Attempt to represent the S^2->S^3 header reorganisation as a series of "hg rename" operations
1 // boost octonion.hpp header file
3 // (C) Copyright Hubert Holin 2001.
4 // Distributed under the Boost Software License, Version 1.0. (See
5 // accompanying file LICENSE_1_0.txt or copy at
6 // http://www.boost.org/LICENSE_1_0.txt)
8 // See http://www.boost.org for updates, documentation, and revision history.
11 #ifndef BOOST_OCTONION_HPP
12 #define BOOST_OCTONION_HPP
14 #include <boost/math/quaternion.hpp>
21 #if BOOST_WORKAROUND(__GNUC__, < 3)
22 // gcc 2.95.x uses expression templates for valarray calculations, but
23 // the result is not conforming. We need BOOST_GET_VALARRAY to get an
24 // actual valarray result when we need to call a member function
25 #define BOOST_GET_VALARRAY(T,x) ::std::valarray<T>(x)
26 // gcc 2.95.x has an "std::ios" class that is similar to
27 // "std::ios_base", so we just use a #define
28 #define BOOST_IOS_BASE ::std::ios
29 // gcc 2.x ignores function scope using declarations,
30 // put them in the scope of the enclosing namespace instead:
31 using ::std::valarray;
37 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
39 #define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \
45 octonion<type> unreal() const \
47 return( octonion<type>(static_cast<type>(0),b,c,d,e,f,g,h)); \
50 type R_component_1() const \
55 type R_component_2() const \
60 type R_component_3() const \
65 type R_component_4() const \
70 type R_component_5() const \
75 type R_component_6() const \
80 type R_component_7() const \
85 type R_component_8() const \
90 ::std::complex<type> C_component_1() const \
92 return(::std::complex<type>(a,b)); \
95 ::std::complex<type> C_component_2() const \
97 return(::std::complex<type>(c,d)); \
100 ::std::complex<type> C_component_3() const \
102 return(::std::complex<type>(e,f)); \
105 ::std::complex<type> C_component_4() const \
107 return(::std::complex<type>(g,h)); \
110 ::boost::math::quaternion<type> H_component_1() const \
112 return(::boost::math::quaternion<type>(a,b,c,d)); \
115 ::boost::math::quaternion<type> H_component_2() const \
117 return(::boost::math::quaternion<type>(e,f,g,h)); \
121 #define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \
122 template<typename X> \
123 octonion<type> & operator = (octonion<X> const & a_affecter) \
125 a = static_cast<type>(a_affecter.R_component_1()); \
126 b = static_cast<type>(a_affecter.R_component_2()); \
127 c = static_cast<type>(a_affecter.R_component_3()); \
128 d = static_cast<type>(a_affecter.R_component_4()); \
129 e = static_cast<type>(a_affecter.R_component_5()); \
130 f = static_cast<type>(a_affecter.R_component_6()); \
131 g = static_cast<type>(a_affecter.R_component_7()); \
132 h = static_cast<type>(a_affecter.R_component_8()); \
137 octonion<type> & operator = (octonion<type> const & a_affecter) \
151 octonion<type> & operator = (type const & a_affecter) \
155 b = c = d = e = f= g = h = static_cast<type>(0); \
160 octonion<type> & operator = (::std::complex<type> const & a_affecter) \
162 a = a_affecter.real(); \
163 b = a_affecter.imag(); \
165 c = d = e = f = g = h = static_cast<type>(0); \
170 octonion<type> & operator = (::boost::math::quaternion<type> const & a_affecter) \
172 a = a_affecter.R_component_1(); \
173 b = a_affecter.R_component_2(); \
174 c = a_affecter.R_component_3(); \
175 d = a_affecter.R_component_4(); \
177 e = f = g = h = static_cast<type>(0); \
183 #define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \
199 typedef T value_type;
201 // constructor for O seen as R^8
202 // (also default constructor)
204 explicit octonion( T const & requested_a = T(),
205 T const & requested_b = T(),
206 T const & requested_c = T(),
207 T const & requested_d = T(),
208 T const & requested_e = T(),
209 T const & requested_f = T(),
210 T const & requested_g = T(),
211 T const & requested_h = T())
225 // constructor for H seen as C^4
227 explicit octonion( ::std::complex<T> const & z0,
228 ::std::complex<T> const & z1 = ::std::complex<T>(),
229 ::std::complex<T> const & z2 = ::std::complex<T>(),
230 ::std::complex<T> const & z3 = ::std::complex<T>())
244 // constructor for O seen as H^2
246 explicit octonion( ::boost::math::quaternion<T> const & q0,
247 ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>())
248 : a(q0.R_component_1()),
249 b(q0.R_component_2()),
250 c(q0.R_component_3()),
251 d(q0.R_component_4()),
252 e(q1.R_component_1()),
253 f(q1.R_component_2()),
254 g(q1.R_component_3()),
255 h(q1.R_component_4())
261 // UNtemplated copy constructor
262 // (this is taken care of by the compiler itself)
265 // templated copy constructor
268 explicit octonion(octonion<X> const & a_recopier)
269 : a(static_cast<T>(a_recopier.R_component_1())),
270 b(static_cast<T>(a_recopier.R_component_2())),
271 c(static_cast<T>(a_recopier.R_component_3())),
272 d(static_cast<T>(a_recopier.R_component_4())),
273 e(static_cast<T>(a_recopier.R_component_5())),
274 f(static_cast<T>(a_recopier.R_component_6())),
275 g(static_cast<T>(a_recopier.R_component_7())),
276 h(static_cast<T>(a_recopier.R_component_8()))
283 // (this is taken care of by the compiler itself)
288 // Note: Like complex number, octonions do have a meaningful notion of "real part",
289 // but unlike them there is no meaningful notion of "imaginary part".
290 // Instead there is an "unreal part" which itself is an octonion, and usually
291 // nothing simpler (as opposed to the complex number case).
292 // However, for practicallity, there are accessors for the other components
293 // (these are necessary for the templated copy constructor, for instance).
295 BOOST_OCTONION_ACCESSOR_GENERATOR(T)
297 // assignment operators
299 BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T)
301 // other assignment-related operators
303 // NOTE: Octonion multiplication is *NOT* commutative;
304 // symbolically, "q *= rhs;" means "q = q * rhs;"
305 // and "q /= rhs;" means "q = q * inverse_of(rhs);";
306 // octonion multiplication is also *NOT* associative
308 octonion<T> & operator += (T const & rhs)
310 T at = a + rhs; // exception guard
318 octonion<T> & operator += (::std::complex<T> const & rhs)
320 T at = a + rhs.real(); // exception guard
321 T bt = b + rhs.imag(); // exception guard
330 octonion<T> & operator += (::boost::math::quaternion<T> const & rhs)
332 T at = a + rhs.R_component_1(); // exception guard
333 T bt = b + rhs.R_component_2(); // exception guard
334 T ct = c + rhs.R_component_3(); // exception guard
335 T dt = d + rhs.R_component_4(); // exception guard
347 octonion<T> & operator += (octonion<X> const & rhs)
349 T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
350 T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
351 T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
352 T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
353 T et = e + static_cast<T>(rhs.R_component_5()); // exception guard
354 T ft = f + static_cast<T>(rhs.R_component_6()); // exception guard
355 T gt = g + static_cast<T>(rhs.R_component_7()); // exception guard
356 T ht = h + static_cast<T>(rhs.R_component_8()); // exception guard
372 octonion<T> & operator -= (T const & rhs)
374 T at = a - rhs; // exception guard
382 octonion<T> & operator -= (::std::complex<T> const & rhs)
384 T at = a - rhs.real(); // exception guard
385 T bt = b - rhs.imag(); // exception guard
394 octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs)
396 T at = a - rhs.R_component_1(); // exception guard
397 T bt = b - rhs.R_component_2(); // exception guard
398 T ct = c - rhs.R_component_3(); // exception guard
399 T dt = d - rhs.R_component_4(); // exception guard
411 octonion<T> & operator -= (octonion<X> const & rhs)
413 T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
414 T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
415 T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
416 T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
417 T et = e - static_cast<T>(rhs.R_component_5()); // exception guard
418 T ft = f - static_cast<T>(rhs.R_component_6()); // exception guard
419 T gt = g - static_cast<T>(rhs.R_component_7()); // exception guard
420 T ht = h - static_cast<T>(rhs.R_component_8()); // exception guard
435 octonion<T> & operator *= (T const & rhs)
437 T at = a * rhs; // exception guard
438 T bt = b * rhs; // exception guard
439 T ct = c * rhs; // exception guard
440 T dt = d * rhs; // exception guard
441 T et = e * rhs; // exception guard
442 T ft = f * rhs; // exception guard
443 T gt = g * rhs; // exception guard
444 T ht = h * rhs; // exception guard
459 octonion<T> & operator *= (::std::complex<T> const & rhs)
486 octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs)
488 T ar = rhs.R_component_1();
489 T br = rhs.R_component_2();
490 T cr = rhs.R_component_2();
491 T dr = rhs.R_component_2();
493 T at = +a*ar-b*br-c*cr-d*dr;
494 T bt = +a*br+b*ar+c*dr-d*cr;
495 T ct = +a*cr-b*dr+c*ar+d*br;
496 T dt = +a*dr+b*cr-c*br+d*ar;
497 T et = +e*ar+f*br+g*cr+h*dr;
498 T ft = -e*br+f*ar-g*dr+h*cr;
499 T gt = -e*cr+f*dr+g*ar-h*br;
500 T ht = -e*dr-f*cr+g*br+h*ar;
516 octonion<T> & operator *= (octonion<X> const & rhs)
518 T ar = static_cast<T>(rhs.R_component_1());
519 T br = static_cast<T>(rhs.R_component_2());
520 T cr = static_cast<T>(rhs.R_component_3());
521 T dr = static_cast<T>(rhs.R_component_4());
522 T er = static_cast<T>(rhs.R_component_5());
523 T fr = static_cast<T>(rhs.R_component_6());
524 T gr = static_cast<T>(rhs.R_component_7());
525 T hr = static_cast<T>(rhs.R_component_8());
527 T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr;
528 T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr;
529 T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr;
530 T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er;
531 T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr;
532 T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr;
533 T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br;
534 T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar;
549 octonion<T> & operator /= (T const & rhs)
551 T at = a / rhs; // exception guard
552 T bt = b / rhs; // exception guard
553 T ct = c / rhs; // exception guard
554 T dt = d / rhs; // exception guard
555 T et = e / rhs; // exception guard
556 T ft = f / rhs; // exception guard
557 T gt = g / rhs; // exception guard
558 T ht = h / rhs; // exception guard
573 octonion<T> & operator /= (::std::complex<T> const & rhs)
578 T denominator = ar*ar+br*br;
580 T at = (+a*ar-b*br)/denominator;
581 T bt = (-a*br+b*ar)/denominator;
582 T ct = (+c*ar-d*br)/denominator;
583 T dt = (+c*br+d*ar)/denominator;
584 T et = (+e*ar-f*br)/denominator;
585 T ft = (+e*br+f*ar)/denominator;
586 T gt = (+g*ar+h*br)/denominator;
587 T ht = (+g*br+h*ar)/denominator;
602 octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs)
604 T ar = rhs.R_component_1();
605 T br = rhs.R_component_2();
606 T cr = rhs.R_component_2();
607 T dr = rhs.R_component_2();
609 T denominator = ar*ar+br*br+cr*cr+dr*dr;
611 T at = (+a*ar+b*br+c*cr+d*dr)/denominator;
612 T bt = (-a*br+b*ar-c*dr+d*cr)/denominator;
613 T ct = (-a*cr+b*dr+c*ar-d*br)/denominator;
614 T dt = (-a*dr-b*cr+c*br+d*ar)/denominator;
615 T et = (+e*ar-f*br-g*cr-h*dr)/denominator;
616 T ft = (+e*br+f*ar+g*dr-h*cr)/denominator;
617 T gt = (+e*cr-f*dr+g*ar+h*br)/denominator;
618 T ht = (+e*dr+f*cr-g*br+h*ar)/denominator;
634 octonion<T> & operator /= (octonion<X> const & rhs)
636 T ar = static_cast<T>(rhs.R_component_1());
637 T br = static_cast<T>(rhs.R_component_2());
638 T cr = static_cast<T>(rhs.R_component_3());
639 T dr = static_cast<T>(rhs.R_component_4());
640 T er = static_cast<T>(rhs.R_component_5());
641 T fr = static_cast<T>(rhs.R_component_6());
642 T gr = static_cast<T>(rhs.R_component_7());
643 T hr = static_cast<T>(rhs.R_component_8());
645 T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr;
647 T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator;
648 T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator;
649 T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator;
650 T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator;
651 T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator;
652 T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator;
653 T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator;
654 T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator;
671 BOOST_OCTONION_MEMBER_DATA_GENERATOR(T)
679 // declaration of octonion specialization
681 template<> class octonion<float>;
682 template<> class octonion<double>;
683 template<> class octonion<long double>;
686 // helper templates for converting copy constructors (declaration)
691 template< typename T,
694 octonion<T> octonion_type_converter(octonion<U> const & rhs);
698 // implementation of octonion specialization
701 #define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \
702 explicit octonion( type const & requested_a = static_cast<type>(0), \
703 type const & requested_b = static_cast<type>(0), \
704 type const & requested_c = static_cast<type>(0), \
705 type const & requested_d = static_cast<type>(0), \
706 type const & requested_e = static_cast<type>(0), \
707 type const & requested_f = static_cast<type>(0), \
708 type const & requested_g = static_cast<type>(0), \
709 type const & requested_h = static_cast<type>(0)) \
721 explicit octonion( ::std::complex<type> const & z0, \
722 ::std::complex<type> const & z1 = ::std::complex<type>(), \
723 ::std::complex<type> const & z2 = ::std::complex<type>(), \
724 ::std::complex<type> const & z3 = ::std::complex<type>()) \
736 explicit octonion( ::boost::math::quaternion<type> const & q0, \
737 ::boost::math::quaternion<type> const & q1 = ::boost::math::quaternion<type>()) \
738 : a(q0.R_component_1()), \
739 b(q0.R_component_2()), \
740 c(q0.R_component_3()), \
741 d(q0.R_component_4()), \
742 e(q1.R_component_1()), \
743 f(q1.R_component_2()), \
744 g(q1.R_component_3()), \
745 h(q1.R_component_4()) \
750 #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
751 octonion<type> & operator += (type const & rhs) \
758 #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
759 octonion<type> & operator += (::std::complex<type> const & rhs) \
767 #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
768 octonion<type> & operator += (::boost::math::quaternion<type> const & rhs) \
770 a += rhs.R_component_1(); \
771 b += rhs.R_component_2(); \
772 c += rhs.R_component_3(); \
773 d += rhs.R_component_4(); \
778 #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \
779 template<typename X> \
780 octonion<type> & operator += (octonion<X> const & rhs) \
782 a += static_cast<type>(rhs.R_component_1()); \
783 b += static_cast<type>(rhs.R_component_2()); \
784 c += static_cast<type>(rhs.R_component_3()); \
785 d += static_cast<type>(rhs.R_component_4()); \
786 e += static_cast<type>(rhs.R_component_5()); \
787 f += static_cast<type>(rhs.R_component_6()); \
788 g += static_cast<type>(rhs.R_component_7()); \
789 h += static_cast<type>(rhs.R_component_8()); \
794 #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
795 octonion<type> & operator -= (type const & rhs) \
802 #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
803 octonion<type> & operator -= (::std::complex<type> const & rhs) \
811 #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
812 octonion<type> & operator -= (::boost::math::quaternion<type> const & rhs) \
814 a -= rhs.R_component_1(); \
815 b -= rhs.R_component_2(); \
816 c -= rhs.R_component_3(); \
817 d -= rhs.R_component_4(); \
822 #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \
823 template<typename X> \
824 octonion<type> & operator -= (octonion<X> const & rhs) \
826 a -= static_cast<type>(rhs.R_component_1()); \
827 b -= static_cast<type>(rhs.R_component_2()); \
828 c -= static_cast<type>(rhs.R_component_3()); \
829 d -= static_cast<type>(rhs.R_component_4()); \
830 e -= static_cast<type>(rhs.R_component_5()); \
831 f -= static_cast<type>(rhs.R_component_6()); \
832 g -= static_cast<type>(rhs.R_component_7()); \
833 h -= static_cast<type>(rhs.R_component_8()); \
838 #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
839 octonion<type> & operator *= (type const & rhs) \
853 #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
854 octonion<type> & operator *= (::std::complex<type> const & rhs) \
856 type ar = rhs.real(); \
857 type br = rhs.imag(); \
859 type at = +a*ar-b*br; \
860 type bt = +a*br+b*ar; \
861 type ct = +c*ar+d*br; \
862 type dt = -c*br+d*ar; \
863 type et = +e*ar+f*br; \
864 type ft = -e*br+f*ar; \
865 type gt = +g*ar-h*br; \
866 type ht = +g*br+h*ar; \
880 #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
881 octonion<type> & operator *= (::boost::math::quaternion<type> const & rhs) \
883 type ar = rhs.R_component_1(); \
884 type br = rhs.R_component_2(); \
885 type cr = rhs.R_component_2(); \
886 type dr = rhs.R_component_2(); \
888 type at = +a*ar-b*br-c*cr-d*dr; \
889 type bt = +a*br+b*ar+c*dr-d*cr; \
890 type ct = +a*cr-b*dr+c*ar+d*br; \
891 type dt = +a*dr+b*cr-c*br+d*ar; \
892 type et = +e*ar+f*br+g*cr+h*dr; \
893 type ft = -e*br+f*ar-g*dr+h*cr; \
894 type gt = -e*cr+f*dr+g*ar-h*br; \
895 type ht = -e*dr-f*cr+g*br+h*ar; \
909 #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \
910 template<typename X> \
911 octonion<type> & operator *= (octonion<X> const & rhs) \
913 type ar = static_cast<type>(rhs.R_component_1()); \
914 type br = static_cast<type>(rhs.R_component_2()); \
915 type cr = static_cast<type>(rhs.R_component_3()); \
916 type dr = static_cast<type>(rhs.R_component_4()); \
917 type er = static_cast<type>(rhs.R_component_5()); \
918 type fr = static_cast<type>(rhs.R_component_6()); \
919 type gr = static_cast<type>(rhs.R_component_7()); \
920 type hr = static_cast<type>(rhs.R_component_8()); \
922 type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \
923 type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \
924 type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \
925 type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \
926 type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \
927 type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \
928 type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \
929 type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \
943 // There is quite a lot of repetition in the code below. This is intentional.
944 // The last conditional block is the normal form, and the others merely
945 // consist of workarounds for various compiler deficiencies. Hopefuly, when
946 // more compilers are conformant and we can retire support for those that are
947 // not, we will be able to remove the clutter. This is makes the situation
948 // (painfully) explicit.
950 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
951 octonion<type> & operator /= (type const & rhs) \
961 #if defined(__GNUC__) && (__GNUC__ < 3)
962 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
963 octonion<type> & operator /= (::std::complex<type> const & rhs) \
965 using ::std::valarray; \
967 valarray<type> tr(2); \
969 tr[0] = rhs.real(); \
970 tr[1] = rhs.imag(); \
972 type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)(); \
976 valarray<type> tt(8); \
978 tt[0] = +a*tr[0]-b*tr[1]; \
979 tt[1] = -a*tr[1]+b*tr[0]; \
980 tt[2] = +c*tr[0]-d*tr[1]; \
981 tt[3] = +c*tr[1]+d*tr[0]; \
982 tt[4] = +e*tr[0]-f*tr[1]; \
983 tt[5] = +e*tr[1]+f*tr[0]; \
984 tt[6] = +g*tr[0]+h*tr[1]; \
985 tt[7] = +g*tr[1]+h*tr[0]; \
989 tt *= (mixam/tr.sum()); \
1002 #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1003 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1004 octonion<type> & operator /= (::std::complex<type> const & rhs) \
1006 using ::std::valarray; \
1009 valarray<type> tr(2); \
1011 tr[0] = rhs.real(); \
1012 tr[1] = rhs.imag(); \
1014 type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1018 valarray<type> tt(8); \
1020 tt[0] = +a*tr[0]-b*tr[1]; \
1021 tt[1] = -a*tr[1]+b*tr[0]; \
1022 tt[2] = +c*tr[0]-d*tr[1]; \
1023 tt[3] = +c*tr[1]+d*tr[0]; \
1024 tt[4] = +e*tr[0]-f*tr[1]; \
1025 tt[5] = +e*tr[1]+f*tr[0]; \
1026 tt[6] = +g*tr[0]+h*tr[1]; \
1027 tt[7] = +g*tr[1]+h*tr[0]; \
1031 tt *= (mixam/tr.sum()); \
1045 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1046 octonion<type> & operator /= (::std::complex<type> const & rhs) \
1048 using ::std::valarray; \
1050 valarray<type> tr(2); \
1052 tr[0] = rhs.real(); \
1053 tr[1] = rhs.imag(); \
1055 type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1059 valarray<type> tt(8); \
1061 tt[0] = +a*tr[0]-b*tr[1]; \
1062 tt[1] = -a*tr[1]+b*tr[0]; \
1063 tt[2] = +c*tr[0]-d*tr[1]; \
1064 tt[3] = +c*tr[1]+d*tr[0]; \
1065 tt[4] = +e*tr[0]-f*tr[1]; \
1066 tt[5] = +e*tr[1]+f*tr[0]; \
1067 tt[6] = +g*tr[0]+h*tr[1]; \
1068 tt[7] = +g*tr[1]+h*tr[0]; \
1072 tt *= (mixam/tr.sum()); \
1085 #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1087 #if defined(__GNUC__) && (__GNUC__ < 3)
1088 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1089 octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1091 using ::std::valarray; \
1093 valarray<type> tr(4); \
1095 tr[0] = static_cast<type>(rhs.R_component_1()); \
1096 tr[1] = static_cast<type>(rhs.R_component_2()); \
1097 tr[2] = static_cast<type>(rhs.R_component_3()); \
1098 tr[3] = static_cast<type>(rhs.R_component_4()); \
1100 type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
1104 valarray<type> tt(8); \
1106 tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
1107 tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
1108 tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
1109 tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
1110 tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1111 tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1112 tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1113 tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1117 tt *= (mixam/tr.sum()); \
1130 #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1131 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1132 octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1134 using ::std::valarray; \
1137 valarray<type> tr(4); \
1139 tr[0] = static_cast<type>(rhs.R_component_1()); \
1140 tr[1] = static_cast<type>(rhs.R_component_2()); \
1141 tr[2] = static_cast<type>(rhs.R_component_3()); \
1142 tr[3] = static_cast<type>(rhs.R_component_4()); \
1144 type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1148 valarray<type> tt(8); \
1150 tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
1151 tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
1152 tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
1153 tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
1154 tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1155 tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1156 tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1157 tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1161 tt *= (mixam/tr.sum()); \
1175 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1176 octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \
1178 using ::std::valarray; \
1180 valarray<type> tr(4); \
1182 tr[0] = static_cast<type>(rhs.R_component_1()); \
1183 tr[1] = static_cast<type>(rhs.R_component_2()); \
1184 tr[2] = static_cast<type>(rhs.R_component_3()); \
1185 tr[3] = static_cast<type>(rhs.R_component_4()); \
1187 type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1191 valarray<type> tt(8); \
1193 tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
1194 tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
1195 tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
1196 tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
1197 tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \
1198 tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \
1199 tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \
1200 tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \
1204 tt *= (mixam/tr.sum()); \
1217 #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1219 #if defined(__GNUC__) && (__GNUC__ < 3)
1220 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1221 template<typename X> \
1222 octonion<type> & operator /= (octonion<X> const & rhs) \
1224 using ::std::valarray; \
1226 valarray<type> tr(8); \
1228 tr[0] = static_cast<type>(rhs.R_component_1()); \
1229 tr[1] = static_cast<type>(rhs.R_component_2()); \
1230 tr[2] = static_cast<type>(rhs.R_component_3()); \
1231 tr[3] = static_cast<type>(rhs.R_component_4()); \
1232 tr[4] = static_cast<type>(rhs.R_component_5()); \
1233 tr[5] = static_cast<type>(rhs.R_component_6()); \
1234 tr[6] = static_cast<type>(rhs.R_component_7()); \
1235 tr[7] = static_cast<type>(rhs.R_component_8()); \
1237 type mixam = (BOOST_GET_VALARRAY(type,static_cast<type>(1)/abs(tr)).max)();\
1241 valarray<type> tt(8); \
1243 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]; \
1244 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]; \
1245 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]; \
1246 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]; \
1247 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]; \
1248 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]; \
1249 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]; \
1250 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]; \
1254 tt *= (mixam/tr.sum()); \
1267 #elif defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
1268 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1269 template<typename X> \
1270 octonion<type> & operator /= (octonion<X> const & rhs) \
1272 using ::std::valarray; \
1275 valarray<type> tr(8); \
1277 tr[0] = static_cast<type>(rhs.R_component_1()); \
1278 tr[1] = static_cast<type>(rhs.R_component_2()); \
1279 tr[2] = static_cast<type>(rhs.R_component_3()); \
1280 tr[3] = static_cast<type>(rhs.R_component_4()); \
1281 tr[4] = static_cast<type>(rhs.R_component_5()); \
1282 tr[5] = static_cast<type>(rhs.R_component_6()); \
1283 tr[6] = static_cast<type>(rhs.R_component_7()); \
1284 tr[7] = static_cast<type>(rhs.R_component_8()); \
1286 type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1290 valarray<type> tt(8); \
1292 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]; \
1293 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]; \
1294 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]; \
1295 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]; \
1296 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]; \
1297 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]; \
1298 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]; \
1299 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]; \
1303 tt *= (mixam/tr.sum()); \
1317 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \
1318 template<typename X> \
1319 octonion<type> & operator /= (octonion<X> const & rhs) \
1321 using ::std::valarray; \
1323 valarray<type> tr(8); \
1325 tr[0] = static_cast<type>(rhs.R_component_1()); \
1326 tr[1] = static_cast<type>(rhs.R_component_2()); \
1327 tr[2] = static_cast<type>(rhs.R_component_3()); \
1328 tr[3] = static_cast<type>(rhs.R_component_4()); \
1329 tr[4] = static_cast<type>(rhs.R_component_5()); \
1330 tr[5] = static_cast<type>(rhs.R_component_6()); \
1331 tr[6] = static_cast<type>(rhs.R_component_7()); \
1332 tr[7] = static_cast<type>(rhs.R_component_8()); \
1334 type mixam = static_cast<type>(1)/(abs(tr).max)(); \
1338 valarray<type> tt(8); \
1340 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]; \
1341 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]; \
1342 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]; \
1343 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]; \
1344 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]; \
1345 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]; \
1346 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]; \
1347 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]; \
1351 tt *= (mixam/tr.sum()); \
1364 #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
1367 #define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
1368 BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \
1369 BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \
1370 BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \
1371 BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type)
1373 #define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
1374 BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \
1375 BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \
1376 BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \
1377 BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type)
1379 #define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
1380 BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \
1381 BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \
1382 BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \
1383 BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type)
1385 #define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \
1386 BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \
1387 BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \
1388 BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \
1389 BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type)
1391 #define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \
1392 BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \
1393 BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \
1394 BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \
1395 BOOST_OCTONION_MEMBER_DIV_GENERATOR(type)
1399 class octonion<float>
1403 typedef float value_type;
1405 BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float)
1407 // UNtemplated copy constructor
1408 // (this is taken care of by the compiler itself)
1410 // explicit copy constructors (precision-loosing converters)
1412 explicit octonion(octonion<double> const & a_recopier)
1414 *this = detail::octonion_type_converter<float, double>(a_recopier);
1417 explicit octonion(octonion<long double> const & a_recopier)
1419 *this = detail::octonion_type_converter<float, long double>(a_recopier);
1423 // (this is taken care of by the compiler itself)
1427 // Note: Like complex number, octonions do have a meaningful notion of "real part",
1428 // but unlike them there is no meaningful notion of "imaginary part".
1429 // Instead there is an "unreal part" which itself is an octonion, and usually
1430 // nothing simpler (as opposed to the complex number case).
1431 // However, for practicallity, there are accessors for the other components
1432 // (these are necessary for the templated copy constructor, for instance).
1434 BOOST_OCTONION_ACCESSOR_GENERATOR(float)
1436 // assignment operators
1438 BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float)
1440 // other assignment-related operators
1442 // NOTE: Octonion multiplication is *NOT* commutative;
1443 // symbolically, "q *= rhs;" means "q = q * rhs;"
1444 // and "q /= rhs;" means "q = q * inverse_of(rhs);";
1445 // octonion multiplication is also *NOT* associative
1447 BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float)
1452 BOOST_OCTONION_MEMBER_DATA_GENERATOR(float)
1461 class octonion<double>
1465 typedef double value_type;
1467 BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double)
1469 // UNtemplated copy constructor
1470 // (this is taken care of by the compiler itself)
1472 // converting copy constructor
1474 explicit octonion(octonion<float> const & a_recopier)
1476 *this = detail::octonion_type_converter<double, float>(a_recopier);
1479 // explicit copy constructors (precision-loosing converters)
1481 explicit octonion(octonion<long double> const & a_recopier)
1483 *this = detail::octonion_type_converter<double, long double>(a_recopier);
1487 // (this is taken care of by the compiler itself)
1491 // Note: Like complex number, octonions do have a meaningful notion of "real part",
1492 // but unlike them there is no meaningful notion of "imaginary part".
1493 // Instead there is an "unreal part" which itself is an octonion, and usually
1494 // nothing simpler (as opposed to the complex number case).
1495 // However, for practicallity, there are accessors for the other components
1496 // (these are necessary for the templated copy constructor, for instance).
1498 BOOST_OCTONION_ACCESSOR_GENERATOR(double)
1500 // assignment operators
1502 BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double)
1504 // other assignment-related operators
1506 // NOTE: Octonion multiplication is *NOT* commutative;
1507 // symbolically, "q *= rhs;" means "q = q * rhs;"
1508 // and "q /= rhs;" means "q = q * inverse_of(rhs);";
1509 // octonion multiplication is also *NOT* associative
1511 BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double)
1516 BOOST_OCTONION_MEMBER_DATA_GENERATOR(double)
1525 class octonion<long double>
1529 typedef long double value_type;
1531 BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double)
1533 // UNtemplated copy constructor
1534 // (this is taken care of by the compiler itself)
1536 // converting copy constructor
1538 explicit octonion(octonion<float> const & a_recopier)
1540 *this = detail::octonion_type_converter<long double, float>(a_recopier);
1544 explicit octonion(octonion<double> const & a_recopier)
1546 *this = detail::octonion_type_converter<long double, double>(a_recopier);
1551 // (this is taken care of by the compiler itself)
1555 // Note: Like complex number, octonions do have a meaningful notion of "real part",
1556 // but unlike them there is no meaningful notion of "imaginary part".
1557 // Instead there is an "unreal part" which itself is an octonion, and usually
1558 // nothing simpler (as opposed to the complex number case).
1559 // However, for practicallity, there are accessors for the other components
1560 // (these are necessary for the templated copy constructor, for instance).
1562 BOOST_OCTONION_ACCESSOR_GENERATOR(long double)
1564 // assignment operators
1566 BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double)
1568 // other assignment-related operators
1570 // NOTE: Octonion multiplication is *NOT* commutative;
1571 // symbolically, "q *= rhs;" means "q = q * rhs;"
1572 // and "q /= rhs;" means "q = q * inverse_of(rhs);";
1573 // octonion multiplication is also *NOT* associative
1575 BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double)
1580 BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double)
1588 #undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR
1590 #undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR
1592 #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR
1593 #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR
1594 #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR
1595 #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR
1597 #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1
1598 #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2
1599 #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3
1600 #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4
1601 #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1
1602 #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2
1603 #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3
1604 #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4
1605 #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1
1606 #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2
1607 #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3
1608 #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4
1609 #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1
1610 #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2
1611 #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3
1612 #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4
1615 #undef BOOST_OCTONION_MEMBER_DATA_GENERATOR
1617 #undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR
1619 #undef BOOST_OCTONION_ACCESSOR_GENERATOR
1624 #define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \
1626 octonion<T> res(lhs); \
1631 #define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
1632 template<typename T> \
1633 inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \
1634 BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1636 #define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
1637 template<typename T> \
1638 inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \
1639 BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1641 #define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
1642 template<typename T> \
1643 inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \
1644 BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1646 #define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
1647 template<typename T> \
1648 inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \
1649 BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1651 #define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
1652 template<typename T> \
1653 inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \
1654 BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1656 #define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
1657 template<typename T> \
1658 inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \
1659 BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1661 #define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \
1662 template<typename T> \
1663 inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \
1664 BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op)
1666 #define BOOST_OCTONION_OPERATOR_GENERATOR(op) \
1667 BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \
1668 BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \
1669 BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \
1670 BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \
1671 BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \
1672 BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \
1673 BOOST_OCTONION_OPERATOR_GENERATOR_4(op)
1676 BOOST_OCTONION_OPERATOR_GENERATOR(+)
1677 BOOST_OCTONION_OPERATOR_GENERATOR(-)
1678 BOOST_OCTONION_OPERATOR_GENERATOR(*)
1679 BOOST_OCTONION_OPERATOR_GENERATOR(/)
1682 #undef BOOST_OCTONION_OPERATOR_GENERATOR
1684 #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L
1685 #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R
1686 #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L
1687 #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R
1688 #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L
1689 #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R
1690 #undef BOOST_OCTONION_OPERATOR_GENERATOR_4
1692 #undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY
1695 template<typename T>
1696 inline octonion<T> operator + (octonion<T> const & o)
1702 template<typename T>
1703 inline octonion<T> operator - (octonion<T> const & o)
1705 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()));
1709 template<typename T>
1710 inline bool operator == (T const & lhs, octonion<T> const & rhs)
1713 (rhs.R_component_1() == lhs)&&
1714 (rhs.R_component_2() == static_cast<T>(0))&&
1715 (rhs.R_component_3() == static_cast<T>(0))&&
1716 (rhs.R_component_4() == static_cast<T>(0))&&
1717 (rhs.R_component_5() == static_cast<T>(0))&&
1718 (rhs.R_component_6() == static_cast<T>(0))&&
1719 (rhs.R_component_7() == static_cast<T>(0))&&
1720 (rhs.R_component_8() == static_cast<T>(0))
1725 template<typename T>
1726 inline bool operator == (octonion<T> const & lhs, T const & rhs)
1729 (lhs.R_component_1() == rhs)&&
1730 (lhs.R_component_2() == static_cast<T>(0))&&
1731 (lhs.R_component_3() == static_cast<T>(0))&&
1732 (lhs.R_component_4() == static_cast<T>(0))&&
1733 (lhs.R_component_5() == static_cast<T>(0))&&
1734 (lhs.R_component_6() == static_cast<T>(0))&&
1735 (lhs.R_component_7() == static_cast<T>(0))&&
1736 (lhs.R_component_8() == static_cast<T>(0))
1741 template<typename T>
1742 inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs)
1745 (rhs.R_component_1() == lhs.real())&&
1746 (rhs.R_component_2() == lhs.imag())&&
1747 (rhs.R_component_3() == static_cast<T>(0))&&
1748 (rhs.R_component_4() == static_cast<T>(0))&&
1749 (rhs.R_component_5() == static_cast<T>(0))&&
1750 (rhs.R_component_6() == static_cast<T>(0))&&
1751 (rhs.R_component_7() == static_cast<T>(0))&&
1752 (rhs.R_component_8() == static_cast<T>(0))
1757 template<typename T>
1758 inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs)
1761 (lhs.R_component_1() == rhs.real())&&
1762 (lhs.R_component_2() == rhs.imag())&&
1763 (lhs.R_component_3() == static_cast<T>(0))&&
1764 (lhs.R_component_4() == static_cast<T>(0))&&
1765 (lhs.R_component_5() == static_cast<T>(0))&&
1766 (lhs.R_component_6() == static_cast<T>(0))&&
1767 (lhs.R_component_7() == static_cast<T>(0))&&
1768 (lhs.R_component_8() == static_cast<T>(0))
1773 template<typename T>
1774 inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
1777 (rhs.R_component_1() == lhs.R_component_1())&&
1778 (rhs.R_component_2() == lhs.R_component_2())&&
1779 (rhs.R_component_3() == lhs.R_component_3())&&
1780 (rhs.R_component_4() == lhs.R_component_4())&&
1781 (rhs.R_component_5() == static_cast<T>(0))&&
1782 (rhs.R_component_6() == static_cast<T>(0))&&
1783 (rhs.R_component_7() == static_cast<T>(0))&&
1784 (rhs.R_component_8() == static_cast<T>(0))
1789 template<typename T>
1790 inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
1793 (lhs.R_component_1() == rhs.R_component_1())&&
1794 (lhs.R_component_2() == rhs.R_component_2())&&
1795 (lhs.R_component_3() == rhs.R_component_3())&&
1796 (lhs.R_component_4() == rhs.R_component_4())&&
1797 (lhs.R_component_5() == static_cast<T>(0))&&
1798 (lhs.R_component_6() == static_cast<T>(0))&&
1799 (lhs.R_component_7() == static_cast<T>(0))&&
1800 (lhs.R_component_8() == static_cast<T>(0))
1805 template<typename T>
1806 inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs)
1809 (rhs.R_component_1() == lhs.R_component_1())&&
1810 (rhs.R_component_2() == lhs.R_component_2())&&
1811 (rhs.R_component_3() == lhs.R_component_3())&&
1812 (rhs.R_component_4() == lhs.R_component_4())&&
1813 (rhs.R_component_5() == lhs.R_component_5())&&
1814 (rhs.R_component_6() == lhs.R_component_6())&&
1815 (rhs.R_component_7() == lhs.R_component_7())&&
1816 (rhs.R_component_8() == lhs.R_component_8())
1821 #define BOOST_OCTONION_NOT_EQUAL_GENERATOR \
1823 return(!(lhs == rhs)); \
1826 template<typename T>
1827 inline bool operator != (T const & lhs, octonion<T> const & rhs)
1828 BOOST_OCTONION_NOT_EQUAL_GENERATOR
1830 template<typename T>
1831 inline bool operator != (octonion<T> const & lhs, T const & rhs)
1832 BOOST_OCTONION_NOT_EQUAL_GENERATOR
1834 template<typename T>
1835 inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs)
1836 BOOST_OCTONION_NOT_EQUAL_GENERATOR
1838 template<typename T>
1839 inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs)
1840 BOOST_OCTONION_NOT_EQUAL_GENERATOR
1842 template<typename T>
1843 inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs)
1844 BOOST_OCTONION_NOT_EQUAL_GENERATOR
1846 template<typename T>
1847 inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs)
1848 BOOST_OCTONION_NOT_EQUAL_GENERATOR
1850 template<typename T>
1851 inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs)
1852 BOOST_OCTONION_NOT_EQUAL_GENERATOR
1854 #undef BOOST_OCTONION_NOT_EQUAL_GENERATOR
1857 // Note: the default values in the constructors of the complex and quaternions make for
1858 // a very complex and ambiguous situation; we have made choices to disambiguate.
1860 #if BOOST_WORKAROUND(__GNUC__, < 3)
1861 template<typename T>
1862 ::std::istream & operator >> ( ::std::istream & is,
1865 template<typename T, typename charT, class traits>
1866 ::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
1868 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1870 #if BOOST_WORKAROUND(__GNUC__, < 3)
1872 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
1874 #ifdef BOOST_NO_STD_LOCALE
1876 const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
1877 #endif /* BOOST_NO_STD_LOCALE */
1888 ::std::complex<T> u = ::std::complex<T>();
1889 ::std::complex<T> v = ::std::complex<T>();
1890 ::std::complex<T> x = ::std::complex<T>();
1891 ::std::complex<T> y = ::std::complex<T>();
1893 ::boost::math::quaternion<T> p = ::boost::math::quaternion<T>();
1894 ::boost::math::quaternion<T> q = ::boost::math::quaternion<T>();
1899 is >> ch; // get the first lexeme
1901 if (!is.good()) goto finish;
1903 #ifdef BOOST_NO_STD_LOCALE
1906 cc = ct.narrow(ch, char());
1907 #endif /* BOOST_NO_STD_LOCALE */
1909 if (cc == '(') // read "("
1911 is >> ch; // get the second lexeme
1913 if (!is.good()) goto finish;
1915 #ifdef BOOST_NO_STD_LOCALE
1918 cc = ct.narrow(ch, char());
1919 #endif /* BOOST_NO_STD_LOCALE */
1921 if (cc == '(') // read "(("
1923 is >> ch; // get the third lexeme
1925 if (!is.good()) goto finish;
1927 #ifdef BOOST_NO_STD_LOCALE
1930 cc = ct.narrow(ch, char());
1931 #endif /* BOOST_NO_STD_LOCALE */
1933 if (cc == '(') // read "((("
1937 is >> u; // read "((u"
1939 if (!is.good()) goto finish;
1941 is >> ch; // get the next lexeme
1943 if (!is.good()) goto finish;
1945 #ifdef BOOST_NO_STD_LOCALE
1948 cc = ct.narrow(ch, char());
1949 #endif /* BOOST_NO_STD_LOCALE */
1951 if (cc == ')') // read "((u)"
1953 is >> ch; // get the next lexeme
1955 if (!is.good()) goto finish;
1957 #ifdef BOOST_NO_STD_LOCALE
1960 cc = ct.narrow(ch, char());
1961 #endif /* BOOST_NO_STD_LOCALE */
1963 if (cc == ')') // format: (((a))), (((a,b)))
1967 else if (cc == ',') // read "((u),"
1969 p = ::boost::math::quaternion<T>(u);
1971 is >> q; // read "((u),q"
1973 if (!is.good()) goto finish;
1975 is >> ch; // get the next lexeme
1977 if (!is.good()) goto finish;
1979 #ifdef BOOST_NO_STD_LOCALE
1982 cc = ct.narrow(ch, char());
1983 #endif /* BOOST_NO_STD_LOCALE */
1985 if (cc == ')') // format: (((a)),q), (((a,b)),q)
1987 o = octonion<T>(p,q);
1991 #if BOOST_WORKAROUND(__GNUC__, < 3)
1992 is.setstate(::std::ios::failbit);
1994 is.setstate(::std::ios_base::failbit);
1995 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2000 #if BOOST_WORKAROUND(__GNUC__, < 3)
2001 is.setstate(::std::ios::failbit);
2003 is.setstate(::std::ios_base::failbit);
2004 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2007 else if (cc ==',') // read "((u,"
2009 is >> v; // read "((u,v"
2011 if (!is.good()) goto finish;
2013 is >> ch; // get the next lexeme
2015 if (!is.good()) goto finish;
2017 #ifdef BOOST_NO_STD_LOCALE
2020 cc = ct.narrow(ch, char());
2021 #endif /* BOOST_NO_STD_LOCALE */
2023 if (cc == ')') // read "((u,v)"
2025 p = ::boost::math::quaternion<T>(u,v);
2027 is >> ch; // get the next lexeme
2029 if (!is.good()) goto finish;
2031 #ifdef BOOST_NO_STD_LOCALE
2034 cc = ct.narrow(ch, char());
2035 #endif /* BOOST_NO_STD_LOCALE */
2037 if (cc == ')') // format: (((a),v)), (((a,b),v))
2041 else if (cc == ',') // read "((u,v),"
2043 is >> q; // read "(p,q"
2045 if (!is.good()) goto finish;
2047 is >> ch; // get the next lexeme
2049 if (!is.good()) goto finish;
2051 #ifdef BOOST_NO_STD_LOCALE
2054 cc = ct.narrow(ch, char());
2055 #endif /* BOOST_NO_STD_LOCALE */
2057 if (cc == ')') // format: (((a),v),q), (((a,b),v),q)
2059 o = octonion<T>(p,q);
2063 #if BOOST_WORKAROUND(__GNUC__, < 3)
2064 is.setstate(::std::ios::failbit);
2066 is.setstate(::std::ios_base::failbit);
2067 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2072 #if BOOST_WORKAROUND(__GNUC__, < 3)
2073 is.setstate(::std::ios::failbit);
2075 is.setstate(::std::ios_base::failbit);
2076 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2081 #if BOOST_WORKAROUND(__GNUC__, < 3)
2082 is.setstate(::std::ios::failbit);
2084 is.setstate(::std::ios_base::failbit);
2085 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2090 #if BOOST_WORKAROUND(__GNUC__, < 3)
2091 is.setstate(::std::ios::failbit);
2093 is.setstate(::std::ios_base::failbit);
2094 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2101 is >> a; // we extract the first component
2103 if (!is.good()) goto finish;
2105 is >> ch; // get the next lexeme
2107 if (!is.good()) goto finish;
2109 #ifdef BOOST_NO_STD_LOCALE
2112 cc = ct.narrow(ch, char());
2113 #endif /* BOOST_NO_STD_LOCALE */
2115 if (cc == ')') // read "((a)"
2117 is >> ch; // get the next lexeme
2119 if (!is.good()) goto finish;
2121 #ifdef BOOST_NO_STD_LOCALE
2124 cc = ct.narrow(ch, char());
2125 #endif /* BOOST_NO_STD_LOCALE */
2127 if (cc == ')') // read "((a))"
2131 else if (cc == ',') // read "((a),"
2133 is >> ch; // get the next lexeme
2135 if (!is.good()) goto finish;
2137 #ifdef BOOST_NO_STD_LOCALE
2140 cc = ct.narrow(ch, char());
2141 #endif /* BOOST_NO_STD_LOCALE */
2143 if (cc == '(') // read "((a),("
2145 is >> ch; // get the next lexeme
2147 if (!is.good()) goto finish;
2149 #ifdef BOOST_NO_STD_LOCALE
2152 cc = ct.narrow(ch, char());
2153 #endif /* BOOST_NO_STD_LOCALE */
2155 if (cc == '(') // read "((a),(("
2159 is.putback(ch); // we backtrack twice, with the same value!
2161 is >> q; // read "((a),q"
2163 if (!is.good()) goto finish;
2165 is >> ch; // get the next lexeme
2167 if (!is.good()) goto finish;
2169 #ifdef BOOST_NO_STD_LOCALE
2172 cc = ct.narrow(ch, char());
2173 #endif /* BOOST_NO_STD_LOCALE */
2175 if (cc == ')') // read "((a),q)"
2177 p = ::boost::math::quaternion<T>(a);
2179 o = octonion<T>(p,q);
2183 #if BOOST_WORKAROUND(__GNUC__, < 3)
2184 is.setstate(::std::ios::failbit);
2186 is.setstate(::std::ios_base::failbit);
2187 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2190 else // read "((a),(c" or "((a),(e"
2196 if (!is.good()) goto finish;
2198 is >> ch; // get the next lexeme
2200 if (!is.good()) goto finish;
2202 #ifdef BOOST_NO_STD_LOCALE
2205 cc = ct.narrow(ch, char());
2206 #endif /* BOOST_NO_STD_LOCALE */
2208 if (cc == ')') // read "((a),(c)" (ambiguity resolution)
2210 is >> ch; // get the next lexeme
2212 if (!is.good()) goto finish;
2214 #ifdef BOOST_NO_STD_LOCALE
2217 cc = ct.narrow(ch, char());
2218 #endif /* BOOST_NO_STD_LOCALE */
2220 if (cc == ')') // read "((a),(c))"
2222 o = octonion<T>(a,b,c);
2224 else if (cc == ',') // read "((a),(c),"
2226 u = ::std::complex<T>(a);
2228 v = ::std::complex<T>(c);
2230 is >> x; // read "((a),(c),x"
2232 if (!is.good()) goto finish;
2234 is >> ch; // get the next lexeme
2236 if (!is.good()) goto finish;
2238 #ifdef BOOST_NO_STD_LOCALE
2241 cc = ct.narrow(ch, char());
2242 #endif /* BOOST_NO_STD_LOCALE */
2244 if (cc == ')') // read "((a),(c),x)"
2246 o = octonion<T>(u,v,x);
2248 else if (cc == ',') // read "((a),(c),x,"
2250 is >> y; // read "((a),(c),x,y"
2252 if (!is.good()) goto finish;
2254 is >> ch; // get the next lexeme
2256 if (!is.good()) goto finish;
2258 #ifdef BOOST_NO_STD_LOCALE
2261 cc = ct.narrow(ch, char());
2262 #endif /* BOOST_NO_STD_LOCALE */
2264 if (cc == ')') // read "((a),(c),x,y)"
2266 o = octonion<T>(u,v,x,y);
2270 #if BOOST_WORKAROUND(__GNUC__, < 3)
2271 is.setstate(::std::ios::failbit);
2273 is.setstate(::std::ios_base::failbit);
2274 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2279 #if BOOST_WORKAROUND(__GNUC__, < 3)
2280 is.setstate(::std::ios::failbit);
2282 is.setstate(::std::ios_base::failbit);
2283 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2288 #if BOOST_WORKAROUND(__GNUC__, < 3)
2289 is.setstate(::std::ios::failbit);
2291 is.setstate(::std::ios_base::failbit);
2292 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2295 else if (cc == ',') // read "((a),(c," or "((a),(e,"
2297 is >> ch; // get the next lexeme
2299 if (!is.good()) goto finish;
2301 #ifdef BOOST_NO_STD_LOCALE
2304 cc = ct.narrow(ch, char());
2305 #endif /* BOOST_NO_STD_LOCALE */
2307 if (cc == '(') // read "((a),(e,(" (ambiguity resolution)
2309 p = ::boost::math::quaternion<T>(a);
2311 x = ::std::complex<T>(c); // "c" was actually "e"
2313 is.putback(ch); // we can only backtrace once
2315 is >> y; // read "((a),(e,y"
2317 if (!is.good()) goto finish;
2319 is >> ch; // get the next lexeme
2321 #ifdef BOOST_NO_STD_LOCALE
2324 cc = ct.narrow(ch, char());
2325 #endif /* BOOST_NO_STD_LOCALE */
2327 if (cc == ')') // read "((a),(e,y)"
2329 q = ::boost::math::quaternion<T>(x,y);
2331 is >> ch; // get the next lexeme
2333 #ifdef BOOST_NO_STD_LOCALE
2336 cc = ct.narrow(ch, char());
2337 #endif /* BOOST_NO_STD_LOCALE */
2339 if (cc == ')') // read "((a),(e,y))"
2341 o = octonion<T>(p,q);
2345 #if BOOST_WORKAROUND(__GNUC__, < 3)
2346 is.setstate(::std::ios::failbit);
2348 is.setstate(::std::ios_base::failbit);
2349 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2354 #if BOOST_WORKAROUND(__GNUC__, < 3)
2355 is.setstate(::std::ios::failbit);
2357 is.setstate(::std::ios_base::failbit);
2358 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2361 else // read "((a),(c,d" or "((a),(e,f"
2367 if (!is.good()) goto finish;
2369 is >> ch; // get the next lexeme
2371 if (!is.good()) goto finish;
2373 #ifdef BOOST_NO_STD_LOCALE
2376 cc = ct.narrow(ch, char());
2377 #endif /* BOOST_NO_STD_LOCALE */
2379 if (cc == ')') // read "((a),(c,d)" (ambiguity resolution)
2381 is >> ch; // get the next lexeme
2383 if (!is.good()) goto finish;
2385 #ifdef BOOST_NO_STD_LOCALE
2388 cc = ct.narrow(ch, char());
2389 #endif /* BOOST_NO_STD_LOCALE */
2391 if (cc == ')') // read "((a),(c,d))"
2393 o = octonion<T>(a,b,c,d);
2395 else if (cc == ',') // read "((a),(c,d),"
2397 u = ::std::complex<T>(a);
2399 v = ::std::complex<T>(c,d);
2401 is >> x; // read "((a),(c,d),x"
2403 if (!is.good()) goto finish;
2405 is >> ch; // get the next lexeme
2407 if (!is.good()) goto finish;
2409 #ifdef BOOST_NO_STD_LOCALE
2412 cc = ct.narrow(ch, char());
2413 #endif /* BOOST_NO_STD_LOCALE */
2415 if (cc == ')') // read "((a),(c,d),x)"
2417 o = octonion<T>(u,v,x);
2419 else if (cc == ',') // read "((a),(c,d),x,"
2421 is >> y; // read "((a),(c,d),x,y"
2423 if (!is.good()) goto finish;
2425 is >> ch; // get the next lexeme
2427 if (!is.good()) goto finish;
2429 #ifdef BOOST_NO_STD_LOCALE
2432 cc = ct.narrow(ch, char());
2433 #endif /* BOOST_NO_STD_LOCALE */
2435 if (cc == ')') // read "((a),(c,d),x,y)"
2437 o = octonion<T>(u,v,x,y);
2441 #if BOOST_WORKAROUND(__GNUC__, < 3)
2442 is.setstate(::std::ios::failbit);
2444 is.setstate(::std::ios_base::failbit);
2445 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2450 #if BOOST_WORKAROUND(__GNUC__, < 3)
2451 is.setstate(::std::ios::failbit);
2453 is.setstate(::std::ios_base::failbit);
2454 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2459 #if BOOST_WORKAROUND(__GNUC__, < 3)
2460 is.setstate(::std::ios::failbit);
2462 is.setstate(::std::ios_base::failbit);
2463 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2466 else if (cc == ',') // read "((a),(e,f," (ambiguity resolution)
2468 p = ::boost::math::quaternion<T>(a);
2470 is >> g; // read "((a),(e,f,g" (too late to backtrack)
2472 if (!is.good()) goto finish;
2474 is >> ch; // get the next lexeme
2476 if (!is.good()) goto finish;
2478 #ifdef BOOST_NO_STD_LOCALE
2481 cc = ct.narrow(ch, char());
2482 #endif /* BOOST_NO_STD_LOCALE */
2484 if (cc == ')') // read "((a),(e,f,g)"
2486 q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f"
2488 is >> ch; // get the next lexeme
2490 if (!is.good()) goto finish;
2492 #ifdef BOOST_NO_STD_LOCALE
2495 cc = ct.narrow(ch, char());
2496 #endif /* BOOST_NO_STD_LOCALE */
2498 if (cc == ')') // read "((a),(e,f,g))"
2500 o = octonion<T>(p,q);
2504 #if BOOST_WORKAROUND(__GNUC__, < 3)
2505 is.setstate(::std::ios::failbit);
2507 is.setstate(::std::ios_base::failbit);
2508 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2511 else if (cc == ',') // read "((a),(e,f,g,"
2513 is >> h; // read "((a),(e,f,g,h"
2515 if (!is.good()) goto finish;
2517 is >> ch; // get the next lexeme
2519 if (!is.good()) goto finish;
2521 #ifdef BOOST_NO_STD_LOCALE
2524 cc = ct.narrow(ch, char());
2525 #endif /* BOOST_NO_STD_LOCALE */
2527 if (cc == ')') // read "((a),(e,f,g,h)"
2529 q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f"
2531 is >> ch; // get the next lexeme
2533 if (!is.good()) goto finish;
2535 #ifdef BOOST_NO_STD_LOCALE
2538 cc = ct.narrow(ch, char());
2539 #endif /* BOOST_NO_STD_LOCALE */
2541 if (cc == ')') // read "((a),(e,f,g,h))"
2543 o = octonion<T>(p,q);
2547 #if BOOST_WORKAROUND(__GNUC__, < 3)
2548 is.setstate(::std::ios::failbit);
2550 is.setstate(::std::ios_base::failbit);
2551 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2556 #if BOOST_WORKAROUND(__GNUC__, < 3)
2557 is.setstate(::std::ios::failbit);
2559 is.setstate(::std::ios_base::failbit);
2560 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2565 #if BOOST_WORKAROUND(__GNUC__, < 3)
2566 is.setstate(::std::ios::failbit);
2568 is.setstate(::std::ios_base::failbit);
2569 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2574 #if BOOST_WORKAROUND(__GNUC__, < 3)
2575 is.setstate(::std::ios::failbit);
2577 is.setstate(::std::ios_base::failbit);
2578 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2584 #if BOOST_WORKAROUND(__GNUC__, < 3)
2585 is.setstate(::std::ios::failbit);
2587 is.setstate(::std::ios_base::failbit);
2588 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2592 else // read "((a),c" (ambiguity resolution)
2596 is >> c; // we extract the third component
2598 if (!is.good()) goto finish;
2600 is >> ch; // get the next lexeme
2602 if (!is.good()) goto finish;
2604 #ifdef BOOST_NO_STD_LOCALE
2607 cc = ct.narrow(ch, char());
2608 #endif /* BOOST_NO_STD_LOCALE */
2610 if (cc == ')') // read "((a),c)"
2612 o = octonion<T>(a,b,c);
2614 else if (cc == ',') // read "((a),c,"
2616 is >> x; // read "((a),c,x"
2618 if (!is.good()) goto finish;
2620 is >> ch; // get the next lexeme
2622 if (!is.good()) goto finish;
2624 #ifdef BOOST_NO_STD_LOCALE
2627 cc = ct.narrow(ch, char());
2628 #endif /* BOOST_NO_STD_LOCALE */
2630 if (cc == ')') // read "((a),c,x)"
2632 o = octonion<T>(a,b,c,d,x.real(),x.imag());
2634 else if (cc == ',') // read "((a),c,x,"
2636 is >> y;if (!is.good()) goto finish; // read "((a),c,x,y"
2638 is >> ch; // get the next lexeme
2640 if (!is.good()) goto finish;
2642 #ifdef BOOST_NO_STD_LOCALE
2645 cc = ct.narrow(ch, char());
2646 #endif /* BOOST_NO_STD_LOCALE */
2648 if (cc == ')') // read "((a),c,x,y)"
2650 o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag());
2654 #if BOOST_WORKAROUND(__GNUC__, < 3)
2655 is.setstate(::std::ios::failbit);
2657 is.setstate(::std::ios_base::failbit);
2658 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2663 #if BOOST_WORKAROUND(__GNUC__, < 3)
2664 is.setstate(::std::ios::failbit);
2666 is.setstate(::std::ios_base::failbit);
2667 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2672 #if BOOST_WORKAROUND(__GNUC__, < 3)
2673 is.setstate(::std::ios::failbit);
2675 is.setstate(::std::ios_base::failbit);
2676 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2682 #if BOOST_WORKAROUND(__GNUC__, < 3)
2683 is.setstate(::std::ios::failbit);
2685 is.setstate(::std::ios_base::failbit);
2686 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2689 else if (cc ==',') // read "((a,"
2691 is >> ch; // get the next lexeme
2693 if (!is.good()) goto finish;
2695 #ifdef BOOST_NO_STD_LOCALE
2698 cc = ct.narrow(ch, char());
2699 #endif /* BOOST_NO_STD_LOCALE */
2701 if (cc == '(') // read "((a,("
2703 u = ::std::complex<T>(a);
2705 is.putback(ch); // can only backtrack so much
2707 is >> v; // read "((a,v"
2709 if (!is.good()) goto finish;
2711 is >> ch; // get the next lexeme
2713 if (!is.good()) goto finish;
2715 #ifdef BOOST_NO_STD_LOCALE
2718 cc = ct.narrow(ch, char());
2719 #endif /* BOOST_NO_STD_LOCALE */
2721 if (cc == ')') // read "((a,v)"
2723 is >> ch; // get the next lexeme
2725 if (!is.good()) goto finish;
2727 #ifdef BOOST_NO_STD_LOCALE
2730 cc = ct.narrow(ch, char());
2731 #endif /* BOOST_NO_STD_LOCALE */
2733 if (cc == ')') // read "((a,v))"
2735 o = octonion<T>(u,v);
2737 else if (cc == ',') // read "((a,v),"
2739 p = ::boost::math::quaternion<T>(u,v);
2741 is >> q; // read "((a,v),q"
2743 if (!is.good()) goto finish;
2745 is >> ch; // get the next lexeme
2747 if (!is.good()) goto finish;
2749 #ifdef BOOST_NO_STD_LOCALE
2752 cc = ct.narrow(ch, char());
2753 #endif /* BOOST_NO_STD_LOCALE */
2755 if (cc == ')') // read "((a,v),q)"
2757 o = octonion<T>(p,q);
2761 #if BOOST_WORKAROUND(__GNUC__, < 3)
2762 is.setstate(::std::ios::failbit);
2764 is.setstate(::std::ios_base::failbit);
2765 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2770 #if BOOST_WORKAROUND(__GNUC__, < 3)
2771 is.setstate(::std::ios::failbit);
2773 is.setstate(::std::ios_base::failbit);
2774 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2779 #if BOOST_WORKAROUND(__GNUC__, < 3)
2780 is.setstate(::std::ios::failbit);
2782 is.setstate(::std::ios_base::failbit);
2783 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2790 is >> b; // read "((a,b"
2792 if (!is.good()) goto finish;
2794 is >> ch; // get the next lexeme
2796 if (!is.good()) goto finish;
2798 #ifdef BOOST_NO_STD_LOCALE
2801 cc = ct.narrow(ch, char());
2802 #endif /* BOOST_NO_STD_LOCALE */
2804 if (cc == ')') // read "((a,b)"
2806 is >> ch; // get the next lexeme
2808 if (!is.good()) goto finish;
2810 #ifdef BOOST_NO_STD_LOCALE
2813 cc = ct.narrow(ch, char());
2814 #endif /* BOOST_NO_STD_LOCALE */
2816 if (cc == ')') // read "((a,b))"
2818 o = octonion<T>(a,b);
2820 else if (cc == ',') // read "((a,b),"
2822 is >> ch; // get the next lexeme
2824 if (!is.good()) goto finish;
2826 #ifdef BOOST_NO_STD_LOCALE
2829 cc = ct.narrow(ch, char());
2830 #endif /* BOOST_NO_STD_LOCALE */
2832 if (cc == '(') // read "((a,b),("
2834 is >> ch; // get the next lexeme
2836 if (!is.good()) goto finish;
2838 #ifdef BOOST_NO_STD_LOCALE
2841 cc = ct.narrow(ch, char());
2842 #endif /* BOOST_NO_STD_LOCALE */
2844 if (cc == '(') // read "((a,b),(("
2846 p = ::boost::math::quaternion<T>(a,b);
2850 is.putback(ch); // we backtrack twice, with the same value
2852 is >> q; // read "((a,b),q"
2854 if (!is.good()) goto finish;
2856 is >> ch; // get the next lexeme
2858 if (!is.good()) goto finish;
2860 #ifdef BOOST_NO_STD_LOCALE
2863 cc = ct.narrow(ch, char());
2864 #endif /* BOOST_NO_STD_LOCALE */
2866 if (cc == ')') // read "((a,b),q)"
2868 o = octonion<T>(p,q);
2872 #if BOOST_WORKAROUND(__GNUC__, < 3)
2873 is.setstate(::std::ios::failbit);
2875 is.setstate(::std::ios_base::failbit);
2876 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2879 else // read "((a,b),(c" or "((a,b),(e"
2885 if (!is.good()) goto finish;
2887 is >> ch; // get the next lexeme
2889 if (!is.good()) goto finish;
2891 #ifdef BOOST_NO_STD_LOCALE
2894 cc = ct.narrow(ch, char());
2895 #endif /* BOOST_NO_STD_LOCALE */
2897 if (cc == ')') // read "((a,b),(c)" (ambiguity resolution)
2899 is >> ch; // get the next lexeme
2901 if (!is.good()) goto finish;
2903 #ifdef BOOST_NO_STD_LOCALE
2906 cc = ct.narrow(ch, char());
2907 #endif /* BOOST_NO_STD_LOCALE */
2909 if (cc == ')') // read "((a,b),(c))"
2911 o = octonion<T>(a,b,c);
2913 else if (cc == ',') // read "((a,b),(c),"
2915 u = ::std::complex<T>(a,b);
2917 v = ::std::complex<T>(c);
2919 is >> x; // read "((a,b),(c),x"
2921 if (!is.good()) goto finish;
2923 is >> ch; // get the next lexeme
2925 if (!is.good()) goto finish;
2927 #ifdef BOOST_NO_STD_LOCALE
2930 cc = ct.narrow(ch, char());
2931 #endif /* BOOST_NO_STD_LOCALE */
2933 if (cc == ')') // read "((a,b),(c),x)"
2935 o = octonion<T>(u,v,x);
2937 else if (cc == ',') // read "((a,b),(c),x,"
2939 is >> y; // read "((a,b),(c),x,y"
2941 if (!is.good()) goto finish;
2943 is >> ch; // get the next lexeme
2945 if (!is.good()) goto finish;
2947 #ifdef BOOST_NO_STD_LOCALE
2950 cc = ct.narrow(ch, char());
2951 #endif /* BOOST_NO_STD_LOCALE */
2953 if (cc == ')') // read "((a,b),(c),x,y)"
2955 o = octonion<T>(u,v,x,y);
2959 #if BOOST_WORKAROUND(__GNUC__, < 3)
2960 is.setstate(::std::ios::failbit);
2962 is.setstate(::std::ios_base::failbit);
2963 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2968 #if BOOST_WORKAROUND(__GNUC__, < 3)
2969 is.setstate(::std::ios::failbit);
2971 is.setstate(::std::ios_base::failbit);
2972 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2977 #if BOOST_WORKAROUND(__GNUC__, < 3)
2978 is.setstate(::std::ios::failbit);
2980 is.setstate(::std::ios_base::failbit);
2981 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
2984 else if (cc == ',') // read "((a,b),(c," or "((a,b),(e,"
2986 is >> ch; // get the next lexeme
2988 if (!is.good()) goto finish;
2990 #ifdef BOOST_NO_STD_LOCALE
2993 cc = ct.narrow(ch, char());
2994 #endif /* BOOST_NO_STD_LOCALE */
2996 if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution)
2998 u = ::std::complex<T>(a,b);
3000 x = ::std::complex<T>(c); // "c" is actually "e"
3004 is >> y; // read "((a,b),(e,y"
3006 if (!is.good()) goto finish;
3008 is >> ch; // get the next lexeme
3010 if (!is.good()) goto finish;
3012 #ifdef BOOST_NO_STD_LOCALE
3015 cc = ct.narrow(ch, char());
3016 #endif /* BOOST_NO_STD_LOCALE */
3018 if (cc == ')') // read "((a,b),(e,y)"
3020 is >> ch; // get the next lexeme
3022 if (!is.good()) goto finish;
3024 #ifdef BOOST_NO_STD_LOCALE
3027 cc = ct.narrow(ch, char());
3028 #endif /* BOOST_NO_STD_LOCALE */
3030 if (cc == ')') // read "((a,b),(e,y))"
3032 o = octonion<T>(u,v,x,y);
3036 #if BOOST_WORKAROUND(__GNUC__, < 3)
3037 is.setstate(::std::ios::failbit);
3039 is.setstate(::std::ios_base::failbit);
3040 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3045 #if BOOST_WORKAROUND(__GNUC__, < 3)
3046 is.setstate(::std::ios::failbit);
3048 is.setstate(::std::ios_base::failbit);
3049 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3052 else // read "((a,b),(c,d" or "((a,b),(e,f"
3058 if (!is.good()) goto finish;
3060 is >> ch; // get the next lexeme
3062 if (!is.good()) goto finish;
3064 #ifdef BOOST_NO_STD_LOCALE
3067 cc = ct.narrow(ch, char());
3068 #endif /* BOOST_NO_STD_LOCALE */
3070 if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution)
3072 u = ::std::complex<T>(a,b);
3074 v = ::std::complex<T>(c,d);
3076 is >> ch; // get the next lexeme
3078 if (!is.good()) goto finish;
3080 #ifdef BOOST_NO_STD_LOCALE
3083 cc = ct.narrow(ch, char());
3084 #endif /* BOOST_NO_STD_LOCALE */
3086 if (cc == ')') // read "((a,b),(c,d))"
3088 o = octonion<T>(u,v);
3090 else if (cc == ',') // read "((a,b),(c,d),"
3092 is >> x; // read "((a,b),(c,d),x
3094 if (!is.good()) goto finish;
3096 is >> ch; // get the next lexeme
3098 if (!is.good()) goto finish;
3100 #ifdef BOOST_NO_STD_LOCALE
3103 cc = ct.narrow(ch, char());
3104 #endif /* BOOST_NO_STD_LOCALE */
3106 if (cc == ')') // read "((a,b),(c,d),x)"
3108 o = octonion<T>(u,v,x);
3110 else if (cc == ',') // read "((a,b),(c,d),x,"
3112 is >> y; // read "((a,b),(c,d),x,y"
3114 if (!is.good()) goto finish;
3116 is >> ch; // get the next lexeme
3118 if (!is.good()) goto finish;
3120 #ifdef BOOST_NO_STD_LOCALE
3123 cc = ct.narrow(ch, char());
3124 #endif /* BOOST_NO_STD_LOCALE */
3126 if (cc == ')') // read "((a,b),(c,d),x,y)"
3128 o = octonion<T>(u,v,x,y);
3132 #if BOOST_WORKAROUND(__GNUC__, < 3)
3133 is.setstate(::std::ios::failbit);
3135 is.setstate(::std::ios_base::failbit);
3136 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3141 #if BOOST_WORKAROUND(__GNUC__, < 3)
3142 is.setstate(::std::ios::failbit);
3144 is.setstate(::std::ios_base::failbit);
3145 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3150 #if BOOST_WORKAROUND(__GNUC__, < 3)
3151 is.setstate(::std::ios::failbit);
3153 is.setstate(::std::ios_base::failbit);
3154 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3157 else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution)
3159 p = ::boost::math::quaternion<T>(a,b); // too late to backtrack
3161 is >> g; // read "((a,b),(e,f,g"
3163 if (!is.good()) goto finish;
3165 is >> ch; // get the next lexeme
3167 if (!is.good()) goto finish;
3169 #ifdef BOOST_NO_STD_LOCALE
3172 cc = ct.narrow(ch, char());
3173 #endif /* BOOST_NO_STD_LOCALE */
3175 if (cc == ')') // read "((a,b),(e,f,g)"
3177 is >> ch; // get the next lexeme
3179 if (!is.good()) goto finish;
3181 #ifdef BOOST_NO_STD_LOCALE
3184 cc = ct.narrow(ch, char());
3185 #endif /* BOOST_NO_STD_LOCALE */
3187 if (cc == ')') // read "((a,b),(e,f,g))"
3189 q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
3191 o = octonion<T>(p,q);
3195 #if BOOST_WORKAROUND(__GNUC__, < 3)
3196 is.setstate(::std::ios::failbit);
3198 is.setstate(::std::ios_base::failbit);
3199 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3202 else if (cc == ',') // read "((a,b),(e,f,g,"
3204 is >> h; // read "((a,b),(e,f,g,h"
3206 if (!is.good()) goto finish;
3208 is >> ch; // get the next lexeme
3210 if (!is.good()) goto finish;
3212 #ifdef BOOST_NO_STD_LOCALE
3215 cc = ct.narrow(ch, char());
3216 #endif /* BOOST_NO_STD_LOCALE */
3218 if (cc == ')') // read "((a,b),(e,f,g,h)"
3220 is >> ch; // get the next lexeme
3222 if (!is.good()) goto finish;
3224 #ifdef BOOST_NO_STD_LOCALE
3227 cc = ct.narrow(ch, char());
3228 #endif /* BOOST_NO_STD_LOCALE */
3230 if (cc == ')') // read ((a,b),(e,f,g,h))"
3232 q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
3234 o = octonion<T>(p,q);
3238 #if BOOST_WORKAROUND(__GNUC__, < 3)
3239 is.setstate(::std::ios::failbit);
3241 is.setstate(::std::ios_base::failbit);
3242 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3247 #if BOOST_WORKAROUND(__GNUC__, < 3)
3248 is.setstate(::std::ios::failbit);
3250 is.setstate(::std::ios_base::failbit);
3251 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3256 #if BOOST_WORKAROUND(__GNUC__, < 3)
3257 is.setstate(::std::ios::failbit);
3259 is.setstate(::std::ios_base::failbit);
3260 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3265 #if BOOST_WORKAROUND(__GNUC__, < 3)
3266 is.setstate(::std::ios::failbit);
3268 is.setstate(::std::ios_base::failbit);
3269 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3275 #if BOOST_WORKAROUND(__GNUC__, < 3)
3276 is.setstate(::std::ios::failbit);
3278 is.setstate(::std::ios_base::failbit);
3279 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3285 #if BOOST_WORKAROUND(__GNUC__, < 3)
3286 is.setstate(::std::ios::failbit);
3288 is.setstate(::std::ios_base::failbit);
3289 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3294 #if BOOST_WORKAROUND(__GNUC__, < 3)
3295 is.setstate(::std::ios::failbit);
3297 is.setstate(::std::ios_base::failbit);
3298 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3301 else if (cc == ',') // read "((a,b,"
3303 is >> c; // read "((a,b,c"
3305 if (!is.good()) goto finish;
3307 is >> ch; // get the next lexeme
3309 if (!is.good()) goto finish;
3311 #ifdef BOOST_NO_STD_LOCALE
3314 cc = ct.narrow(ch, char());
3315 #endif /* BOOST_NO_STD_LOCALE */
3317 if (cc == ')') // read "((a,b,c)"
3319 is >> ch; // get the next lexeme
3321 if (!is.good()) goto finish;
3323 #ifdef BOOST_NO_STD_LOCALE
3326 cc = ct.narrow(ch, char());
3327 #endif /* BOOST_NO_STD_LOCALE */
3329 if (cc == ')') // read "((a,b,c))"
3331 o = octonion<T>(a,b,c);
3333 else if (cc == ',') // read "((a,b,c),"
3335 p = ::boost::math::quaternion<T>(a,b,c);
3337 is >> q; // read "((a,b,c),q"
3339 if (!is.good()) goto finish;
3341 is >> ch; // get the next lexeme
3343 if (!is.good()) goto finish;
3345 #ifdef BOOST_NO_STD_LOCALE
3348 cc = ct.narrow(ch, char());
3349 #endif /* BOOST_NO_STD_LOCALE */
3351 if (cc == ')') // read "((a,b,c),q)"
3353 o = octonion<T>(p,q);
3357 #if BOOST_WORKAROUND(__GNUC__, < 3)
3358 is.setstate(::std::ios::failbit);
3360 is.setstate(::std::ios_base::failbit);
3361 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3366 #if BOOST_WORKAROUND(__GNUC__, < 3)
3367 is.setstate(::std::ios::failbit);
3369 is.setstate(::std::ios_base::failbit);
3370 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3373 else if (cc == ',') // read "((a,b,c,"
3375 is >> d; // read "((a,b,c,d"
3377 if (!is.good()) goto finish;
3379 is >> ch; // get the next lexeme
3381 if (!is.good()) goto finish;
3383 #ifdef BOOST_NO_STD_LOCALE
3386 cc = ct.narrow(ch, char());
3387 #endif /* BOOST_NO_STD_LOCALE */
3389 if (cc == ')') // read "((a,b,c,d)"
3391 is >> ch; // get the next lexeme
3393 if (!is.good()) goto finish;
3395 #ifdef BOOST_NO_STD_LOCALE
3398 cc = ct.narrow(ch, char());
3399 #endif /* BOOST_NO_STD_LOCALE */
3401 if (cc == ')') // read "((a,b,c,d))"
3403 o = octonion<T>(a,b,c,d);
3405 else if (cc == ',') // read "((a,b,c,d),"
3407 p = ::boost::math::quaternion<T>(a,b,c,d);
3409 is >> q; // read "((a,b,c,d),q"
3411 if (!is.good()) goto finish;
3413 is >> ch; // get the next lexeme
3415 if (!is.good()) goto finish;
3417 #ifdef BOOST_NO_STD_LOCALE
3420 cc = ct.narrow(ch, char());
3421 #endif /* BOOST_NO_STD_LOCALE */
3423 if (cc == ')') // read "((a,b,c,d),q)"
3425 o = octonion<T>(p,q);
3429 #if BOOST_WORKAROUND(__GNUC__, < 3)
3430 is.setstate(::std::ios::failbit);
3432 is.setstate(::std::ios_base::failbit);
3433 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3438 #if BOOST_WORKAROUND(__GNUC__, < 3)
3439 is.setstate(::std::ios::failbit);
3441 is.setstate(::std::ios_base::failbit);
3442 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3447 #if BOOST_WORKAROUND(__GNUC__, < 3)
3448 is.setstate(::std::ios::failbit);
3450 is.setstate(::std::ios_base::failbit);
3451 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3456 #if BOOST_WORKAROUND(__GNUC__, < 3)
3457 is.setstate(::std::ios::failbit);
3459 is.setstate(::std::ios_base::failbit);
3460 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3465 #if BOOST_WORKAROUND(__GNUC__, < 3)
3466 is.setstate(::std::ios::failbit);
3468 is.setstate(::std::ios_base::failbit);
3469 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3475 #if BOOST_WORKAROUND(__GNUC__, < 3)
3476 is.setstate(::std::ios::failbit);
3478 is.setstate(::std::ios_base::failbit);
3479 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3487 is >> a; // we extract the first component
3489 if (!is.good()) goto finish;
3491 is >> ch; // get the next lexeme
3493 if (!is.good()) goto finish;
3495 #ifdef BOOST_NO_STD_LOCALE
3498 cc = ct.narrow(ch, char());
3499 #endif /* BOOST_NO_STD_LOCALE */
3501 if (cc == ')') // read "(a)"
3505 else if (cc == ',') // read "(a,"
3507 is >> ch; // get the next lexeme
3509 if (!is.good()) goto finish;
3511 #ifdef BOOST_NO_STD_LOCALE
3514 cc = ct.narrow(ch, char());
3515 #endif /* BOOST_NO_STD_LOCALE */
3517 if (cc == '(') // read "(a,("
3519 is >> ch; // get the next lexeme
3521 if (!is.good()) goto finish;
3523 #ifdef BOOST_NO_STD_LOCALE
3526 cc = ct.narrow(ch, char());
3527 #endif /* BOOST_NO_STD_LOCALE */
3529 if (cc == '(') // read "(a,(("
3531 p = ::boost::math::quaternion<T>(a);
3535 is.putback(ch); // we backtrack twice, with the same value
3537 is >> q; // read "(a,q"
3539 if (!is.good()) goto finish;
3541 is >> ch; // get the next lexeme
3543 if (!is.good()) goto finish;
3545 #ifdef BOOST_NO_STD_LOCALE
3548 cc = ct.narrow(ch, char());
3549 #endif /* BOOST_NO_STD_LOCALE */
3551 if (cc == ')') // read "(a,q)"
3553 o = octonion<T>(p,q);
3557 #if BOOST_WORKAROUND(__GNUC__, < 3)
3558 is.setstate(::std::ios::failbit);
3560 is.setstate(::std::ios_base::failbit);
3561 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3564 else // read "(a,(c" or "(a,(e"
3570 if (!is.good()) goto finish;
3572 is >> ch; // get the next lexeme
3574 if (!is.good()) goto finish;
3576 #ifdef BOOST_NO_STD_LOCALE
3579 cc = ct.narrow(ch, char());
3580 #endif /* BOOST_NO_STD_LOCALE */
3582 if (cc == ')') // read "(a,(c)" (ambiguity resolution)
3584 is >> ch; // get the next lexeme
3586 if (!is.good()) goto finish;
3588 #ifdef BOOST_NO_STD_LOCALE
3591 cc = ct.narrow(ch, char());
3592 #endif /* BOOST_NO_STD_LOCALE */
3594 if (cc == ')') // read "(a,(c))"
3596 o = octonion<T>(a,b,c);
3598 else if (cc == ',') // read "(a,(c),"
3600 u = ::std::complex<T>(a);
3602 v = ::std::complex<T>(c);
3604 is >> x; // read "(a,(c),x"
3606 if (!is.good()) goto finish;
3608 is >> ch; // get the next lexeme
3610 if (!is.good()) goto finish;
3612 #ifdef BOOST_NO_STD_LOCALE
3615 cc = ct.narrow(ch, char());
3616 #endif /* BOOST_NO_STD_LOCALE */
3618 if (cc == ')') // read "(a,(c),x)"
3620 o = octonion<T>(u,v,x);
3622 else if (cc == ',') // read "(a,(c),x,"
3624 is >> y; // read "(a,(c),x,y"
3626 if (!is.good()) goto finish;
3628 is >> ch; // get the next lexeme
3630 if (!is.good()) goto finish;
3632 #ifdef BOOST_NO_STD_LOCALE
3635 cc = ct.narrow(ch, char());
3636 #endif /* BOOST_NO_STD_LOCALE */
3638 if (cc == ')') // read "(a,(c),x,y)"
3640 o = octonion<T>(u,v,x,y);
3644 #if BOOST_WORKAROUND(__GNUC__, < 3)
3645 is.setstate(::std::ios::failbit);
3647 is.setstate(::std::ios_base::failbit);
3648 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3653 #if BOOST_WORKAROUND(__GNUC__, < 3)
3654 is.setstate(::std::ios::failbit);
3656 is.setstate(::std::ios_base::failbit);
3657 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3662 #if BOOST_WORKAROUND(__GNUC__, < 3)
3663 is.setstate(::std::ios::failbit);
3665 is.setstate(::std::ios_base::failbit);
3666 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3669 else if (cc == ',') // read "(a,(c," or "(a,(e,"
3671 is >> ch; // get the next lexeme
3673 if (!is.good()) goto finish;
3675 #ifdef BOOST_NO_STD_LOCALE
3678 cc = ct.narrow(ch, char());
3679 #endif /* BOOST_NO_STD_LOCALE */
3681 if (cc == '(') // read "(a,(e,(" (ambiguity resolution)
3683 u = ::std::complex<T>(a);
3685 x = ::std::complex<T>(c); // "c" is actually "e"
3687 is.putback(ch); // we backtrack
3689 is >> y; // read "(a,(e,y"
3691 if (!is.good()) goto finish;
3693 is >> ch; // get the next lexeme
3695 if (!is.good()) goto finish;
3697 #ifdef BOOST_NO_STD_LOCALE
3700 cc = ct.narrow(ch, char());
3701 #endif /* BOOST_NO_STD_LOCALE */
3703 if (cc == ')') // read "(a,(e,y)"
3705 is >> ch; // get the next lexeme
3707 if (!is.good()) goto finish;
3709 #ifdef BOOST_NO_STD_LOCALE
3712 cc = ct.narrow(ch, char());
3713 #endif /* BOOST_NO_STD_LOCALE */
3715 if (cc == ')') // read "(a,(e,y))"
3717 o = octonion<T>(u,v,x,y);
3721 #if BOOST_WORKAROUND(__GNUC__, < 3)
3722 is.setstate(::std::ios::failbit);
3724 is.setstate(::std::ios_base::failbit);
3725 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3730 #if BOOST_WORKAROUND(__GNUC__, < 3)
3731 is.setstate(::std::ios::failbit);
3733 is.setstate(::std::ios_base::failbit);
3734 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3737 else // read "(a,(c,d" or "(a,(e,f"
3743 if (!is.good()) goto finish;
3745 is >> ch; // get the next lexeme
3747 if (!is.good()) goto finish;
3749 #ifdef BOOST_NO_STD_LOCALE
3752 cc = ct.narrow(ch, char());
3753 #endif /* BOOST_NO_STD_LOCALE */
3755 if (cc == ')') // read "(a,(c,d)" (ambiguity resolution)
3757 is >> ch; // get the next lexeme
3759 if (!is.good()) goto finish;
3761 #ifdef BOOST_NO_STD_LOCALE
3764 cc = ct.narrow(ch, char());
3765 #endif /* BOOST_NO_STD_LOCALE */
3767 if (cc == ')') // read "(a,(c,d))"
3769 o = octonion<T>(a,b,c,d);
3771 else if (cc == ',') // read "(a,(c,d),"
3773 u = ::std::complex<T>(a);
3775 v = ::std::complex<T>(c,d);
3777 is >> x; // read "(a,(c,d),x"
3779 if (!is.good()) goto finish;
3781 is >> ch; // get the next lexeme
3783 if (!is.good()) goto finish;
3785 #ifdef BOOST_NO_STD_LOCALE
3788 cc = ct.narrow(ch, char());
3789 #endif /* BOOST_NO_STD_LOCALE */
3791 if (cc == ')') // read "(a,(c,d),x)"
3793 o = octonion<T>(u,v,x);
3795 else if (cc == ',') // read "(a,(c,d),x,"
3797 is >> y; // read "(a,(c,d),x,y"
3799 if (!is.good()) goto finish;
3801 is >> ch; // get the next lexeme
3803 if (!is.good()) goto finish;
3805 #ifdef BOOST_NO_STD_LOCALE
3808 cc = ct.narrow(ch, char());
3809 #endif /* BOOST_NO_STD_LOCALE */
3811 if (cc == ')') // read "(a,(c,d),x,y)"
3813 o = octonion<T>(u,v,x,y);
3817 #if BOOST_WORKAROUND(__GNUC__, < 3)
3818 is.setstate(::std::ios::failbit);
3820 is.setstate(::std::ios_base::failbit);
3821 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3826 #if BOOST_WORKAROUND(__GNUC__, < 3)
3827 is.setstate(::std::ios::failbit);
3829 is.setstate(::std::ios_base::failbit);
3830 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3835 #if BOOST_WORKAROUND(__GNUC__, < 3)
3836 is.setstate(::std::ios::failbit);
3838 is.setstate(::std::ios_base::failbit);
3839 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3842 else if (cc == ',') // read "(a,(e,f," (ambiguity resolution)
3844 p = ::boost::math::quaternion<T>(a);
3846 is >> g; // read "(a,(e,f,g"
3848 if (!is.good()) goto finish;
3850 is >> ch; // get the next lexeme
3852 if (!is.good()) goto finish;
3854 #ifdef BOOST_NO_STD_LOCALE
3857 cc = ct.narrow(ch, char());
3858 #endif /* BOOST_NO_STD_LOCALE */
3860 if (cc == ')') // read "(a,(e,f,g)"
3862 is >> ch; // get the next lexeme
3864 if (!is.good()) goto finish;
3866 #ifdef BOOST_NO_STD_LOCALE
3869 cc = ct.narrow(ch, char());
3870 #endif /* BOOST_NO_STD_LOCALE */
3872 if (cc == ')') // read "(a,(e,f,g))"
3874 q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f"
3876 o = octonion<T>(p,q);
3880 #if BOOST_WORKAROUND(__GNUC__, < 3)
3881 is.setstate(::std::ios::failbit);
3883 is.setstate(::std::ios_base::failbit);
3884 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3887 else if (cc == ',') // read "(a,(e,f,g,"
3889 is >> h; // read "(a,(e,f,g,h"
3891 if (!is.good()) goto finish;
3893 is >> ch; // get the next lexeme
3895 if (!is.good()) goto finish;
3897 #ifdef BOOST_NO_STD_LOCALE
3900 cc = ct.narrow(ch, char());
3901 #endif /* BOOST_NO_STD_LOCALE */
3903 if (cc == ')') // read "(a,(e,f,g,h)"
3905 is >> ch; // get the next lexeme
3907 if (!is.good()) goto finish;
3909 #ifdef BOOST_NO_STD_LOCALE
3912 cc = ct.narrow(ch, char());
3913 #endif /* BOOST_NO_STD_LOCALE */
3915 if (cc == ')') // read "(a,(e,f,g,h))"
3917 q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f"
3919 o = octonion<T>(p,q);
3923 #if BOOST_WORKAROUND(__GNUC__, < 3)
3924 is.setstate(::std::ios::failbit);
3926 is.setstate(::std::ios_base::failbit);
3927 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3932 #if BOOST_WORKAROUND(__GNUC__, < 3)
3933 is.setstate(::std::ios::failbit);
3935 is.setstate(::std::ios_base::failbit);
3936 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3941 #if BOOST_WORKAROUND(__GNUC__, < 3)
3942 is.setstate(::std::ios::failbit);
3944 is.setstate(::std::ios_base::failbit);
3945 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3950 #if BOOST_WORKAROUND(__GNUC__, < 3)
3951 is.setstate(::std::ios::failbit);
3953 is.setstate(::std::ios_base::failbit);
3954 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3960 #if BOOST_WORKAROUND(__GNUC__, < 3)
3961 is.setstate(::std::ios::failbit);
3963 is.setstate(::std::ios_base::failbit);
3964 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
3968 else // read "(a,b" or "(a,c" (ambiguity resolution)
3974 if (!is.good()) goto finish;
3976 is >> ch; // get the next lexeme
3978 if (!is.good()) goto finish;
3980 #ifdef BOOST_NO_STD_LOCALE
3983 cc = ct.narrow(ch, char());
3984 #endif /* BOOST_NO_STD_LOCALE */
3986 if (cc == ')') // read "(a,b)" (ambiguity resolution)
3988 o = octonion<T>(a,b);
3990 else if (cc == ',') // read "(a,b," or "(a,c,"
3992 is >> ch; // get the next lexeme
3994 if (!is.good()) goto finish;
3996 #ifdef BOOST_NO_STD_LOCALE
3999 cc = ct.narrow(ch, char());
4000 #endif /* BOOST_NO_STD_LOCALE */
4002 if (cc == '(') // read "(a,c,(" (ambiguity resolution)
4004 u = ::std::complex<T>(a);
4006 v = ::std::complex<T>(b); // "b" is actually "c"
4008 is.putback(ch); // we backtrack
4010 is >> x; // read "(a,c,x"
4012 if (!is.good()) goto finish;
4014 is >> ch; // get the next lexeme
4016 if (!is.good()) goto finish;
4018 #ifdef BOOST_NO_STD_LOCALE
4021 cc = ct.narrow(ch, char());
4022 #endif /* BOOST_NO_STD_LOCALE */
4024 if (cc == ')') // read "(a,c,x)"
4026 o = octonion<T>(u,v,x);
4028 else if (cc == ',') // read "(a,c,x,"
4030 is >> y; // read "(a,c,x,y" // read "(a,c,x"
4032 if (!is.good()) goto finish;
4034 is >> ch; // get the next lexeme
4036 if (!is.good()) goto finish;
4038 #ifdef BOOST_NO_STD_LOCALE
4041 cc = ct.narrow(ch, char());
4042 #endif /* BOOST_NO_STD_LOCALE */
4044 if (cc == ')') // read "(a,c,x,y)"
4046 o = octonion<T>(u,v,x,y);
4050 #if BOOST_WORKAROUND(__GNUC__, < 3)
4051 is.setstate(::std::ios::failbit);
4053 is.setstate(::std::ios_base::failbit);
4054 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4059 #if BOOST_WORKAROUND(__GNUC__, < 3)
4060 is.setstate(::std::ios::failbit);
4062 is.setstate(::std::ios_base::failbit);
4063 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4066 else // read "(a,b,c" or "(a,c,e"
4072 if (!is.good()) goto finish;
4074 is >> ch; // get the next lexeme
4076 if (!is.good()) goto finish;
4078 #ifdef BOOST_NO_STD_LOCALE
4081 cc = ct.narrow(ch, char());
4082 #endif /* BOOST_NO_STD_LOCALE */
4084 if (cc == ')') // read "(a,b,c)" (ambiguity resolution)
4086 o = octonion<T>(a,b,c);
4088 else if (cc == ',') // read "(a,b,c," or "(a,c,e,"
4090 is >> ch; // get the next lexeme
4092 if (!is.good()) goto finish;
4094 #ifdef BOOST_NO_STD_LOCALE
4097 cc = ct.narrow(ch, char());
4098 #endif /* BOOST_NO_STD_LOCALE */
4100 if (cc == '(') // read "(a,c,e,(") (ambiguity resolution)
4102 u = ::std::complex<T>(a);
4104 v = ::std::complex<T>(b); // "b" is actually "c"
4106 x = ::std::complex<T>(c); // "c" is actually "e"
4108 is.putback(ch); // we backtrack
4110 is >> y; // read "(a,c,e,y"
4112 if (!is.good()) goto finish;
4114 is >> ch; // get the next lexeme
4116 if (!is.good()) goto finish;
4118 #ifdef BOOST_NO_STD_LOCALE
4121 cc = ct.narrow(ch, char());
4122 #endif /* BOOST_NO_STD_LOCALE */
4124 if (cc == ')') // read "(a,c,e,y)"
4126 o = octonion<T>(u,v,x,y);
4130 #if BOOST_WORKAROUND(__GNUC__, < 3)
4131 is.setstate(::std::ios::failbit);
4133 is.setstate(::std::ios_base::failbit);
4134 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4137 else // read "(a,b,c,d" (ambiguity resolution)
4139 is.putback(ch); // we backtrack
4143 if (!is.good()) goto finish;
4145 is >> ch; // get the next lexeme
4147 if (!is.good()) goto finish;
4149 #ifdef BOOST_NO_STD_LOCALE
4152 cc = ct.narrow(ch, char());
4153 #endif /* BOOST_NO_STD_LOCALE */
4155 if (cc == ')') // read "(a,b,c,d)"
4157 o = octonion<T>(a,b,c,d);
4159 else if (cc == ',') // read "(a,b,c,d,"
4161 is >> e; // read "(a,b,c,d,e"
4163 if (!is.good()) goto finish;
4165 is >> ch; // get the next lexeme
4167 if (!is.good()) goto finish;
4169 #ifdef BOOST_NO_STD_LOCALE
4172 cc = ct.narrow(ch, char());
4173 #endif /* BOOST_NO_STD_LOCALE */
4175 if (cc == ')') // read "(a,b,c,d,e)"
4177 o = octonion<T>(a,b,c,d,e);
4179 else if (cc == ',') // read "(a,b,c,d,e,"
4181 is >> f; // read "(a,b,c,d,e,f"
4183 if (!is.good()) goto finish;
4185 is >> ch; // get the next lexeme
4187 if (!is.good()) goto finish;
4189 #ifdef BOOST_NO_STD_LOCALE
4192 cc = ct.narrow(ch, char());
4193 #endif /* BOOST_NO_STD_LOCALE */
4195 if (cc == ')') // read "(a,b,c,d,e,f)"
4197 o = octonion<T>(a,b,c,d,e,f);
4199 else if (cc == ',') // read "(a,b,c,d,e,f,"
4201 is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f"
4203 if (!is.good()) goto finish;
4205 is >> ch; // get the next lexeme
4207 if (!is.good()) goto finish;
4209 #ifdef BOOST_NO_STD_LOCALE
4212 cc = ct.narrow(ch, char());
4213 #endif /* BOOST_NO_STD_LOCALE */
4215 if (cc == ')') // read "(a,b,c,d,e,f,g)"
4217 o = octonion<T>(a,b,c,d,e,f,g);
4219 else if (cc == ',') // read "(a,b,c,d,e,f,g,"
4221 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"
4223 if (!is.good()) goto finish;
4225 is >> ch; // get the next lexeme
4227 if (!is.good()) goto finish;
4229 #ifdef BOOST_NO_STD_LOCALE
4232 cc = ct.narrow(ch, char());
4233 #endif /* BOOST_NO_STD_LOCALE */
4235 if (cc == ')') // read "(a,b,c,d,e,f,g,h)"
4237 o = octonion<T>(a,b,c,d,e,f,g,h);
4241 #if BOOST_WORKAROUND(__GNUC__, < 3)
4242 is.setstate(::std::ios::failbit);
4244 is.setstate(::std::ios_base::failbit);
4245 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4250 #if BOOST_WORKAROUND(__GNUC__, < 3)
4251 is.setstate(::std::ios::failbit);
4253 is.setstate(::std::ios_base::failbit);
4254 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4259 #if BOOST_WORKAROUND(__GNUC__, < 3)
4260 is.setstate(::std::ios::failbit);
4262 is.setstate(::std::ios_base::failbit);
4263 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4268 #if BOOST_WORKAROUND(__GNUC__, < 3)
4269 is.setstate(::std::ios::failbit);
4271 is.setstate(::std::ios_base::failbit);
4272 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4277 #if BOOST_WORKAROUND(__GNUC__, < 3)
4278 is.setstate(::std::ios::failbit);
4280 is.setstate(::std::ios_base::failbit);
4281 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4287 #if BOOST_WORKAROUND(__GNUC__, < 3)
4288 is.setstate(::std::ios::failbit);
4290 is.setstate(::std::ios_base::failbit);
4291 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4297 #if BOOST_WORKAROUND(__GNUC__, < 3)
4298 is.setstate(::std::ios::failbit);
4300 is.setstate(::std::ios_base::failbit);
4301 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4307 #if BOOST_WORKAROUND(__GNUC__, < 3)
4308 is.setstate(::std::ios::failbit);
4310 is.setstate(::std::ios_base::failbit);
4311 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4319 is >> a; // we extract the first component
4321 if (!is.good()) goto finish;
4331 #if BOOST_WORKAROUND(__GNUC__, < 3)
4332 template<typename T>
4333 ::std::ostream & operator << ( ::std::ostream & os,
4334 octonion<T> const & o)
4336 template<typename T, typename charT, class traits>
4337 ::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
4338 octonion<T> const & o)
4339 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4341 #if BOOST_WORKAROUND(__GNUC__, < 3)
4342 ::std::ostringstream s;
4344 ::std::basic_ostringstream<charT,traits> s;
4345 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4347 s.flags(os.flags());
4348 #ifdef BOOST_NO_STD_LOCALE
4350 s.imbue(os.getloc());
4351 #endif /* BOOST_NO_STD_LOCALE */
4352 s.precision(os.precision());
4354 s << '(' << o.R_component_1() << ','
4355 << o.R_component_2() << ','
4356 << o.R_component_3() << ','
4357 << o.R_component_4() << ','
4358 << o.R_component_5() << ','
4359 << o.R_component_6() << ','
4360 << o.R_component_7() << ','
4361 << o.R_component_8() << ')';
4363 return os << s.str();
4369 template<typename T>
4370 inline T real(octonion<T> const & o)
4376 template<typename T>
4377 inline octonion<T> unreal(octonion<T> const & o)
4383 #define BOOST_OCTONION_VALARRAY_LOADER \
4384 using ::std::valarray; \
4386 valarray<T> temp(8); \
4388 temp[0] = o.R_component_1(); \
4389 temp[1] = o.R_component_2(); \
4390 temp[2] = o.R_component_3(); \
4391 temp[3] = o.R_component_4(); \
4392 temp[4] = o.R_component_5(); \
4393 temp[5] = o.R_component_6(); \
4394 temp[6] = o.R_component_7(); \
4395 temp[7] = o.R_component_8();
4398 template<typename T>
4399 inline T sup(octonion<T> const & o)
4401 #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
4403 #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
4405 BOOST_OCTONION_VALARRAY_LOADER
4407 #if BOOST_WORKAROUND(__GNUC__, < 3)
4408 return((BOOST_GET_VALARRAY(T, abs(temp)).max)());
4410 return((abs(temp).max)());
4411 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4415 template<typename T>
4416 inline T l1(octonion<T> const & o)
4418 #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
4420 #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
4422 BOOST_OCTONION_VALARRAY_LOADER
4424 #if BOOST_WORKAROUND(__GNUC__, < 3)
4425 return(BOOST_GET_VALARRAY(T, abs(temp)).sum());
4427 return(abs(temp).sum());
4428 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4432 template<typename T>
4433 inline T abs(const octonion<T> & o)
4435 #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
4437 #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
4441 BOOST_OCTONION_VALARRAY_LOADER
4443 #if BOOST_WORKAROUND(__GNUC__, < 3)
4444 T maxim = (BOOST_GET_VALARRAY(T,abs(temp)).max)(); // overflow protection
4446 T maxim = (abs(temp).max)(); // overflow protection
4447 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4449 if (maxim == static_cast<T>(0))
4455 T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
4461 return(maxim*sqrt(temp.sum()));
4464 //return(::std::sqrt(norm(o)));
4468 #undef BOOST_OCTONION_VALARRAY_LOADER
4471 // Note: This is the Cayley norm, not the Euclidian norm...
4473 template<typename T>
4474 inline T norm(octonion<T> const & o)
4476 return(real(o*conj(o)));
4480 template<typename T>
4481 inline octonion<T> conj(octonion<T> const & o)
4483 return(octonion<T>( +o.R_component_1(),
4490 -o.R_component_8()));
4494 // Note: There is little point, for the octonions, to introduce the equivalents
4495 // to the complex "arg" and the quaternionic "cylindropolar".
4498 template<typename T>
4499 inline octonion<T> spherical(T const & rho,
4511 //T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
4512 //T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
4513 //T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
4514 //T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
4515 //T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6);
4516 //T f = sin(phi4)*cos(phi5)*cos(phi6);
4517 //T g = sin(phi5)*cos(phi6);
4520 T courrant = static_cast<T>(1);
4524 courrant *= cos(phi6);
4526 T g = sin(phi5)*courrant;
4528 courrant *= cos(phi5);
4530 T f = sin(phi4)*courrant;
4532 courrant *= cos(phi4);
4534 T e = sin(phi3)*courrant;
4536 courrant *= cos(phi3);
4538 T d = sin(phi2)*courrant;
4540 courrant *= cos(phi2);
4542 T c = sin(phi1)*courrant;
4544 courrant *= cos(phi1);
4546 T b = sin(theta)*courrant;
4547 T a = cos(theta)*courrant;
4549 return(rho*octonion<T>(a,b,c,d,e,f,g,h));
4553 template<typename T>
4554 inline octonion<T> multipolar(T const & rho1,
4566 T a = rho1*cos(theta1);
4567 T b = rho1*sin(theta1);
4568 T c = rho2*cos(theta2);
4569 T d = rho2*sin(theta2);
4570 T e = rho3*cos(theta3);
4571 T f = rho3*sin(theta3);
4572 T g = rho4*cos(theta4);
4573 T h = rho4*sin(theta4);
4575 return(octonion<T>(a,b,c,d,e,f,g,h));
4579 template<typename T>
4580 inline octonion<T> cylindrical(T const & r,
4595 return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6));
4599 template<typename T>
4600 inline octonion<T> exp(octonion<T> const & o)
4605 using ::boost::math::sinc_pi;
4609 T z = abs(unreal(o));
4613 return(u*octonion<T>(cos(z),
4614 w*o.R_component_2(), w*o.R_component_3(),
4615 w*o.R_component_4(), w*o.R_component_5(),
4616 w*o.R_component_6(), w*o.R_component_7(),
4617 w*o.R_component_8()));
4621 template<typename T>
4622 inline octonion<T> cos(octonion<T> const & o)
4628 using ::boost::math::sinhc_pi;
4630 T z = abs(unreal(o));
4632 T w = -sin(o.real())*sinhc_pi(z);
4634 return(octonion<T>(cos(o.real())*cosh(z),
4635 w*o.R_component_2(), w*o.R_component_3(),
4636 w*o.R_component_4(), w*o.R_component_5(),
4637 w*o.R_component_6(), w*o.R_component_7(),
4638 w*o.R_component_8()));
4642 template<typename T>
4643 inline octonion<T> sin(octonion<T> const & o)
4649 using ::boost::math::sinhc_pi;
4651 T z = abs(unreal(o));
4653 T w = +cos(o.real())*sinhc_pi(z);
4655 return(octonion<T>(sin(o.real())*cosh(z),
4656 w*o.R_component_2(), w*o.R_component_3(),
4657 w*o.R_component_4(), w*o.R_component_5(),
4658 w*o.R_component_6(), w*o.R_component_7(),
4659 w*o.R_component_8()));
4663 template<typename T>
4664 inline octonion<T> tan(octonion<T> const & o)
4666 return(sin(o)/cos(o));
4670 template<typename T>
4671 inline octonion<T> cosh(octonion<T> const & o)
4673 return((exp(+o)+exp(-o))/static_cast<T>(2));
4677 template<typename T>
4678 inline octonion<T> sinh(octonion<T> const & o)
4680 return((exp(+o)-exp(-o))/static_cast<T>(2));
4684 template<typename T>
4685 inline octonion<T> tanh(octonion<T> const & o)
4687 return(sinh(o)/cosh(o));
4691 template<typename T>
4692 octonion<T> pow(octonion<T> const & o,
4699 octonion<T> result = pow(o, m);
4705 result *= o; // n odd
4716 return(octonion<T>(1));
4720 return(pow(octonion<T>(1)/o,-n));
4725 // helper templates for converting copy constructors (definition)
4730 template< typename T,
4733 octonion<T> octonion_type_converter(octonion<U> const & rhs)
4735 return(octonion<T>( static_cast<T>(rhs.R_component_1()),
4736 static_cast<T>(rhs.R_component_2()),
4737 static_cast<T>(rhs.R_component_3()),
4738 static_cast<T>(rhs.R_component_4()),
4739 static_cast<T>(rhs.R_component_5()),
4740 static_cast<T>(rhs.R_component_6()),
4741 static_cast<T>(rhs.R_component_7()),
4742 static_cast<T>(rhs.R_component_8())));
4749 #if BOOST_WORKAROUND(__GNUC__, < 3)
4750 #undef BOOST_GET_VALARRAY
4751 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
4754 #endif /* BOOST_OCTONION_HPP */