 +
1.3514 +#ifdef BOOST_NO_STD_LOCALE
1.3515 + cc = ch;
1.3516 +#else
1.3517 + cc = ct.narrow(ch, char());
1.3518 +#endif /* BOOST_NO_STD_LOCALE */
1.3519 +
1.3520 + if (cc == '(') // read "(a,("
1.3521 + {
1.3522 + is >> ch; // get the next lexeme
1.3523 +
1.3524 + if (!is.good()) goto finish;
1.3525 +
1.3526 +#ifdef BOOST_NO_STD_LOCALE
1.3527 + cc = ch;
1.3528 +#else
1.3529 + cc = ct.narrow(ch, char());
1.3530 +#endif /* BOOST_NO_STD_LOCALE */
1.3531 +
1.3532 + if (cc == '(') // read "(a,(("
1.3533 + {
1.3534 + p = ::boost::math::quaternion<T>(a);
1.3535 +
1.3536 + is.putback(ch);
1.3537 +
1.3538 + is.putback(ch); // we backtrack twice, with the same value
1.3539 +
1.3540 + is >> q; // read "(a,q"
1.3541 +
1.3542 + if (!is.good()) goto finish;
1.3543 +
1.3544 + is >> ch; // get the next lexeme
1.3545 +
1.3546 + if (!is.good()) goto finish;
1.3547 +
1.3548 +#ifdef BOOST_NO_STD_LOCALE
1.3549 + cc = ch;
1.3550 +#else
1.3551 + cc = ct.narrow(ch, char());
1.3552 +#endif /* BOOST_NO_STD_LOCALE */
1.3553 +
1.3554 + if (cc == ')') // read "(a,q)"
1.3555 + {
1.3556 + o = octonion<T>(p,q);
1.3557 + }
1.3558 + else // error
1.3559 + {
1.3560 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3561 + is.setstate(::std::ios::failbit);
1.3562 +#else
1.3563 + is.setstate(::std::ios_base::failbit);
1.3564 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3565 + }
1.3566 + }
1.3567 + else // read "(a,(c" or "(a,(e"
1.3568 + {
1.3569 + is.putback(ch);
1.3570 +
1.3571 + is >> c;
1.3572 +
1.3573 + if (!is.good()) goto finish;
1.3574 +
1.3575 + is >> ch; // get the next lexeme
1.3576 +
1.3577 + if (!is.good()) goto finish;
1.3578 +
1.3579 +#ifdef BOOST_NO_STD_LOCALE
1.3580 + cc = ch;
1.3581 +#else
1.3582 + cc = ct.narrow(ch, char());
1.3583 +#endif /* BOOST_NO_STD_LOCALE */
1.3584 +
1.3585 + if (cc == ')') // read "(a,(c)" (ambiguity resolution)
1.3586 + {
1.3587 + is >> ch; // get the next lexeme
1.3588 +
1.3589 + if (!is.good()) goto finish;
1.3590 +
1.3591 +#ifdef BOOST_NO_STD_LOCALE
1.3592 + cc = ch;
1.3593 +#else
1.3594 + cc = ct.narrow(ch, char());
1.3595 +#endif /* BOOST_NO_STD_LOCALE */
1.3596 +
1.3597 + if (cc == ')') // read "(a,(c))"
1.3598 + {
1.3599 + o = octonion<T>(a,b,c);
1.3600 + }
1.3601 + else if (cc == ',') // read "(a,(c),"
1.3602 + {
1.3603 + u = ::std::complex<T>(a);
1.3604 +
1.3605 + v = ::std::complex<T>(c);
1.3606 +
1.3607 + is >> x; // read "(a,(c),x"
1.3608 +
1.3609 + if (!is.good()) goto finish;
1.3610 +
1.3611 + is >> ch; // get the next lexeme
1.3612 +
1.3613 + if (!is.good()) goto finish;
1.3614 +
1.3615 +#ifdef BOOST_NO_STD_LOCALE
1.3616 + cc = ch;
1.3617 +#else
1.3618 + cc = ct.narrow(ch, char());
1.3619 +#endif /* BOOST_NO_STD_LOCALE */
1.3620 +
1.3621 + if (cc == ')') // read "(a,(c),x)"
1.3622 + {
1.3623 + o = octonion<T>(u,v,x);
1.3624 + }
1.3625 + else if (cc == ',') // read "(a,(c),x,"
1.3626 + {
1.3627 + is >> y; // read "(a,(c),x,y"
1.3628 +
1.3629 + if (!is.good()) goto finish;
1.3630 +
1.3631 + is >> ch; // get the next lexeme
1.3632 +
1.3633 + if (!is.good()) goto finish;
1.3634 +
1.3635 +#ifdef BOOST_NO_STD_LOCALE
1.3636 + cc = ch;
1.3637 +#else
1.3638 + cc = ct.narrow(ch, char());
1.3639 +#endif /* BOOST_NO_STD_LOCALE */
1.3640 +
1.3641 + if (cc == ')') // read "(a,(c),x,y)"
1.3642 + {
1.3643 + o = octonion<T>(u,v,x,y);
1.3644 + }
1.3645 + else // error
1.3646 + {
1.3647 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3648 + is.setstate(::std::ios::failbit);
1.3649 +#else
1.3650 + is.setstate(::std::ios_base::failbit);
1.3651 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3652 + }
1.3653 + }
1.3654 + else // error
1.3655 + {
1.3656 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3657 + is.setstate(::std::ios::failbit);
1.3658 +#else
1.3659 + is.setstate(::std::ios_base::failbit);
1.3660 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3661 + }
1.3662 + }
1.3663 + else // error
1.3664 + {
1.3665 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3666 + is.setstate(::std::ios::failbit);
1.3667 +#else
1.3668 + is.setstate(::std::ios_base::failbit);
1.3669 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3670 + }
1.3671 + }
1.3672 + else if (cc == ',') // read "(a,(c," or "(a,(e,"
1.3673 + {
1.3674 + is >> ch; // get the next lexeme
1.3675 +
1.3676 + if (!is.good()) goto finish;
1.3677 +
1.3678 +#ifdef BOOST_NO_STD_LOCALE
1.3679 + cc = ch;
1.3680 +#else
1.3681 + cc = ct.narrow(ch, char());
1.3682 +#endif /* BOOST_NO_STD_LOCALE */
1.3683 +
1.3684 + if (cc == '(') // read "(a,(e,(" (ambiguity resolution)
1.3685 + {
1.3686 + u = ::std::complex<T>(a);
1.3687 +
1.3688 + x = ::std::complex<T>(c); // "c" is actually "e"
1.3689 +
1.3690 + is.putback(ch); // we backtrack
1.3691 +
1.3692 + is >> y; // read "(a,(e,y"
1.3693 +
1.3694 + if (!is.good()) goto finish;
1.3695 +
1.3696 + is >> ch; // get the next lexeme
1.3697 +
1.3698 + if (!is.good()) goto finish;
1.3699 +
1.3700 +#ifdef BOOST_NO_STD_LOCALE
1.3701 + cc = ch;
1.3702 +#else
1.3703 + cc = ct.narrow(ch, char());
1.3704 +#endif /* BOOST_NO_STD_LOCALE */
1.3705 +
1.3706 + if (cc == ')') // read "(a,(e,y)"
1.3707 + {
1.3708 + is >> ch; // get the next lexeme
1.3709 +
1.3710 + if (!is.good()) goto finish;
1.3711 +
1.3712 +#ifdef BOOST_NO_STD_LOCALE
1.3713 + cc = ch;
1.3714 +#else
1.3715 + cc = ct.narrow(ch, char());
1.3716 +#endif /* BOOST_NO_STD_LOCALE */
1.3717 +
1.3718 + if (cc == ')') // read "(a,(e,y))"
1.3719 + {
1.3720 + o = octonion<T>(u,v,x,y);
1.3721 + }
1.3722 + else // error
1.3723 + {
1.3724 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3725 + is.setstate(::std::ios::failbit);
1.3726 +#else
1.3727 + is.setstate(::std::ios_base::failbit);
1.3728 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3729 + }
1.3730 + }
1.3731 + else // error
1.3732 + {
1.3733 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3734 + is.setstate(::std::ios::failbit);
1.3735 +#else
1.3736 + is.setstate(::std::ios_base::failbit);
1.3737 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3738 + }
1.3739 + }
1.3740 + else // read "(a,(c,d" or "(a,(e,f"
1.3741 + {
1.3742 + is.putback(ch);
1.3743 +
1.3744 + is >> d;
1.3745 +
1.3746 + if (!is.good()) goto finish;
1.3747 +
1.3748 + is >> ch; // get the next lexeme
1.3749 +
1.3750 + if (!is.good()) goto finish;
1.3751 +
1.3752 +#ifdef BOOST_NO_STD_LOCALE
1.3753 + cc = ch;
1.3754 +#else
1.3755 + cc = ct.narrow(ch, char());
1.3756 +#endif /* BOOST_NO_STD_LOCALE */
1.3757 +
1.3758 + if (cc == ')') // read "(a,(c,d)" (ambiguity resolution)
1.3759 + {
1.3760 + is >> ch; // get the next lexeme
1.3761 +
1.3762 + if (!is.good()) goto finish;
1.3763 +
1.3764 +#ifdef BOOST_NO_STD_LOCALE
1.3765 + cc = ch;
1.3766 +#else
1.3767 + cc = ct.narrow(ch, char());
1.3768 +#endif /* BOOST_NO_STD_LOCALE */
1.3769 +
1.3770 + if (cc == ')') // read "(a,(c,d))"
1.3771 + {
1.3772 + o = octonion<T>(a,b,c,d);
1.3773 + }
1.3774 + else if (cc == ',') // read "(a,(c,d),"
1.3775 + {
1.3776 + u = ::std::complex<T>(a);
1.3777 +
1.3778 + v = ::std::complex<T>(c,d);
1.3779 +
1.3780 + is >> x; // read "(a,(c,d),x"
1.3781 +
1.3782 + if (!is.good()) goto finish;
1.3783 +
1.3784 + is >> ch; // get the next lexeme
1.3785 +
1.3786 + if (!is.good()) goto finish;
1.3787 +
1.3788 +#ifdef BOOST_NO_STD_LOCALE
1.3789 + cc = ch;
1.3790 +#else
1.3791 + cc = ct.narrow(ch, char());
1.3792 +#endif /* BOOST_NO_STD_LOCALE */
1.3793 +
1.3794 + if (cc == ')') // read "(a,(c,d),x)"
1.3795 + {
1.3796 + o = octonion<T>(u,v,x);
1.3797 + }
1.3798 + else if (cc == ',') // read "(a,(c,d),x,"
1.3799 + {
1.3800 + is >> y; // read "(a,(c,d),x,y"
1.3801 +
1.3802 + if (!is.good()) goto finish;
1.3803 +
1.3804 + is >> ch; // get the next lexeme
1.3805 +
1.3806 + if (!is.good()) goto finish;
1.3807 +
1.3808 +#ifdef BOOST_NO_STD_LOCALE
1.3809 + cc = ch;
1.3810 +#else
1.3811 + cc = ct.narrow(ch, char());
1.3812 +#endif /* BOOST_NO_STD_LOCALE */
1.3813 +
1.3814 + if (cc == ')') // read "(a,(c,d),x,y)"
1.3815 + {
1.3816 + o = octonion<T>(u,v,x,y);
1.3817 + }
1.3818 + else // error
1.3819 + {
1.3820 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3821 + is.setstate(::std::ios::failbit);
1.3822 +#else
1.3823 + is.setstate(::std::ios_base::failbit);
1.3824 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3825 + }
1.3826 + }
1.3827 + else // error
1.3828 + {
1.3829 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3830 + is.setstate(::std::ios::failbit);
1.3831 +#else
1.3832 + is.setstate(::std::ios_base::failbit);
1.3833 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3834 + }
1.3835 + }
1.3836 + else // error
1.3837 + {
1.3838 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3839 + is.setstate(::std::ios::failbit);
1.3840 +#else
1.3841 + is.setstate(::std::ios_base::failbit);
1.3842 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3843 + }
1.3844 + }
1.3845 + else if (cc == ',') // read "(a,(e,f," (ambiguity resolution)
1.3846 + {
1.3847 + p = ::boost::math::quaternion<T>(a);
1.3848 +
1.3849 + is >> g; // read "(a,(e,f,g"
1.3850 +
1.3851 + if (!is.good()) goto finish;
1.3852 +
1.3853 + is >> ch; // get the next lexeme
1.3854 +
1.3855 + if (!is.good()) goto finish;
1.3856 +
1.3857 +#ifdef BOOST_NO_STD_LOCALE
1.3858 + cc = ch;
1.3859 +#else
1.3860 + cc = ct.narrow(ch, char());
1.3861 +#endif /* BOOST_NO_STD_LOCALE */
1.3862 +
1.3863 + if (cc == ')') // read "(a,(e,f,g)"
1.3864 + {
1.3865 + is >> ch; // get the next lexeme
1.3866 +
1.3867 + if (!is.good()) goto finish;
1.3868 +
1.3869 +#ifdef BOOST_NO_STD_LOCALE
1.3870 + cc = ch;
1.3871 +#else
1.3872 + cc = ct.narrow(ch, char());
1.3873 +#endif /* BOOST_NO_STD_LOCALE */
1.3874 +
1.3875 + if (cc == ')') // read "(a,(e,f,g))"
1.3876 + {
1.3877 + q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
1.3878 +
1.3879 + o = octonion<T>(p,q);
1.3880 + }
1.3881 + else // error
1.3882 + {
1.3883 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3884 + is.setstate(::std::ios::failbit);
1.3885 +#else
1.3886 + is.setstate(::std::ios_base::failbit);
1.3887 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3888 + }
1.3889 + }
1.3890 + else if (cc == ',') // read "(a,(e,f,g,"
1.3891 + {
1.3892 + is >> h; // read "(a,(e,f,g,h"
1.3893 +
1.3894 + if (!is.good()) goto finish;
1.3895 +
1.3896 + is >> ch; // get the next lexeme
1.3897 +
1.3898 + if (!is.good()) goto finish;
1.3899 +
1.3900 +#ifdef BOOST_NO_STD_LOCALE
1.3901 + cc = ch;
1.3902 +#else
1.3903 + cc = ct.narrow(ch, char());
1.3904 +#endif /* BOOST_NO_STD_LOCALE */
1.3905 +
1.3906 + if (cc == ')') // read "(a,(e,f,g,h)"
1.3907 + {
1.3908 + is >> ch; // get the next lexeme
1.3909 +
1.3910 + if (!is.good()) goto finish;
1.3911 +
1.3912 +#ifdef BOOST_NO_STD_LOCALE
1.3913 + cc = ch;
1.3914 +#else
1.3915 + cc = ct.narrow(ch, char());
1.3916 +#endif /* BOOST_NO_STD_LOCALE */
1.3917 +
1.3918 + if (cc == ')') // read "(a,(e,f,g,h))"
1.3919 + {
1.3920 + q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
1.3921 +
1.3922 + o = octonion<T>(p,q);
1.3923 + }
1.3924 + else // error
1.3925 + {
1.3926 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3927 + is.setstate(::std::ios::failbit);
1.3928 +#else
1.3929 + is.setstate(::std::ios_base::failbit);
1.3930 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3931 + }
1.3932 + }
1.3933 + else // error
1.3934 + {
1.3935 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3936 + is.setstate(::std::ios::failbit);
1.3937 +#else
1.3938 + is.setstate(::std::ios_base::failbit);
1.3939 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3940 + }
1.3941 + }
1.3942 + else // error
1.3943 + {
1.3944 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3945 + is.setstate(::std::ios::failbit);
1.3946 +#else
1.3947 + is.setstate(::std::ios_base::failbit);
1.3948 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3949 + }
1.3950 + }
1.3951 + else // error
1.3952 + {
1.3953 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3954 + is.setstate(::std::ios::failbit);
1.3955 +#else
1.3956 + is.setstate(::std::ios_base::failbit);
1.3957 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3958 + }
1.3959 + }
1.3960 + }
1.3961 + else // error
1.3962 + {
1.3963 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.3964 + is.setstate(::std::ios::failbit);
1.3965 +#else
1.3966 + is.setstate(::std::ios_base::failbit);
1.3967 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.3968 + }
1.3969 + }
1.3970 + }
1.3971 + else // read "(a,b" or "(a,c" (ambiguity resolution)
1.3972 + {
1.3973 + is.putback(ch);
1.3974 +
1.3975 + is >> b;
1.3976 +
1.3977 + if (!is.good()) goto finish;
1.3978 +
1.3979 + is >> ch; // get the next lexeme
1.3980 +
1.3981 + if (!is.good()) goto finish;
1.3982 +
1.3983 +#ifdef BOOST_NO_STD_LOCALE
1.3984 + cc = ch;
1.3985 +#else
1.3986 + cc = ct.narrow(ch, char());
1.3987 +#endif /* BOOST_NO_STD_LOCALE */
1.3988 +
1.3989 + if (cc == ')') // read "(a,b)" (ambiguity resolution)
1.3990 + {
1.3991 + o = octonion<T>(a,b);
1.3992 + }
1.3993 + else if (cc == ',') // read "(a,b," or "(a,c,"
1.3994 + {
1.3995 + is >> ch; // get the next lexeme
1.3996 +
1.3997 + if (!is.good()) goto finish;
1.3998 +
1.3999 +#ifdef BOOST_NO_STD_LOCALE
1.4000 + cc = ch;
1.4001 +#else
1.4002 + cc = ct.narrow(ch, char());
1.4003 +#endif /* BOOST_NO_STD_LOCALE */
1.4004 +
1.4005 + if (cc == '(') // read "(a,c,(" (ambiguity resolution)
1.4006 + {
1.4007 + u = ::std::complex<T>(a);
1.4008 +
1.4009 + v = ::std::complex<T>(b); // "b" is actually "c"
1.4010 +
1.4011 + is.putback(ch); // we backtrack
1.4012 +
1.4013 + is >> x; // read "(a,c,x"
1.4014 +
1.4015 + if (!is.good()) goto finish;
1.4016 +
1.4017 + is >> ch; // get the next lexeme
1.4018 +
1.4019 + if (!is.good()) goto finish;
1.4020 +
1.4021 +#ifdef BOOST_NO_STD_LOCALE
1.4022 + cc = ch;
1.4023 +#else
1.4024 + cc = ct.narrow(ch, char());
1.4025 +#endif /* BOOST_NO_STD_LOCALE */
1.4026 +
1.4027 + if (cc == ')') // read "(a,c,x)"
1.4028 + {
1.4029 + o = octonion<T>(u,v,x);
1.4030 + }
1.4031 + else if (cc == ',') // read "(a,c,x,"
1.4032 + {
1.4033 + is >> y; // read "(a,c,x,y" // read "(a,c,x"
1.4034 +
1.4035 + if (!is.good()) goto finish;
1.4036 +
1.4037 + is >> ch; // get the next lexeme
1.4038 +
1.4039 + if (!is.good()) goto finish;
1.4040 +
1.4041 +#ifdef BOOST_NO_STD_LOCALE
1.4042 + cc = ch;
1.4043 +#else
1.4044 + cc = ct.narrow(ch, char());
1.4045 +#endif /* BOOST_NO_STD_LOCALE */
1.4046 +
1.4047 + if (cc == ')') // read "(a,c,x,y)"
1.4048 + {
1.4049 + o = octonion<T>(u,v,x,y);
1.4050 + }
1.4051 + else // error
1.4052 + {
1.4053 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4054 + is.setstate(::std::ios::failbit);
1.4055 +#else
1.4056 + is.setstate(::std::ios_base::failbit);
1.4057 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4058 + }
1.4059 + }
1.4060 + else // error
1.4061 + {
1.4062 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4063 + is.setstate(::std::ios::failbit);
1.4064 +#else
1.4065 + is.setstate(::std::ios_base::failbit);
1.4066 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4067 + }
1.4068 + }
1.4069 + else // read "(a,b,c" or "(a,c,e"
1.4070 + {
1.4071 + is.putback(ch);
1.4072 +
1.4073 + is >> c;
1.4074 +
1.4075 + if (!is.good()) goto finish;
1.4076 +
1.4077 + is >> ch; // get the next lexeme
1.4078 +
1.4079 + if (!is.good()) goto finish;
1.4080 +
1.4081 +#ifdef BOOST_NO_STD_LOCALE
1.4082 + cc = ch;
1.4083 +#else
1.4084 + cc = ct.narrow(ch, char());
1.4085 +#endif /* BOOST_NO_STD_LOCALE */
1.4086 +
1.4087 + if (cc == ')') // read "(a,b,c)" (ambiguity resolution)
1.4088 + {
1.4089 + o = octonion<T>(a,b,c);
1.4090 + }
1.4091 + else if (cc == ',') // read "(a,b,c," or "(a,c,e,"
1.4092 + {
1.4093 + is >> ch; // get the next lexeme
1.4094 +
1.4095 + if (!is.good()) goto finish;
1.4096 +
1.4097 +#ifdef BOOST_NO_STD_LOCALE
1.4098 + cc = ch;
1.4099 +#else
1.4100 + cc = ct.narrow(ch, char());
1.4101 +#endif /* BOOST_NO_STD_LOCALE */
1.4102 +
1.4103 + if (cc == '(') // read "(a,c,e,(") (ambiguity resolution)
1.4104 + {
1.4105 + u = ::std::complex<T>(a);
1.4106 +
1.4107 + v = ::std::complex<T>(b); // "b" is actually "c"
1.4108 +
1.4109 + x = ::std::complex<T>(c); // "c" is actually "e"
1.4110 +
1.4111 + is.putback(ch); // we backtrack
1.4112 +
1.4113 + is >> y; // read "(a,c,e,y"
1.4114 +
1.4115 + if (!is.good()) goto finish;
1.4116 +
1.4117 + is >> ch; // get the next lexeme
1.4118 +
1.4119 + if (!is.good()) goto finish;
1.4120 +
1.4121 +#ifdef BOOST_NO_STD_LOCALE
1.4122 + cc = ch;
1.4123 +#else
1.4124 + cc = ct.narrow(ch, char());
1.4125 +#endif /* BOOST_NO_STD_LOCALE */
1.4126 +
1.4127 + if (cc == ')') // read "(a,c,e,y)"
1.4128 + {
1.4129 + o = octonion<T>(u,v,x,y);
1.4130 + }
1.4131 + else // error
1.4132 + {
1.4133 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4134 + is.setstate(::std::ios::failbit);
1.4135 +#else
1.4136 + is.setstate(::std::ios_base::failbit);
1.4137 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4138 + }
1.4139 + }
1.4140 + else // read "(a,b,c,d" (ambiguity resolution)
1.4141 + {
1.4142 + is.putback(ch); // we backtrack
1.4143 +
1.4144 + is >> d;
1.4145 +
1.4146 + if (!is.good()) goto finish;
1.4147 +
1.4148 + is >> ch; // get the next lexeme
1.4149 +
1.4150 + if (!is.good()) goto finish;
1.4151 +
1.4152 +#ifdef BOOST_NO_STD_LOCALE
1.4153 + cc = ch;
1.4154 +#else
1.4155 + cc = ct.narrow(ch, char());
1.4156 +#endif /* BOOST_NO_STD_LOCALE */
1.4157 +
1.4158 + if (cc == ')') // read "(a,b,c,d)"
1.4159 + {
1.4160 + o = octonion<T>(a,b,c,d);
1.4161 + }
1.4162 + else if (cc == ',') // read "(a,b,c,d,"
1.4163 + {
1.4164 + is >> e; // read "(a,b,c,d,e"
1.4165 +
1.4166 + if (!is.good()) goto finish;
1.4167 +
1.4168 + is >> ch; // get the next lexeme
1.4169 +
1.4170 + if (!is.good()) goto finish;
1.4171 +
1.4172 +#ifdef BOOST_NO_STD_LOCALE
1.4173 + cc = ch;
1.4174 +#else
1.4175 + cc = ct.narrow(ch, char());
1.4176 +#endif /* BOOST_NO_STD_LOCALE */
1.4177 +
1.4178 + if (cc == ')') // read "(a,b,c,d,e)"
1.4179 + {
1.4180 + o = octonion<T>(a,b,c,d,e);
1.4181 + }
1.4182 + else if (cc == ',') // read "(a,b,c,d,e,"
1.4183 + {
1.4184 + is >> f; // read "(a,b,c,d,e,f"
1.4185 +
1.4186 + if (!is.good()) goto finish;
1.4187 +
1.4188 + is >> ch; // get the next lexeme
1.4189 +
1.4190 + if (!is.good()) goto finish;
1.4191 +
1.4192 +#ifdef BOOST_NO_STD_LOCALE
1.4193 + cc = ch;
1.4194 +#else
1.4195 + cc = ct.narrow(ch, char());
1.4196 +#endif /* BOOST_NO_STD_LOCALE */
1.4197 +
1.4198 + if (cc == ')') // read "(a,b,c,d,e,f)"
1.4199 + {
1.4200 + o = octonion<T>(a,b,c,d,e,f);
1.4201 + }
1.4202 + else if (cc == ',') // read "(a,b,c,d,e,f,"
1.4203 + {
1.4204 + is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
1.4205 +
1.4206 + if (!is.good()) goto finish;
1.4207 +
1.4208 + is >> ch; // get the next lexeme
1.4209 +
1.4210 + if (!is.good()) goto finish;
1.4211 +
1.4212 +#ifdef BOOST_NO_STD_LOCALE
1.4213 + cc = ch;
1.4214 +#else
1.4215 + cc = ct.narrow(ch, char());
1.4216 +#endif /* BOOST_NO_STD_LOCALE */
1.4217 +
1.4218 + if (cc == ')') // read "(a,b,c,d,e,f,g)"
1.4219 + {
1.4220 + o = octonion<T>(a,b,c,d,e,f,g);
1.4221 + }
1.4222 + else if (cc == ',') // read "(a,b,c,d,e,f,g,"
1.4223 + {
1.4224 + is >> h; // read "(a,b,c,d,e,f,g,h" // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
1.4225 +
1.4226 + if (!is.good()) goto finish;
1.4227 +
1.4228 + is >> ch; // get the next lexeme
1.4229 +
1.4230 + if (!is.good()) goto finish;
1.4231 +
1.4232 +#ifdef BOOST_NO_STD_LOCALE
1.4233 + cc = ch;
1.4234 +#else
1.4235 + cc = ct.narrow(ch, char());
1.4236 +#endif /* BOOST_NO_STD_LOCALE */
1.4237 +
1.4238 + if (cc == ')') // read "(a,b,c,d,e,f,g,h)"
1.4239 + {
1.4240 + o = octonion<T>(a,b,c,d,e,f,g,h);
1.4241 + }
1.4242 + else // error
1.4243 + {
1.4244 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4245 + is.setstate(::std::ios::failbit);
1.4246 +#else
1.4247 + is.setstate(::std::ios_base::failbit);
1.4248 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4249 + }
1.4250 + }
1.4251 + else // error
1.4252 + {
1.4253 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4254 + is.setstate(::std::ios::failbit);
1.4255 +#else
1.4256 + is.setstate(::std::ios_base::failbit);
1.4257 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4258 + }
1.4259 + }
1.4260 + else // error
1.4261 + {
1.4262 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4263 + is.setstate(::std::ios::failbit);
1.4264 +#else
1.4265 + is.setstate(::std::ios_base::failbit);
1.4266 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4267 + }
1.4268 + }
1.4269 + else // error
1.4270 + {
1.4271 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4272 + is.setstate(::std::ios::failbit);
1.4273 +#else
1.4274 + is.setstate(::std::ios_base::failbit);
1.4275 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4276 + }
1.4277 + }
1.4278 + else // error
1.4279 + {
1.4280 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4281 + is.setstate(::std::ios::failbit);
1.4282 +#else
1.4283 + is.setstate(::std::ios_base::failbit);
1.4284 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4285 + }
1.4286 + }
1.4287 + }
1.4288 + else // error
1.4289 + {
1.4290 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4291 + is.setstate(::std::ios::failbit);
1.4292 +#else
1.4293 + is.setstate(::std::ios_base::failbit);
1.4294 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4295 + }
1.4296 + }
1.4297 + }
1.4298 + else // error
1.4299 + {
1.4300 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4301 + is.setstate(::std::ios::failbit);
1.4302 +#else
1.4303 + is.setstate(::std::ios_base::failbit);
1.4304 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4305 + }
1.4306 + }
1.4307 + }
1.4308 + else // error
1.4309 + {
1.4310 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4311 + is.setstate(::std::ios::failbit);
1.4312 +#else
1.4313 + is.setstate(::std::ios_base::failbit);
1.4314 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4315 + }
1.4316 + }
1.4317 + }
1.4318 + else // format: a
1.4319 + {
1.4320 + is.putback(ch);
1.4321 +
1.4322 + is >> a; // we extract the first component
1.4323 +
1.4324 + if (!is.good()) goto finish;
1.4325 +
1.4326 + o = octonion<T>(a);
1.4327 + }
1.4328 +
1.4329 + finish:
1.4330 + return(is);
1.4331 + }
1.4332 +
1.4333 +
1.4334 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4335 + template<typename T>
1.4336 + ::std::ostream & operator << ( ::std::ostream & os,
1.4337 + octonion<T> const & o)
1.4338 +#else
1.4339 + template<typename T, typename charT, class traits>
1.4340 + ::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
1.4341 + octonion<T> const & o)
1.4342 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4343 + {
1.4344 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4345 + ::std::ostringstream s;
1.4346 +#else
1.4347 + ::std::basic_ostringstream<charT,traits> s;
1.4348 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4349 +
1.4350 + s.flags(os.flags());
1.4351 +#ifdef BOOST_NO_STD_LOCALE
1.4352 +#else
1.4353 + s.imbue(os.getloc());
1.4354 +#endif /* BOOST_NO_STD_LOCALE */
1.4355 + s.precision(os.precision());
1.4356 +
1.4357 + s << '(' << o.R_component_1() << ','
1.4358 + << o.R_component_2() << ','
1.4359 + << o.R_component_3() << ','
1.4360 + << o.R_component_4() << ','
1.4361 + << o.R_component_5() << ','
1.4362 + << o.R_component_6() << ','
1.4363 + << o.R_component_7() << ','
1.4364 + << o.R_component_8() << ')';
1.4365 +
1.4366 + return os << s.str();
1.4367 + }
1.4368 +
1.4369 +
1.4370 + // values
1.4371 +
1.4372 + template<typename T>
1.4373 + inline T real(octonion<T> const & o)
1.4374 + {
1.4375 + return(o.real());
1.4376 + }
1.4377 +
1.4378 +
1.4379 + template<typename T>
1.4380 + inline octonion<T> unreal(octonion<T> const & o)
1.4381 + {
1.4382 + return(o.unreal());
1.4383 + }
1.4384 +
1.4385 +
1.4386 +#define BOOST_OCTONION_VALARRAY_LOADER \
1.4387 + using ::std::valarray; \
1.4388 + \
1.4389 + valarray<T> temp(8); \
1.4390 + \
1.4391 + temp[0] = o.R_component_1(); \
1.4392 + temp[1] = o.R_component_2(); \
1.4393 + temp[2] = o.R_component_3(); \
1.4394 + temp[3] = o.R_component_4(); \
1.4395 + temp[4] = o.R_component_5(); \
1.4396 + temp[5] = o.R_component_6(); \
1.4397 + temp[6] = o.R_component_7(); \
1.4398 + temp[7] = o.R_component_8();
1.4399 +
1.4400 +
1.4401 + template<typename T>
1.4402 + inline T sup(octonion<T> const & o)
1.4403 + {
1.4404 +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
1.4405 + using ::std::abs;
1.4406 +#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1.4407 +
1.4408 + BOOST_OCTONION_VALARRAY_LOADER
1.4409 +
1.4410 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4411 + return((BOOST_GET_VALARRAY(T, abs(temp)).max)());
1.4412 +#else
1.4413 + return((abs(temp).max)());
1.4414 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4415 + }
1.4416 +
1.4417 +
1.4418 + template<typename T>
1.4419 + inline T l1(octonion<T> const & o)
1.4420 + {
1.4421 +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
1.4422 + using ::std::abs;
1.4423 +#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1.4424 +
1.4425 + BOOST_OCTONION_VALARRAY_LOADER
1.4426 +
1.4427 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4428 + return(BOOST_GET_VALARRAY(T, abs(temp)).sum());
1.4429 +#else
1.4430 + return(abs(temp).sum());
1.4431 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4432 + }
1.4433 +
1.4434 +
1.4435 + template<typename T>
1.4436 + inline T abs(const octonion<T> & o)
1.4437 + {
1.4438 +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
1.4439 + using ::std::abs;
1.4440 +#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1.4441 +
1.4442 + using ::std::sqrt;
1.4443 +
1.4444 + BOOST_OCTONION_VALARRAY_LOADER
1.4445 +
1.4446 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4447 + T maxim = (BOOST_GET_VALARRAY(T,abs(temp)).max)(); // overflow protection
1.4448 +#else
1.4449 + T maxim = (abs(temp).max)(); // overflow protection
1.4450 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4451 +
1.4452 + if (maxim == static_cast<T>(0))
1.4453 + {
1.4454 + return(maxim);
1.4455 + }
1.4456 + else
1.4457 + {
1.4458 + T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
1.4459 +
1.4460 + temp *= mixam;
1.4461 +
1.4462 + temp *= temp;
1.4463 +
1.4464 + return(maxim*sqrt(temp.sum()));
1.4465 + }
1.4466 +
1.4467 + //return(::std::sqrt(norm(o)));
1.4468 + }
1.4469 +
1.4470 +
1.4471 +#undef BOOST_OCTONION_VALARRAY_LOADER
1.4472 +
1.4473 +
1.4474 + // Note: This is the Cayley norm, not the Euclidian norm...
1.4475 +
1.4476 + template<typename T>
1.4477 + inline T norm(octonion<T> const & o)
1.4478 + {
1.4479 + return(real(o*conj(o)));
1.4480 + }
1.4481 +
1.4482 +
1.4483 + template<typename T>
1.4484 + inline octonion<T> conj(octonion<T> const & o)
1.4485 + {
1.4486 + return(octonion<T>( +o.R_component_1(),
1.4487 + -o.R_component_2(),
1.4488 + -o.R_component_3(),
1.4489 + -o.R_component_4(),
1.4490 + -o.R_component_5(),
1.4491 + -o.R_component_6(),
1.4492 + -o.R_component_7(),
1.4493 + -o.R_component_8()));
1.4494 + }
1.4495 +
1.4496 +
1.4497 + // Note: There is little point, for the octonions, to introduce the equivalents
1.4498 + // to the complex "arg" and the quaternionic "cylindropolar".
1.4499 +
1.4500 +
1.4501 + template<typename T>
1.4502 + inline octonion<T> spherical(T const & rho,
1.4503 + T const & theta,
1.4504 + T const & phi1,
1.4505 + T const & phi2,
1.4506 + T const & phi3,
1.4507 + T const & phi4,
1.4508 + T const & phi5,
1.4509 + T const & phi6)
1.4510 + {
1.4511 + using ::std::cos;
1.4512 + using ::std::sin;
1.4513 +
1.4514 + //T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
1.4515 + //T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
1.4516 + //T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
1.4517 + //T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
1.4518 + //T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
1.4519 + //T f = sin(phi4)*cos(phi5)*cos(phi6);
1.4520 + //T g = sin(phi5)*cos(phi6);
1.4521 + //T h = sin(phi6);
1.4522 +
1.4523 + T courrant = static_cast<T>(1);
1.4524 +
1.4525 + T h = sin(phi6);
1.4526 +
1.4527 + courrant *= cos(phi6);
1.4528 +
1.4529 + T g = sin(phi5)*courrant;
1.4530 +
1.4531 + courrant *= cos(phi5);
1.4532 +
1.4533 + T f = sin(phi4)*courrant;
1.4534 +
1.4535 + courrant *= cos(phi4);
1.4536 +
1.4537 + T e = sin(phi3)*courrant;
1.4538 +
1.4539 + courrant *= cos(phi3);
1.4540 +
1.4541 + T d = sin(phi2)*courrant;
1.4542 +
1.4543 + courrant *= cos(phi2);
1.4544 +
1.4545 + T c = sin(phi1)*courrant;
1.4546 +
1.4547 + courrant *= cos(phi1);
1.4548 +
1.4549 + T b = sin(theta)*courrant;
1.4550 + T a = cos(theta)*courrant;
1.4551 +
1.4552 + return(rho*octonion<T>(a,b,c,d,e,f,g,h));
1.4553 + }
1.4554 +
1.4555 +
1.4556 + template<typename T>
1.4557 + inline octonion<T> multipolar(T const & rho1,
1.4558 + T const & theta1,
1.4559 + T const & rho2,
1.4560 + T const & theta2,
1.4561 + T const & rho3,
1.4562 + T const & theta3,
1.4563 + T const & rho4,
1.4564 + T const & theta4)
1.4565 + {
1.4566 + using ::std::cos;
1.4567 + using ::std::sin;
1.4568 +
1.4569 + T a = rho1*cos(theta1);
1.4570 + T b = rho1*sin(theta1);
1.4571 + T c = rho2*cos(theta2);
1.4572 + T d = rho2*sin(theta2);
1.4573 + T e = rho3*cos(theta3);
1.4574 + T f = rho3*sin(theta3);
1.4575 + T g = rho4*cos(theta4);
1.4576 + T h = rho4*sin(theta4);
1.4577 +
1.4578 + return(octonion<T>(a,b,c,d,e,f,g,h));
1.4579 + }
1.4580 +
1.4581 +
1.4582 + template<typename T>
1.4583 + inline octonion<T> cylindrical(T const & r,
1.4584 + T const & angle,
1.4585 + T const & h1,
1.4586 + T const & h2,
1.4587 + T const & h3,
1.4588 + T const & h4,
1.4589 + T const & h5,
1.4590 + T const & h6)
1.4591 + {
1.4592 + using ::std::cos;
1.4593 + using ::std::sin;
1.4594 +
1.4595 + T a = r*cos(angle);
1.4596 + T b = r*sin(angle);
1.4597 +
1.4598 + return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6));
1.4599 + }
1.4600 +
1.4601 +
1.4602 + template<typename T>
1.4603 + inline octonion<T> exp(octonion<T> const & o)
1.4604 + {
1.4605 + using ::std::exp;
1.4606 + using ::std::cos;
1.4607 +
1.4608 + using ::boost::math::sinc_pi;
1.4609 +
1.4610 + T u = exp(real(o));
1.4611 +
1.4612 + T z = abs(unreal(o));
1.4613 +
1.4614 + T w = sinc_pi(z);
1.4615 +
1.4616 + return(u*octonion<T>(cos(z),
1.4617 + w*o.R_component_2(), w*o.R_component_3(),
1.4618 + w*o.R_component_4(), w*o.R_component_5(),
1.4619 + w*o.R_component_6(), w*o.R_component_7(),
1.4620 + w*o.R_component_8()));
1.4621 + }
1.4622 +
1.4623 +
1.4624 + template<typename T>
1.4625 + inline octonion<T> cos(octonion<T> const & o)
1.4626 + {
1.4627 + using ::std::sin;
1.4628 + using ::std::cos;
1.4629 + using ::std::cosh;
1.4630 +
1.4631 + using ::boost::math::sinhc_pi;
1.4632 +
1.4633 + T z = abs(unreal(o));
1.4634 +
1.4635 + T w = -sin(o.real())*sinhc_pi(z);
1.4636 +
1.4637 + return(octonion<T>(cos(o.real())*cosh(z),
1.4638 + w*o.R_component_2(), w*o.R_component_3(),
1.4639 + w*o.R_component_4(), w*o.R_component_5(),
1.4640 + w*o.R_component_6(), w*o.R_component_7(),
1.4641 + w*o.R_component_8()));
1.4642 + }
1.4643 +
1.4644 +
1.4645 + template<typename T>
1.4646 + inline octonion<T> sin(octonion<T> const & o)
1.4647 + {
1.4648 + using ::std::sin;
1.4649 + using ::std::cos;
1.4650 + using ::std::cosh;
1.4651 +
1.4652 + using ::boost::math::sinhc_pi;
1.4653 +
1.4654 + T z = abs(unreal(o));
1.4655 +
1.4656 + T w = +cos(o.real())*sinhc_pi(z);
1.4657 +
1.4658 + return(octonion<T>(sin(o.real())*cosh(z),
1.4659 + w*o.R_component_2(), w*o.R_component_3(),
1.4660 + w*o.R_component_4(), w*o.R_component_5(),
1.4661 + w*o.R_component_6(), w*o.R_component_7(),
1.4662 + w*o.R_component_8()));
1.4663 + }
1.4664 +
1.4665 +
1.4666 + template<typename T>
1.4667 + inline octonion<T> tan(octonion<T> const & o)
1.4668 + {
1.4669 + return(sin(o)/cos(o));
1.4670 + }
1.4671 +
1.4672 +
1.4673 + template<typename T>
1.4674 + inline octonion<T> cosh(octonion<T> const & o)
1.4675 + {
1.4676 + return((exp(+o)+exp(-o))/static_cast<T>(2));
1.4677 + }
1.4678 +
1.4679 +
1.4680 + template<typename T>
1.4681 + inline octonion<T> sinh(octonion<T> const & o)
1.4682 + {
1.4683 + return((exp(+o)-exp(-o))/static_cast<T>(2));
1.4684 + }
1.4685 +
1.4686 +
1.4687 + template<typename T>
1.4688 + inline octonion<T> tanh(octonion<T> const & o)
1.4689 + {
1.4690 + return(sinh(o)/cosh(o));
1.4691 + }
1.4692 +
1.4693 +
1.4694 + template<typename T>
1.4695 + octonion<T> pow(octonion<T> const & o,
1.4696 + int n)
1.4697 + {
1.4698 + if (n > 1)
1.4699 + {
1.4700 + int m = n>>1;
1.4701 +
1.4702 + octonion<T> result = pow(o, m);
1.4703 +
1.4704 + result *= result;
1.4705 +
1.4706 + if (n != (m<<1))
1.4707 + {
1.4708 + result *= o; // n odd
1.4709 + }
1.4710 +
1.4711 + return(result);
1.4712 + }
1.4713 + else if (n == 1)
1.4714 + {
1.4715 + return(o);
1.4716 + }
1.4717 + else if (n == 0)
1.4718 + {
1.4719 + return(octonion<T>(1));
1.4720 + }
1.4721 + else /* n < 0 */
1.4722 + {
1.4723 + return(pow(octonion<T>(1)/o,-n));
1.4724 + }
1.4725 + }
1.4726 +
1.4727 +
1.4728 + // helper templates for converting copy constructors (definition)
1.4729 +
1.4730 + namespace detail
1.4731 + {
1.4732 +
1.4733 + template< typename T,
1.4734 + typename U
1.4735 + >
1.4736 + octonion<T> octonion_type_converter(octonion<U> const & rhs)
1.4737 + {
1.4738 + return(octonion<T>( static_cast<T>(rhs.R_component_1()),
1.4739 + static_cast<T>(rhs.R_component_2()),
1.4740 + static_cast<T>(rhs.R_component_3()),
1.4741 + static_cast<T>(rhs.R_component_4()),
1.4742 + static_cast<T>(rhs.R_component_5()),
1.4743 + static_cast<T>(rhs.R_component_6()),
1.4744 + static_cast<T>(rhs.R_component_7()),
1.4745 + static_cast<T>(rhs.R_component_8())));
1.4746 + }
1.4747 + }
1.4748 + }
1.4749 +}
1.4750 +
1.4751 +
1.4752 +#if BOOST_WORKAROUND(__GNUC__, < 3)
1.4753 + #undef BOOST_GET_VALARRAY
1.4754 +#endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1.4755 +
1.4756 +
1.4757 +#endif /* BOOST_OCTONION_HPP */