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1 | // boost octonion.hpp header file |
2 | ||
3 | // (C) Copyright Hubert Holin 2001. | |
4 | // Distributed under the Boost Software License, Version 1.0. (See | |
5 | // accompanying file LICENSE_1_0.txt or copy at | |
6 | // http://www.boost.org/LICENSE_1_0.txt) | |
7 | ||
8 | // See http://www.boost.org for updates, documentation, and revision history. | |
9 | ||
10 | ||
11 | #ifndef BOOST_OCTONION_HPP | |
12 | #define BOOST_OCTONION_HPP | |
13 | ||
14 | #include <boost/math/quaternion.hpp> | |
15 | ||
16 | ||
17 | namespace boost | |
18 | { | |
19 | namespace math | |
20 | { | |
21 | ||
22 | #define BOOST_OCTONION_ACCESSOR_GENERATOR(type) \ | |
23 | type real() const \ | |
24 | { \ | |
25 | return(a); \ | |
26 | } \ | |
27 | \ | |
28 | octonion<type> unreal() const \ | |
29 | { \ | |
30 | return( octonion<type>(static_cast<type>(0),b,c,d,e,f,g,h)); \ | |
31 | } \ | |
32 | \ | |
33 | type R_component_1() const \ | |
34 | { \ | |
35 | return(a); \ | |
36 | } \ | |
37 | \ | |
38 | type R_component_2() const \ | |
39 | { \ | |
40 | return(b); \ | |
41 | } \ | |
42 | \ | |
43 | type R_component_3() const \ | |
44 | { \ | |
45 | return(c); \ | |
46 | } \ | |
47 | \ | |
48 | type R_component_4() const \ | |
49 | { \ | |
50 | return(d); \ | |
51 | } \ | |
52 | \ | |
53 | type R_component_5() const \ | |
54 | { \ | |
55 | return(e); \ | |
56 | } \ | |
57 | \ | |
58 | type R_component_6() const \ | |
59 | { \ | |
60 | return(f); \ | |
61 | } \ | |
62 | \ | |
63 | type R_component_7() const \ | |
64 | { \ | |
65 | return(g); \ | |
66 | } \ | |
67 | \ | |
68 | type R_component_8() const \ | |
69 | { \ | |
70 | return(h); \ | |
71 | } \ | |
72 | \ | |
73 | ::std::complex<type> C_component_1() const \ | |
74 | { \ | |
75 | return(::std::complex<type>(a,b)); \ | |
76 | } \ | |
77 | \ | |
78 | ::std::complex<type> C_component_2() const \ | |
79 | { \ | |
80 | return(::std::complex<type>(c,d)); \ | |
81 | } \ | |
82 | \ | |
83 | ::std::complex<type> C_component_3() const \ | |
84 | { \ | |
85 | return(::std::complex<type>(e,f)); \ | |
86 | } \ | |
87 | \ | |
88 | ::std::complex<type> C_component_4() const \ | |
89 | { \ | |
90 | return(::std::complex<type>(g,h)); \ | |
91 | } \ | |
92 | \ | |
93 | ::boost::math::quaternion<type> H_component_1() const \ | |
94 | { \ | |
95 | return(::boost::math::quaternion<type>(a,b,c,d)); \ | |
96 | } \ | |
97 | \ | |
98 | ::boost::math::quaternion<type> H_component_2() const \ | |
99 | { \ | |
100 | return(::boost::math::quaternion<type>(e,f,g,h)); \ | |
101 | } | |
102 | ||
103 | ||
104 | #define BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(type) \ | |
105 | template<typename X> \ | |
106 | octonion<type> & operator = (octonion<X> const & a_affecter) \ | |
107 | { \ | |
108 | a = static_cast<type>(a_affecter.R_component_1()); \ | |
109 | b = static_cast<type>(a_affecter.R_component_2()); \ | |
110 | c = static_cast<type>(a_affecter.R_component_3()); \ | |
111 | d = static_cast<type>(a_affecter.R_component_4()); \ | |
112 | e = static_cast<type>(a_affecter.R_component_5()); \ | |
113 | f = static_cast<type>(a_affecter.R_component_6()); \ | |
114 | g = static_cast<type>(a_affecter.R_component_7()); \ | |
115 | h = static_cast<type>(a_affecter.R_component_8()); \ | |
116 | \ | |
117 | return(*this); \ | |
118 | } \ | |
119 | \ | |
120 | octonion<type> & operator = (octonion<type> const & a_affecter) \ | |
121 | { \ | |
122 | a = a_affecter.a; \ | |
123 | b = a_affecter.b; \ | |
124 | c = a_affecter.c; \ | |
125 | d = a_affecter.d; \ | |
126 | e = a_affecter.e; \ | |
127 | f = a_affecter.f; \ | |
128 | g = a_affecter.g; \ | |
129 | h = a_affecter.h; \ | |
130 | \ | |
131 | return(*this); \ | |
132 | } \ | |
133 | \ | |
134 | octonion<type> & operator = (type const & a_affecter) \ | |
135 | { \ | |
136 | a = a_affecter; \ | |
137 | \ | |
138 | b = c = d = e = f= g = h = static_cast<type>(0); \ | |
139 | \ | |
140 | return(*this); \ | |
141 | } \ | |
142 | \ | |
143 | octonion<type> & operator = (::std::complex<type> const & a_affecter) \ | |
144 | { \ | |
145 | a = a_affecter.real(); \ | |
146 | b = a_affecter.imag(); \ | |
147 | \ | |
148 | c = d = e = f = g = h = static_cast<type>(0); \ | |
149 | \ | |
150 | return(*this); \ | |
151 | } \ | |
152 | \ | |
153 | octonion<type> & operator = (::boost::math::quaternion<type> const & a_affecter) \ | |
154 | { \ | |
155 | a = a_affecter.R_component_1(); \ | |
156 | b = a_affecter.R_component_2(); \ | |
157 | c = a_affecter.R_component_3(); \ | |
158 | d = a_affecter.R_component_4(); \ | |
159 | \ | |
160 | e = f = g = h = static_cast<type>(0); \ | |
161 | \ | |
162 | return(*this); \ | |
163 | } | |
164 | ||
165 | ||
166 | #define BOOST_OCTONION_MEMBER_DATA_GENERATOR(type) \ | |
167 | type a; \ | |
168 | type b; \ | |
169 | type c; \ | |
170 | type d; \ | |
171 | type e; \ | |
172 | type f; \ | |
173 | type g; \ | |
174 | type h; \ | |
175 | ||
176 | ||
177 | template<typename T> | |
178 | class octonion | |
179 | { | |
180 | public: | |
181 | ||
182 | typedef T value_type; | |
183 | ||
184 | // constructor for O seen as R^8 | |
185 | // (also default constructor) | |
186 | ||
187 | explicit octonion( T const & requested_a = T(), | |
188 | T const & requested_b = T(), | |
189 | T const & requested_c = T(), | |
190 | T const & requested_d = T(), | |
191 | T const & requested_e = T(), | |
192 | T const & requested_f = T(), | |
193 | T const & requested_g = T(), | |
194 | T const & requested_h = T()) | |
195 | : a(requested_a), | |
196 | b(requested_b), | |
197 | c(requested_c), | |
198 | d(requested_d), | |
199 | e(requested_e), | |
200 | f(requested_f), | |
201 | g(requested_g), | |
202 | h(requested_h) | |
203 | { | |
204 | // nothing to do! | |
205 | } | |
206 | ||
207 | ||
208 | // constructor for H seen as C^4 | |
209 | ||
210 | explicit octonion( ::std::complex<T> const & z0, | |
211 | ::std::complex<T> const & z1 = ::std::complex<T>(), | |
212 | ::std::complex<T> const & z2 = ::std::complex<T>(), | |
213 | ::std::complex<T> const & z3 = ::std::complex<T>()) | |
214 | : a(z0.real()), | |
215 | b(z0.imag()), | |
216 | c(z1.real()), | |
217 | d(z1.imag()), | |
218 | e(z2.real()), | |
219 | f(z2.imag()), | |
220 | g(z3.real()), | |
221 | h(z3.imag()) | |
222 | { | |
223 | // nothing to do! | |
224 | } | |
225 | ||
226 | ||
227 | // constructor for O seen as H^2 | |
228 | ||
229 | explicit octonion( ::boost::math::quaternion<T> const & q0, | |
230 | ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>()) | |
231 | : a(q0.R_component_1()), | |
232 | b(q0.R_component_2()), | |
233 | c(q0.R_component_3()), | |
234 | d(q0.R_component_4()), | |
235 | e(q1.R_component_1()), | |
236 | f(q1.R_component_2()), | |
237 | g(q1.R_component_3()), | |
238 | h(q1.R_component_4()) | |
239 | { | |
240 | // nothing to do! | |
241 | } | |
242 | ||
243 | ||
244 | // UNtemplated copy constructor | |
245 | // (this is taken care of by the compiler itself) | |
246 | ||
247 | ||
248 | // templated copy constructor | |
249 | ||
250 | template<typename X> | |
251 | explicit octonion(octonion<X> const & a_recopier) | |
252 | : a(static_cast<T>(a_recopier.R_component_1())), | |
253 | b(static_cast<T>(a_recopier.R_component_2())), | |
254 | c(static_cast<T>(a_recopier.R_component_3())), | |
255 | d(static_cast<T>(a_recopier.R_component_4())), | |
256 | e(static_cast<T>(a_recopier.R_component_5())), | |
257 | f(static_cast<T>(a_recopier.R_component_6())), | |
258 | g(static_cast<T>(a_recopier.R_component_7())), | |
259 | h(static_cast<T>(a_recopier.R_component_8())) | |
260 | { | |
261 | // nothing to do! | |
262 | } | |
263 | ||
264 | ||
265 | // destructor | |
266 | // (this is taken care of by the compiler itself) | |
267 | ||
268 | ||
269 | // accessors | |
270 | // | |
271 | // Note: Like complex number, octonions do have a meaningful notion of "real part", | |
272 | // but unlike them there is no meaningful notion of "imaginary part". | |
273 | // Instead there is an "unreal part" which itself is an octonion, and usually | |
274 | // nothing simpler (as opposed to the complex number case). | |
275 | // However, for practicallity, there are accessors for the other components | |
276 | // (these are necessary for the templated copy constructor, for instance). | |
277 | ||
278 | BOOST_OCTONION_ACCESSOR_GENERATOR(T) | |
279 | ||
280 | // assignment operators | |
281 | ||
282 | BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(T) | |
283 | ||
284 | // other assignment-related operators | |
285 | // | |
286 | // NOTE: Octonion multiplication is *NOT* commutative; | |
287 | // symbolically, "q *= rhs;" means "q = q * rhs;" | |
288 | // and "q /= rhs;" means "q = q * inverse_of(rhs);"; | |
289 | // octonion multiplication is also *NOT* associative | |
290 | ||
291 | octonion<T> & operator += (T const & rhs) | |
292 | { | |
293 | T at = a + rhs; // exception guard | |
294 | ||
295 | a = at; | |
296 | ||
297 | return(*this); | |
298 | } | |
299 | ||
300 | ||
301 | octonion<T> & operator += (::std::complex<T> const & rhs) | |
302 | { | |
303 | T at = a + rhs.real(); // exception guard | |
304 | T bt = b + rhs.imag(); // exception guard | |
305 | ||
306 | a = at; | |
307 | b = bt; | |
308 | ||
309 | return(*this); | |
310 | } | |
311 | ||
312 | ||
313 | octonion<T> & operator += (::boost::math::quaternion<T> const & rhs) | |
314 | { | |
315 | T at = a + rhs.R_component_1(); // exception guard | |
316 | T bt = b + rhs.R_component_2(); // exception guard | |
317 | T ct = c + rhs.R_component_3(); // exception guard | |
318 | T dt = d + rhs.R_component_4(); // exception guard | |
319 | ||
320 | a = at; | |
321 | b = bt; | |
322 | c = ct; | |
323 | d = dt; | |
324 | ||
325 | return(*this); | |
326 | } | |
327 | ||
328 | ||
329 | template<typename X> | |
330 | octonion<T> & operator += (octonion<X> const & rhs) | |
331 | { | |
332 | T at = a + static_cast<T>(rhs.R_component_1()); // exception guard | |
333 | T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard | |
334 | T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard | |
335 | T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard | |
336 | T et = e + static_cast<T>(rhs.R_component_5()); // exception guard | |
337 | T ft = f + static_cast<T>(rhs.R_component_6()); // exception guard | |
338 | T gt = g + static_cast<T>(rhs.R_component_7()); // exception guard | |
339 | T ht = h + static_cast<T>(rhs.R_component_8()); // exception guard | |
340 | ||
341 | a = at; | |
342 | b = bt; | |
343 | c = ct; | |
344 | d = dt; | |
345 | e = et; | |
346 | f = ft; | |
347 | g = gt; | |
348 | h = ht; | |
349 | ||
350 | return(*this); | |
351 | } | |
352 | ||
353 | ||
354 | ||
355 | octonion<T> & operator -= (T const & rhs) | |
356 | { | |
357 | T at = a - rhs; // exception guard | |
358 | ||
359 | a = at; | |
360 | ||
361 | return(*this); | |
362 | } | |
363 | ||
364 | ||
365 | octonion<T> & operator -= (::std::complex<T> const & rhs) | |
366 | { | |
367 | T at = a - rhs.real(); // exception guard | |
368 | T bt = b - rhs.imag(); // exception guard | |
369 | ||
370 | a = at; | |
371 | b = bt; | |
372 | ||
373 | return(*this); | |
374 | } | |
375 | ||
376 | ||
377 | octonion<T> & operator -= (::boost::math::quaternion<T> const & rhs) | |
378 | { | |
379 | T at = a - rhs.R_component_1(); // exception guard | |
380 | T bt = b - rhs.R_component_2(); // exception guard | |
381 | T ct = c - rhs.R_component_3(); // exception guard | |
382 | T dt = d - rhs.R_component_4(); // exception guard | |
383 | ||
384 | a = at; | |
385 | b = bt; | |
386 | c = ct; | |
387 | d = dt; | |
388 | ||
389 | return(*this); | |
390 | } | |
391 | ||
392 | ||
393 | template<typename X> | |
394 | octonion<T> & operator -= (octonion<X> const & rhs) | |
395 | { | |
396 | T at = a - static_cast<T>(rhs.R_component_1()); // exception guard | |
397 | T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard | |
398 | T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard | |
399 | T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard | |
400 | T et = e - static_cast<T>(rhs.R_component_5()); // exception guard | |
401 | T ft = f - static_cast<T>(rhs.R_component_6()); // exception guard | |
402 | T gt = g - static_cast<T>(rhs.R_component_7()); // exception guard | |
403 | T ht = h - static_cast<T>(rhs.R_component_8()); // exception guard | |
404 | ||
405 | a = at; | |
406 | b = bt; | |
407 | c = ct; | |
408 | d = dt; | |
409 | e = et; | |
410 | f = ft; | |
411 | g = gt; | |
412 | h = ht; | |
413 | ||
414 | return(*this); | |
415 | } | |
416 | ||
417 | ||
418 | octonion<T> & operator *= (T const & rhs) | |
419 | { | |
420 | T at = a * rhs; // exception guard | |
421 | T bt = b * rhs; // exception guard | |
422 | T ct = c * rhs; // exception guard | |
423 | T dt = d * rhs; // exception guard | |
424 | T et = e * rhs; // exception guard | |
425 | T ft = f * rhs; // exception guard | |
426 | T gt = g * rhs; // exception guard | |
427 | T ht = h * rhs; // exception guard | |
428 | ||
429 | a = at; | |
430 | b = bt; | |
431 | c = ct; | |
432 | d = dt; | |
433 | e = et; | |
434 | f = ft; | |
435 | g = gt; | |
436 | h = ht; | |
437 | ||
438 | return(*this); | |
439 | } | |
440 | ||
441 | ||
442 | octonion<T> & operator *= (::std::complex<T> const & rhs) | |
443 | { | |
444 | T ar = rhs.real(); | |
445 | T br = rhs.imag(); | |
446 | ||
447 | T at = +a*ar-b*br; | |
448 | T bt = +a*br+b*ar; | |
449 | T ct = +c*ar+d*br; | |
450 | T dt = -c*br+d*ar; | |
451 | T et = +e*ar+f*br; | |
452 | T ft = -e*br+f*ar; | |
453 | T gt = +g*ar-h*br; | |
454 | T ht = +g*br+h*ar; | |
455 | ||
456 | a = at; | |
457 | b = bt; | |
458 | c = ct; | |
459 | d = dt; | |
460 | e = et; | |
461 | f = ft; | |
462 | g = gt; | |
463 | h = ht; | |
464 | ||
465 | return(*this); | |
466 | } | |
467 | ||
468 | ||
469 | octonion<T> & operator *= (::boost::math::quaternion<T> const & rhs) | |
470 | { | |
471 | T ar = rhs.R_component_1(); | |
472 | T br = rhs.R_component_2(); | |
473 | T cr = rhs.R_component_2(); | |
474 | T dr = rhs.R_component_2(); | |
475 | ||
476 | T at = +a*ar-b*br-c*cr-d*dr; | |
477 | T bt = +a*br+b*ar+c*dr-d*cr; | |
478 | T ct = +a*cr-b*dr+c*ar+d*br; | |
479 | T dt = +a*dr+b*cr-c*br+d*ar; | |
480 | T et = +e*ar+f*br+g*cr+h*dr; | |
481 | T ft = -e*br+f*ar-g*dr+h*cr; | |
482 | T gt = -e*cr+f*dr+g*ar-h*br; | |
483 | T ht = -e*dr-f*cr+g*br+h*ar; | |
484 | ||
485 | a = at; | |
486 | b = bt; | |
487 | c = ct; | |
488 | d = dt; | |
489 | e = et; | |
490 | f = ft; | |
491 | g = gt; | |
492 | h = ht; | |
493 | ||
494 | return(*this); | |
495 | } | |
496 | ||
497 | ||
498 | template<typename X> | |
499 | octonion<T> & operator *= (octonion<X> const & rhs) | |
500 | { | |
501 | T ar = static_cast<T>(rhs.R_component_1()); | |
502 | T br = static_cast<T>(rhs.R_component_2()); | |
503 | T cr = static_cast<T>(rhs.R_component_3()); | |
504 | T dr = static_cast<T>(rhs.R_component_4()); | |
505 | T er = static_cast<T>(rhs.R_component_5()); | |
506 | T fr = static_cast<T>(rhs.R_component_6()); | |
507 | T gr = static_cast<T>(rhs.R_component_7()); | |
508 | T hr = static_cast<T>(rhs.R_component_8()); | |
509 | ||
510 | T at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; | |
511 | T bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; | |
512 | T ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; | |
513 | T dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; | |
514 | T et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; | |
515 | T ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; | |
516 | T gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; | |
517 | T ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; | |
518 | ||
519 | a = at; | |
520 | b = bt; | |
521 | c = ct; | |
522 | d = dt; | |
523 | e = et; | |
524 | f = ft; | |
525 | g = gt; | |
526 | h = ht; | |
527 | ||
528 | return(*this); | |
529 | } | |
530 | ||
531 | ||
532 | octonion<T> & operator /= (T const & rhs) | |
533 | { | |
534 | T at = a / rhs; // exception guard | |
535 | T bt = b / rhs; // exception guard | |
536 | T ct = c / rhs; // exception guard | |
537 | T dt = d / rhs; // exception guard | |
538 | T et = e / rhs; // exception guard | |
539 | T ft = f / rhs; // exception guard | |
540 | T gt = g / rhs; // exception guard | |
541 | T ht = h / rhs; // exception guard | |
542 | ||
543 | a = at; | |
544 | b = bt; | |
545 | c = ct; | |
546 | d = dt; | |
547 | e = et; | |
548 | f = ft; | |
549 | g = gt; | |
550 | h = ht; | |
551 | ||
552 | return(*this); | |
553 | } | |
554 | ||
555 | ||
556 | octonion<T> & operator /= (::std::complex<T> const & rhs) | |
557 | { | |
558 | T ar = rhs.real(); | |
559 | T br = rhs.imag(); | |
560 | ||
561 | T denominator = ar*ar+br*br; | |
562 | ||
563 | T at = (+a*ar-b*br)/denominator; | |
564 | T bt = (-a*br+b*ar)/denominator; | |
565 | T ct = (+c*ar-d*br)/denominator; | |
566 | T dt = (+c*br+d*ar)/denominator; | |
567 | T et = (+e*ar-f*br)/denominator; | |
568 | T ft = (+e*br+f*ar)/denominator; | |
569 | T gt = (+g*ar+h*br)/denominator; | |
570 | T ht = (+g*br+h*ar)/denominator; | |
571 | ||
572 | a = at; | |
573 | b = bt; | |
574 | c = ct; | |
575 | d = dt; | |
576 | e = et; | |
577 | f = ft; | |
578 | g = gt; | |
579 | h = ht; | |
580 | ||
581 | return(*this); | |
582 | } | |
583 | ||
584 | ||
585 | octonion<T> & operator /= (::boost::math::quaternion<T> const & rhs) | |
586 | { | |
587 | T ar = rhs.R_component_1(); | |
588 | T br = rhs.R_component_2(); | |
589 | T cr = rhs.R_component_2(); | |
590 | T dr = rhs.R_component_2(); | |
591 | ||
592 | T denominator = ar*ar+br*br+cr*cr+dr*dr; | |
593 | ||
594 | T at = (+a*ar+b*br+c*cr+d*dr)/denominator; | |
595 | T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; | |
596 | T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; | |
597 | T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; | |
598 | T et = (+e*ar-f*br-g*cr-h*dr)/denominator; | |
599 | T ft = (+e*br+f*ar+g*dr-h*cr)/denominator; | |
600 | T gt = (+e*cr-f*dr+g*ar+h*br)/denominator; | |
601 | T ht = (+e*dr+f*cr-g*br+h*ar)/denominator; | |
602 | ||
603 | a = at; | |
604 | b = bt; | |
605 | c = ct; | |
606 | d = dt; | |
607 | e = et; | |
608 | f = ft; | |
609 | g = gt; | |
610 | h = ht; | |
611 | ||
612 | return(*this); | |
613 | } | |
614 | ||
615 | ||
616 | template<typename X> | |
617 | octonion<T> & operator /= (octonion<X> const & rhs) | |
618 | { | |
619 | T ar = static_cast<T>(rhs.R_component_1()); | |
620 | T br = static_cast<T>(rhs.R_component_2()); | |
621 | T cr = static_cast<T>(rhs.R_component_3()); | |
622 | T dr = static_cast<T>(rhs.R_component_4()); | |
623 | T er = static_cast<T>(rhs.R_component_5()); | |
624 | T fr = static_cast<T>(rhs.R_component_6()); | |
625 | T gr = static_cast<T>(rhs.R_component_7()); | |
626 | T hr = static_cast<T>(rhs.R_component_8()); | |
627 | ||
628 | T denominator = ar*ar+br*br+cr*cr+dr*dr+er*er+fr*fr+gr*gr+hr*hr; | |
629 | ||
630 | T at = (+a*ar+b*br+c*cr+d*dr+e*er+f*fr+g*gr+h*hr)/denominator; | |
631 | T bt = (-a*br+b*ar-c*dr+d*cr-e*fr+f*er+g*hr-h*gr)/denominator; | |
632 | T ct = (-a*cr+b*dr+c*ar-d*br-e*gr-f*hr+g*er+h*fr)/denominator; | |
633 | T dt = (-a*dr-b*cr+c*br+d*ar-e*hr+f*gr-g*fr+h*er)/denominator; | |
634 | T et = (-a*er+b*fr+c*gr+d*hr+e*ar-f*br-g*cr-h*dr)/denominator; | |
635 | T ft = (-a*fr-b*er+c*hr-d*gr+e*br+f*ar+g*dr-h*cr)/denominator; | |
636 | T gt = (-a*gr-b*hr-c*er+d*fr+e*cr-f*dr+g*ar+h*br)/denominator; | |
637 | T ht = (-a*hr+b*gr-c*fr-d*er+e*dr+f*cr-g*br+h*ar)/denominator; | |
638 | ||
639 | a = at; | |
640 | b = bt; | |
641 | c = ct; | |
642 | d = dt; | |
643 | e = et; | |
644 | f = ft; | |
645 | g = gt; | |
646 | h = ht; | |
647 | ||
648 | return(*this); | |
649 | } | |
650 | ||
651 | ||
652 | protected: | |
653 | ||
654 | BOOST_OCTONION_MEMBER_DATA_GENERATOR(T) | |
655 | ||
656 | ||
657 | private: | |
658 | ||
659 | }; | |
660 | ||
661 | ||
662 | // declaration of octonion specialization | |
663 | ||
664 | template<> class octonion<float>; | |
665 | template<> class octonion<double>; | |
666 | template<> class octonion<long double>; | |
667 | ||
668 | ||
669 | // helper templates for converting copy constructors (declaration) | |
670 | ||
671 | namespace detail | |
672 | { | |
673 | ||
674 | template< typename T, | |
675 | typename U | |
676 | > | |
677 | octonion<T> octonion_type_converter(octonion<U> const & rhs); | |
678 | } | |
679 | ||
680 | ||
681 | // implementation of octonion specialization | |
682 | ||
683 | ||
684 | #define BOOST_OCTONION_CONSTRUCTOR_GENERATOR(type) \ | |
685 | explicit octonion( type const & requested_a = static_cast<type>(0), \ | |
686 | type const & requested_b = static_cast<type>(0), \ | |
687 | type const & requested_c = static_cast<type>(0), \ | |
688 | type const & requested_d = static_cast<type>(0), \ | |
689 | type const & requested_e = static_cast<type>(0), \ | |
690 | type const & requested_f = static_cast<type>(0), \ | |
691 | type const & requested_g = static_cast<type>(0), \ | |
692 | type const & requested_h = static_cast<type>(0)) \ | |
693 | : a(requested_a), \ | |
694 | b(requested_b), \ | |
695 | c(requested_c), \ | |
696 | d(requested_d), \ | |
697 | e(requested_e), \ | |
698 | f(requested_f), \ | |
699 | g(requested_g), \ | |
700 | h(requested_h) \ | |
701 | { \ | |
702 | } \ | |
703 | \ | |
704 | explicit octonion( ::std::complex<type> const & z0, \ | |
705 | ::std::complex<type> const & z1 = ::std::complex<type>(), \ | |
706 | ::std::complex<type> const & z2 = ::std::complex<type>(), \ | |
707 | ::std::complex<type> const & z3 = ::std::complex<type>()) \ | |
708 | : a(z0.real()), \ | |
709 | b(z0.imag()), \ | |
710 | c(z1.real()), \ | |
711 | d(z1.imag()), \ | |
712 | e(z2.real()), \ | |
713 | f(z2.imag()), \ | |
714 | g(z3.real()), \ | |
715 | h(z3.imag()) \ | |
716 | { \ | |
717 | } \ | |
718 | \ | |
719 | explicit octonion( ::boost::math::quaternion<type> const & q0, \ | |
720 | ::boost::math::quaternion<type> const & q1 = ::boost::math::quaternion<type>()) \ | |
721 | : a(q0.R_component_1()), \ | |
722 | b(q0.R_component_2()), \ | |
723 | c(q0.R_component_3()), \ | |
724 | d(q0.R_component_4()), \ | |
725 | e(q1.R_component_1()), \ | |
726 | f(q1.R_component_2()), \ | |
727 | g(q1.R_component_3()), \ | |
728 | h(q1.R_component_4()) \ | |
729 | { \ | |
730 | } | |
731 | ||
732 | ||
733 | #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \ | |
734 | octonion<type> & operator += (type const & rhs) \ | |
735 | { \ | |
736 | a += rhs; \ | |
737 | \ | |
738 | return(*this); \ | |
739 | } | |
740 | ||
741 | #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \ | |
742 | octonion<type> & operator += (::std::complex<type> const & rhs) \ | |
743 | { \ | |
744 | a += rhs.real(); \ | |
745 | b += rhs.imag(); \ | |
746 | \ | |
747 | return(*this); \ | |
748 | } | |
749 | ||
750 | #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \ | |
751 | octonion<type> & operator += (::boost::math::quaternion<type> const & rhs) \ | |
752 | { \ | |
753 | a += rhs.R_component_1(); \ | |
754 | b += rhs.R_component_2(); \ | |
755 | c += rhs.R_component_3(); \ | |
756 | d += rhs.R_component_4(); \ | |
757 | \ | |
758 | return(*this); \ | |
759 | } | |
760 | ||
761 | #define BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) \ | |
762 | template<typename X> \ | |
763 | octonion<type> & operator += (octonion<X> const & rhs) \ | |
764 | { \ | |
765 | a += static_cast<type>(rhs.R_component_1()); \ | |
766 | b += static_cast<type>(rhs.R_component_2()); \ | |
767 | c += static_cast<type>(rhs.R_component_3()); \ | |
768 | d += static_cast<type>(rhs.R_component_4()); \ | |
769 | e += static_cast<type>(rhs.R_component_5()); \ | |
770 | f += static_cast<type>(rhs.R_component_6()); \ | |
771 | g += static_cast<type>(rhs.R_component_7()); \ | |
772 | h += static_cast<type>(rhs.R_component_8()); \ | |
773 | \ | |
774 | return(*this); \ | |
775 | } | |
776 | ||
777 | #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \ | |
778 | octonion<type> & operator -= (type const & rhs) \ | |
779 | { \ | |
780 | a -= rhs; \ | |
781 | \ | |
782 | return(*this); \ | |
783 | } | |
784 | ||
785 | #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \ | |
786 | octonion<type> & operator -= (::std::complex<type> const & rhs) \ | |
787 | { \ | |
788 | a -= rhs.real(); \ | |
789 | b -= rhs.imag(); \ | |
790 | \ | |
791 | return(*this); \ | |
792 | } | |
793 | ||
794 | #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \ | |
795 | octonion<type> & operator -= (::boost::math::quaternion<type> const & rhs) \ | |
796 | { \ | |
797 | a -= rhs.R_component_1(); \ | |
798 | b -= rhs.R_component_2(); \ | |
799 | c -= rhs.R_component_3(); \ | |
800 | d -= rhs.R_component_4(); \ | |
801 | \ | |
802 | return(*this); \ | |
803 | } | |
804 | ||
805 | #define BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) \ | |
806 | template<typename X> \ | |
807 | octonion<type> & operator -= (octonion<X> const & rhs) \ | |
808 | { \ | |
809 | a -= static_cast<type>(rhs.R_component_1()); \ | |
810 | b -= static_cast<type>(rhs.R_component_2()); \ | |
811 | c -= static_cast<type>(rhs.R_component_3()); \ | |
812 | d -= static_cast<type>(rhs.R_component_4()); \ | |
813 | e -= static_cast<type>(rhs.R_component_5()); \ | |
814 | f -= static_cast<type>(rhs.R_component_6()); \ | |
815 | g -= static_cast<type>(rhs.R_component_7()); \ | |
816 | h -= static_cast<type>(rhs.R_component_8()); \ | |
817 | \ | |
818 | return(*this); \ | |
819 | } | |
820 | ||
821 | #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \ | |
822 | octonion<type> & operator *= (type const & rhs) \ | |
823 | { \ | |
824 | a *= rhs; \ | |
825 | b *= rhs; \ | |
826 | c *= rhs; \ | |
827 | d *= rhs; \ | |
828 | e *= rhs; \ | |
829 | f *= rhs; \ | |
830 | g *= rhs; \ | |
831 | h *= rhs; \ | |
832 | \ | |
833 | return(*this); \ | |
834 | } | |
835 | ||
836 | #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \ | |
837 | octonion<type> & operator *= (::std::complex<type> const & rhs) \ | |
838 | { \ | |
839 | type ar = rhs.real(); \ | |
840 | type br = rhs.imag(); \ | |
841 | \ | |
842 | type at = +a*ar-b*br; \ | |
843 | type bt = +a*br+b*ar; \ | |
844 | type ct = +c*ar+d*br; \ | |
845 | type dt = -c*br+d*ar; \ | |
846 | type et = +e*ar+f*br; \ | |
847 | type ft = -e*br+f*ar; \ | |
848 | type gt = +g*ar-h*br; \ | |
849 | type ht = +g*br+h*ar; \ | |
850 | \ | |
851 | a = at; \ | |
852 | b = bt; \ | |
853 | c = ct; \ | |
854 | d = dt; \ | |
855 | e = et; \ | |
856 | f = ft; \ | |
857 | g = gt; \ | |
858 | h = ht; \ | |
859 | \ | |
860 | return(*this); \ | |
861 | } | |
862 | ||
863 | #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \ | |
864 | octonion<type> & operator *= (::boost::math::quaternion<type> const & rhs) \ | |
865 | { \ | |
866 | type ar = rhs.R_component_1(); \ | |
867 | type br = rhs.R_component_2(); \ | |
868 | type cr = rhs.R_component_2(); \ | |
869 | type dr = rhs.R_component_2(); \ | |
870 | \ | |
871 | type at = +a*ar-b*br-c*cr-d*dr; \ | |
872 | type bt = +a*br+b*ar+c*dr-d*cr; \ | |
873 | type ct = +a*cr-b*dr+c*ar+d*br; \ | |
874 | type dt = +a*dr+b*cr-c*br+d*ar; \ | |
875 | type et = +e*ar+f*br+g*cr+h*dr; \ | |
876 | type ft = -e*br+f*ar-g*dr+h*cr; \ | |
877 | type gt = -e*cr+f*dr+g*ar-h*br; \ | |
878 | type ht = -e*dr-f*cr+g*br+h*ar; \ | |
879 | \ | |
880 | a = at; \ | |
881 | b = bt; \ | |
882 | c = ct; \ | |
883 | d = dt; \ | |
884 | e = et; \ | |
885 | f = ft; \ | |
886 | g = gt; \ | |
887 | h = ht; \ | |
888 | \ | |
889 | return(*this); \ | |
890 | } | |
891 | ||
892 | #define BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) \ | |
893 | template<typename X> \ | |
894 | octonion<type> & operator *= (octonion<X> const & rhs) \ | |
895 | { \ | |
896 | type ar = static_cast<type>(rhs.R_component_1()); \ | |
897 | type br = static_cast<type>(rhs.R_component_2()); \ | |
898 | type cr = static_cast<type>(rhs.R_component_3()); \ | |
899 | type dr = static_cast<type>(rhs.R_component_4()); \ | |
900 | type er = static_cast<type>(rhs.R_component_5()); \ | |
901 | type fr = static_cast<type>(rhs.R_component_6()); \ | |
902 | type gr = static_cast<type>(rhs.R_component_7()); \ | |
903 | type hr = static_cast<type>(rhs.R_component_8()); \ | |
904 | \ | |
905 | type at = +a*ar-b*br-c*cr-d*dr-e*er-f*fr-g*gr-h*hr; \ | |
906 | type bt = +a*br+b*ar+c*dr-d*cr+e*fr-f*er-g*hr+h*gr; \ | |
907 | type ct = +a*cr-b*dr+c*ar+d*br+e*gr+f*hr-g*er-h*fr; \ | |
908 | type dt = +a*dr+b*cr-c*br+d*ar+e*hr-f*gr+g*fr-h*er; \ | |
909 | type et = +a*er-b*fr-c*gr-d*hr+e*ar+f*br+g*cr+h*dr; \ | |
910 | type ft = +a*fr+b*er-c*hr+d*gr-e*br+f*ar-g*dr+h*cr; \ | |
911 | type gt = +a*gr+b*hr+c*er-d*fr-e*cr+f*dr+g*ar-h*br; \ | |
912 | type ht = +a*hr-b*gr+c*fr+d*er-e*dr-f*cr+g*br+h*ar; \ | |
913 | \ | |
914 | a = at; \ | |
915 | b = bt; \ | |
916 | c = ct; \ | |
917 | d = dt; \ | |
918 | e = et; \ | |
919 | f = ft; \ | |
920 | g = gt; \ | |
921 | h = ht; \ | |
922 | \ | |
923 | return(*this); \ | |
924 | } | |
925 | ||
926 | // There is quite a lot of repetition in the code below. This is intentional. | |
927 | // The last conditional block is the normal form, and the others merely | |
928 | // consist of workarounds for various compiler deficiencies. Hopefuly, when | |
929 | // more compilers are conformant and we can retire support for those that are | |
930 | // not, we will be able to remove the clutter. This is makes the situation | |
931 | // (painfully) explicit. | |
932 | ||
933 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \ | |
934 | octonion<type> & operator /= (type const & rhs) \ | |
935 | { \ | |
936 | a /= rhs; \ | |
937 | b /= rhs; \ | |
938 | c /= rhs; \ | |
939 | d /= rhs; \ | |
940 | \ | |
941 | return(*this); \ | |
942 | } | |
943 | ||
944 | #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) | |
945 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ | |
946 | octonion<type> & operator /= (::std::complex<type> const & rhs) \ | |
947 | { \ | |
948 | using ::std::valarray; \ | |
949 | using ::std::abs; \ | |
950 | \ | |
951 | valarray<type> tr(2); \ | |
952 | \ | |
953 | tr[0] = rhs.real(); \ | |
954 | tr[1] = rhs.imag(); \ | |
955 | \ | |
956 | type mixam = static_cast<type>(1)/(abs(tr).max)(); \ | |
957 | \ | |
958 | tr *= mixam; \ | |
959 | \ | |
960 | valarray<type> tt(8); \ | |
961 | \ | |
962 | tt[0] = +a*tr[0]-b*tr[1]; \ | |
963 | tt[1] = -a*tr[1]+b*tr[0]; \ | |
964 | tt[2] = +c*tr[0]-d*tr[1]; \ | |
965 | tt[3] = +c*tr[1]+d*tr[0]; \ | |
966 | tt[4] = +e*tr[0]-f*tr[1]; \ | |
967 | tt[5] = +e*tr[1]+f*tr[0]; \ | |
968 | tt[6] = +g*tr[0]+h*tr[1]; \ | |
969 | tt[7] = +g*tr[1]+h*tr[0]; \ | |
970 | \ | |
971 | tr *= tr; \ | |
972 | \ | |
973 | tt *= (mixam/tr.sum()); \ | |
974 | \ | |
975 | a = tt[0]; \ | |
976 | b = tt[1]; \ | |
977 | c = tt[2]; \ | |
978 | d = tt[3]; \ | |
979 | e = tt[4]; \ | |
980 | f = tt[5]; \ | |
981 | g = tt[6]; \ | |
982 | h = tt[7]; \ | |
983 | \ | |
984 | return(*this); \ | |
985 | } | |
986 | #else | |
987 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ | |
988 | octonion<type> & operator /= (::std::complex<type> const & rhs) \ | |
989 | { \ | |
990 | using ::std::valarray; \ | |
991 | \ | |
992 | valarray<type> tr(2); \ | |
993 | \ | |
994 | tr[0] = rhs.real(); \ | |
995 | tr[1] = rhs.imag(); \ | |
996 | \ | |
997 | type mixam = static_cast<type>(1)/(abs(tr).max)(); \ | |
998 | \ | |
999 | tr *= mixam; \ | |
1000 | \ | |
1001 | valarray<type> tt(8); \ | |
1002 | \ | |
1003 | tt[0] = +a*tr[0]-b*tr[1]; \ | |
1004 | tt[1] = -a*tr[1]+b*tr[0]; \ | |
1005 | tt[2] = +c*tr[0]-d*tr[1]; \ | |
1006 | tt[3] = +c*tr[1]+d*tr[0]; \ | |
1007 | tt[4] = +e*tr[0]-f*tr[1]; \ | |
1008 | tt[5] = +e*tr[1]+f*tr[0]; \ | |
1009 | tt[6] = +g*tr[0]+h*tr[1]; \ | |
1010 | tt[7] = +g*tr[1]+h*tr[0]; \ | |
1011 | \ | |
1012 | tr *= tr; \ | |
1013 | \ | |
1014 | tt *= (mixam/tr.sum()); \ | |
1015 | \ | |
1016 | a = tt[0]; \ | |
1017 | b = tt[1]; \ | |
1018 | c = tt[2]; \ | |
1019 | d = tt[3]; \ | |
1020 | e = tt[4]; \ | |
1021 | f = tt[5]; \ | |
1022 | g = tt[6]; \ | |
1023 | h = tt[7]; \ | |
1024 | \ | |
1025 | return(*this); \ | |
1026 | } | |
1027 | #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ | |
1028 | ||
1029 | #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) | |
1030 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ | |
1031 | octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \ | |
1032 | { \ | |
1033 | using ::std::valarray; \ | |
1034 | using ::std::abs; \ | |
1035 | \ | |
1036 | valarray<type> tr(4); \ | |
1037 | \ | |
1038 | tr[0] = static_cast<type>(rhs.R_component_1()); \ | |
1039 | tr[1] = static_cast<type>(rhs.R_component_2()); \ | |
1040 | tr[2] = static_cast<type>(rhs.R_component_3()); \ | |
1041 | tr[3] = static_cast<type>(rhs.R_component_4()); \ | |
1042 | \ | |
1043 | type mixam = static_cast<type>(1)/(abs(tr).max)(); \ | |
1044 | \ | |
1045 | tr *= mixam; \ | |
1046 | \ | |
1047 | valarray<type> tt(8); \ | |
1048 | \ | |
1049 | tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ | |
1050 | tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ | |
1051 | tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ | |
1052 | tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ | |
1053 | tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ | |
1054 | tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ | |
1055 | tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ | |
1056 | tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ | |
1057 | \ | |
1058 | tr *= tr; \ | |
1059 | \ | |
1060 | tt *= (mixam/tr.sum()); \ | |
1061 | \ | |
1062 | a = tt[0]; \ | |
1063 | b = tt[1]; \ | |
1064 | c = tt[2]; \ | |
1065 | d = tt[3]; \ | |
1066 | e = tt[4]; \ | |
1067 | f = tt[5]; \ | |
1068 | g = tt[6]; \ | |
1069 | h = tt[7]; \ | |
1070 | \ | |
1071 | return(*this); \ | |
1072 | } | |
1073 | #else | |
1074 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ | |
1075 | octonion<type> & operator /= (::boost::math::quaternion<type> const & rhs) \ | |
1076 | { \ | |
1077 | using ::std::valarray; \ | |
1078 | \ | |
1079 | valarray<type> tr(4); \ | |
1080 | \ | |
1081 | tr[0] = static_cast<type>(rhs.R_component_1()); \ | |
1082 | tr[1] = static_cast<type>(rhs.R_component_2()); \ | |
1083 | tr[2] = static_cast<type>(rhs.R_component_3()); \ | |
1084 | tr[3] = static_cast<type>(rhs.R_component_4()); \ | |
1085 | \ | |
1086 | type mixam = static_cast<type>(1)/(abs(tr).max)(); \ | |
1087 | \ | |
1088 | tr *= mixam; \ | |
1089 | \ | |
1090 | valarray<type> tt(8); \ | |
1091 | \ | |
1092 | tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \ | |
1093 | tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \ | |
1094 | tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \ | |
1095 | tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \ | |
1096 | tt[4] = +e*tr[0]-f*tr[1]-g*tr[2]-h*tr[3]; \ | |
1097 | tt[5] = +e*tr[1]+f*tr[0]+g*tr[3]-h*tr[2]; \ | |
1098 | tt[6] = +e*tr[2]-f*tr[3]+g*tr[0]+h*tr[1]; \ | |
1099 | tt[7] = +e*tr[3]+f*tr[2]-g*tr[1]+h*tr[0]; \ | |
1100 | \ | |
1101 | tr *= tr; \ | |
1102 | \ | |
1103 | tt *= (mixam/tr.sum()); \ | |
1104 | \ | |
1105 | a = tt[0]; \ | |
1106 | b = tt[1]; \ | |
1107 | c = tt[2]; \ | |
1108 | d = tt[3]; \ | |
1109 | e = tt[4]; \ | |
1110 | f = tt[5]; \ | |
1111 | g = tt[6]; \ | |
1112 | h = tt[7]; \ | |
1113 | \ | |
1114 | return(*this); \ | |
1115 | } | |
1116 | #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ | |
1117 | ||
1118 | #if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) | |
1119 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \ | |
1120 | template<typename X> \ | |
1121 | octonion<type> & operator /= (octonion<X> const & rhs) \ | |
1122 | { \ | |
1123 | using ::std::valarray; \ | |
1124 | using ::std::abs; \ | |
1125 | \ | |
1126 | valarray<type> tr(8); \ | |
1127 | \ | |
1128 | tr[0] = static_cast<type>(rhs.R_component_1()); \ | |
1129 | tr[1] = static_cast<type>(rhs.R_component_2()); \ | |
1130 | tr[2] = static_cast<type>(rhs.R_component_3()); \ | |
1131 | tr[3] = static_cast<type>(rhs.R_component_4()); \ | |
1132 | tr[4] = static_cast<type>(rhs.R_component_5()); \ | |
1133 | tr[5] = static_cast<type>(rhs.R_component_6()); \ | |
1134 | tr[6] = static_cast<type>(rhs.R_component_7()); \ | |
1135 | tr[7] = static_cast<type>(rhs.R_component_8()); \ | |
1136 | \ | |
1137 | type mixam = static_cast<type>(1)/(abs(tr).max)(); \ | |
1138 | \ | |
1139 | tr *= mixam; \ | |
1140 | \ | |
1141 | valarray<type> tt(8); \ | |
1142 | \ | |
1143 | 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]; \ | |
1144 | 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]; \ | |
1145 | 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]; \ | |
1146 | 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]; \ | |
1147 | 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]; \ | |
1148 | 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]; \ | |
1149 | 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]; \ | |
1150 | 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]; \ | |
1151 | \ | |
1152 | tr *= tr; \ | |
1153 | \ | |
1154 | tt *= (mixam/tr.sum()); \ | |
1155 | \ | |
1156 | a = tt[0]; \ | |
1157 | b = tt[1]; \ | |
1158 | c = tt[2]; \ | |
1159 | d = tt[3]; \ | |
1160 | e = tt[4]; \ | |
1161 | f = tt[5]; \ | |
1162 | g = tt[6]; \ | |
1163 | h = tt[7]; \ | |
1164 | \ | |
1165 | return(*this); \ | |
1166 | } | |
1167 | #else | |
1168 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) \ | |
1169 | template<typename X> \ | |
1170 | octonion<type> & operator /= (octonion<X> const & rhs) \ | |
1171 | { \ | |
1172 | using ::std::valarray; \ | |
1173 | \ | |
1174 | valarray<type> tr(8); \ | |
1175 | \ | |
1176 | tr[0] = static_cast<type>(rhs.R_component_1()); \ | |
1177 | tr[1] = static_cast<type>(rhs.R_component_2()); \ | |
1178 | tr[2] = static_cast<type>(rhs.R_component_3()); \ | |
1179 | tr[3] = static_cast<type>(rhs.R_component_4()); \ | |
1180 | tr[4] = static_cast<type>(rhs.R_component_5()); \ | |
1181 | tr[5] = static_cast<type>(rhs.R_component_6()); \ | |
1182 | tr[6] = static_cast<type>(rhs.R_component_7()); \ | |
1183 | tr[7] = static_cast<type>(rhs.R_component_8()); \ | |
1184 | \ | |
1185 | type mixam = static_cast<type>(1)/(abs(tr).max)(); \ | |
1186 | \ | |
1187 | tr *= mixam; \ | |
1188 | \ | |
1189 | valarray<type> tt(8); \ | |
1190 | \ | |
1191 | 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]; \ | |
1192 | 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]; \ | |
1193 | 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]; \ | |
1194 | 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]; \ | |
1195 | 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]; \ | |
1196 | 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]; \ | |
1197 | 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]; \ | |
1198 | 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]; \ | |
1199 | \ | |
1200 | tr *= tr; \ | |
1201 | \ | |
1202 | tt *= (mixam/tr.sum()); \ | |
1203 | \ | |
1204 | a = tt[0]; \ | |
1205 | b = tt[1]; \ | |
1206 | c = tt[2]; \ | |
1207 | d = tt[3]; \ | |
1208 | e = tt[4]; \ | |
1209 | f = tt[5]; \ | |
1210 | g = tt[6]; \ | |
1211 | h = tt[7]; \ | |
1212 | \ | |
1213 | return(*this); \ | |
1214 | } | |
1215 | #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ | |
1216 | ||
1217 | ||
1218 | #define BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \ | |
1219 | BOOST_OCTONION_MEMBER_ADD_GENERATOR_1(type) \ | |
1220 | BOOST_OCTONION_MEMBER_ADD_GENERATOR_2(type) \ | |
1221 | BOOST_OCTONION_MEMBER_ADD_GENERATOR_3(type) \ | |
1222 | BOOST_OCTONION_MEMBER_ADD_GENERATOR_4(type) | |
1223 | ||
1224 | #define BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \ | |
1225 | BOOST_OCTONION_MEMBER_SUB_GENERATOR_1(type) \ | |
1226 | BOOST_OCTONION_MEMBER_SUB_GENERATOR_2(type) \ | |
1227 | BOOST_OCTONION_MEMBER_SUB_GENERATOR_3(type) \ | |
1228 | BOOST_OCTONION_MEMBER_SUB_GENERATOR_4(type) | |
1229 | ||
1230 | #define BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \ | |
1231 | BOOST_OCTONION_MEMBER_MUL_GENERATOR_1(type) \ | |
1232 | BOOST_OCTONION_MEMBER_MUL_GENERATOR_2(type) \ | |
1233 | BOOST_OCTONION_MEMBER_MUL_GENERATOR_3(type) \ | |
1234 | BOOST_OCTONION_MEMBER_MUL_GENERATOR_4(type) | |
1235 | ||
1236 | #define BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) \ | |
1237 | BOOST_OCTONION_MEMBER_DIV_GENERATOR_1(type) \ | |
1238 | BOOST_OCTONION_MEMBER_DIV_GENERATOR_2(type) \ | |
1239 | BOOST_OCTONION_MEMBER_DIV_GENERATOR_3(type) \ | |
1240 | BOOST_OCTONION_MEMBER_DIV_GENERATOR_4(type) | |
1241 | ||
1242 | #define BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(type) \ | |
1243 | BOOST_OCTONION_MEMBER_ADD_GENERATOR(type) \ | |
1244 | BOOST_OCTONION_MEMBER_SUB_GENERATOR(type) \ | |
1245 | BOOST_OCTONION_MEMBER_MUL_GENERATOR(type) \ | |
1246 | BOOST_OCTONION_MEMBER_DIV_GENERATOR(type) | |
1247 | ||
1248 | ||
1249 | template<> | |
1250 | class octonion<float> | |
1251 | { | |
1252 | public: | |
1253 | ||
1254 | typedef float value_type; | |
1255 | ||
1256 | BOOST_OCTONION_CONSTRUCTOR_GENERATOR(float) | |
1257 | ||
1258 | // UNtemplated copy constructor | |
1259 | // (this is taken care of by the compiler itself) | |
1260 | ||
1261 | // explicit copy constructors (precision-loosing converters) | |
1262 | ||
1263 | explicit octonion(octonion<double> const & a_recopier) | |
1264 | { | |
1265 | *this = detail::octonion_type_converter<float, double>(a_recopier); | |
1266 | } | |
1267 | ||
1268 | explicit octonion(octonion<long double> const & a_recopier) | |
1269 | { | |
1270 | *this = detail::octonion_type_converter<float, long double>(a_recopier); | |
1271 | } | |
1272 | ||
1273 | // destructor | |
1274 | // (this is taken care of by the compiler itself) | |
1275 | ||
1276 | // accessors | |
1277 | // | |
1278 | // Note: Like complex number, octonions do have a meaningful notion of "real part", | |
1279 | // but unlike them there is no meaningful notion of "imaginary part". | |
1280 | // Instead there is an "unreal part" which itself is an octonion, and usually | |
1281 | // nothing simpler (as opposed to the complex number case). | |
1282 | // However, for practicallity, there are accessors for the other components | |
1283 | // (these are necessary for the templated copy constructor, for instance). | |
1284 | ||
1285 | BOOST_OCTONION_ACCESSOR_GENERATOR(float) | |
1286 | ||
1287 | // assignment operators | |
1288 | ||
1289 | BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(float) | |
1290 | ||
1291 | // other assignment-related operators | |
1292 | // | |
1293 | // NOTE: Octonion multiplication is *NOT* commutative; | |
1294 | // symbolically, "q *= rhs;" means "q = q * rhs;" | |
1295 | // and "q /= rhs;" means "q = q * inverse_of(rhs);"; | |
1296 | // octonion multiplication is also *NOT* associative | |
1297 | ||
1298 | BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(float) | |
1299 | ||
1300 | ||
1301 | protected: | |
1302 | ||
1303 | BOOST_OCTONION_MEMBER_DATA_GENERATOR(float) | |
1304 | ||
1305 | ||
1306 | private: | |
1307 | ||
1308 | }; | |
1309 | ||
1310 | ||
1311 | template<> | |
1312 | class octonion<double> | |
1313 | { | |
1314 | public: | |
1315 | ||
1316 | typedef double value_type; | |
1317 | ||
1318 | BOOST_OCTONION_CONSTRUCTOR_GENERATOR(double) | |
1319 | ||
1320 | // UNtemplated copy constructor | |
1321 | // (this is taken care of by the compiler itself) | |
1322 | ||
1323 | // converting copy constructor | |
1324 | ||
1325 | explicit octonion(octonion<float> const & a_recopier) | |
1326 | { | |
1327 | *this = detail::octonion_type_converter<double, float>(a_recopier); | |
1328 | } | |
1329 | ||
1330 | // explicit copy constructors (precision-loosing converters) | |
1331 | ||
1332 | explicit octonion(octonion<long double> const & a_recopier) | |
1333 | { | |
1334 | *this = detail::octonion_type_converter<double, long double>(a_recopier); | |
1335 | } | |
1336 | ||
1337 | // destructor | |
1338 | // (this is taken care of by the compiler itself) | |
1339 | ||
1340 | // accessors | |
1341 | // | |
1342 | // Note: Like complex number, octonions do have a meaningful notion of "real part", | |
1343 | // but unlike them there is no meaningful notion of "imaginary part". | |
1344 | // Instead there is an "unreal part" which itself is an octonion, and usually | |
1345 | // nothing simpler (as opposed to the complex number case). | |
1346 | // However, for practicallity, there are accessors for the other components | |
1347 | // (these are necessary for the templated copy constructor, for instance). | |
1348 | ||
1349 | BOOST_OCTONION_ACCESSOR_GENERATOR(double) | |
1350 | ||
1351 | // assignment operators | |
1352 | ||
1353 | BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(double) | |
1354 | ||
1355 | // other assignment-related operators | |
1356 | // | |
1357 | // NOTE: Octonion multiplication is *NOT* commutative; | |
1358 | // symbolically, "q *= rhs;" means "q = q * rhs;" | |
1359 | // and "q /= rhs;" means "q = q * inverse_of(rhs);"; | |
1360 | // octonion multiplication is also *NOT* associative | |
1361 | ||
1362 | BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(double) | |
1363 | ||
1364 | ||
1365 | protected: | |
1366 | ||
1367 | BOOST_OCTONION_MEMBER_DATA_GENERATOR(double) | |
1368 | ||
1369 | ||
1370 | private: | |
1371 | ||
1372 | }; | |
1373 | ||
1374 | ||
1375 | template<> | |
1376 | class octonion<long double> | |
1377 | { | |
1378 | public: | |
1379 | ||
1380 | typedef long double value_type; | |
1381 | ||
1382 | BOOST_OCTONION_CONSTRUCTOR_GENERATOR(long double) | |
1383 | ||
1384 | // UNtemplated copy constructor | |
1385 | // (this is taken care of by the compiler itself) | |
1386 | ||
1387 | // converting copy constructor | |
1388 | ||
1389 | explicit octonion(octonion<float> const & a_recopier) | |
1390 | { | |
1391 | *this = detail::octonion_type_converter<long double, float>(a_recopier); | |
1392 | } | |
1393 | ||
1394 | ||
1395 | explicit octonion(octonion<double> const & a_recopier) | |
1396 | { | |
1397 | *this = detail::octonion_type_converter<long double, double>(a_recopier); | |
1398 | } | |
1399 | ||
1400 | ||
1401 | // destructor | |
1402 | // (this is taken care of by the compiler itself) | |
1403 | ||
1404 | // accessors | |
1405 | // | |
1406 | // Note: Like complex number, octonions do have a meaningful notion of "real part", | |
1407 | // but unlike them there is no meaningful notion of "imaginary part". | |
1408 | // Instead there is an "unreal part" which itself is an octonion, and usually | |
1409 | // nothing simpler (as opposed to the complex number case). | |
1410 | // However, for practicallity, there are accessors for the other components | |
1411 | // (these are necessary for the templated copy constructor, for instance). | |
1412 | ||
1413 | BOOST_OCTONION_ACCESSOR_GENERATOR(long double) | |
1414 | ||
1415 | // assignment operators | |
1416 | ||
1417 | BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR(long double) | |
1418 | ||
1419 | // other assignment-related operators | |
1420 | // | |
1421 | // NOTE: Octonion multiplication is *NOT* commutative; | |
1422 | // symbolically, "q *= rhs;" means "q = q * rhs;" | |
1423 | // and "q /= rhs;" means "q = q * inverse_of(rhs);"; | |
1424 | // octonion multiplication is also *NOT* associative | |
1425 | ||
1426 | BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR(long double) | |
1427 | ||
1428 | ||
1429 | protected: | |
1430 | ||
1431 | BOOST_OCTONION_MEMBER_DATA_GENERATOR(long double) | |
1432 | ||
1433 | ||
1434 | private: | |
1435 | ||
1436 | }; | |
1437 | ||
1438 | ||
1439 | #undef BOOST_OCTONION_CONSTRUCTOR_GENERATOR | |
1440 | ||
1441 | #undef BOOST_OCTONION_MEMBER_ALGEBRAIC_GENERATOR | |
1442 | ||
1443 | #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR | |
1444 | #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR | |
1445 | #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR | |
1446 | #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR | |
1447 | ||
1448 | #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_1 | |
1449 | #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_2 | |
1450 | #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_3 | |
1451 | #undef BOOST_OCTONION_MEMBER_ADD_GENERATOR_4 | |
1452 | #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_1 | |
1453 | #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_2 | |
1454 | #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_3 | |
1455 | #undef BOOST_OCTONION_MEMBER_SUB_GENERATOR_4 | |
1456 | #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_1 | |
1457 | #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_2 | |
1458 | #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_3 | |
1459 | #undef BOOST_OCTONION_MEMBER_MUL_GENERATOR_4 | |
1460 | #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_1 | |
1461 | #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_2 | |
1462 | #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_3 | |
1463 | #undef BOOST_OCTONION_MEMBER_DIV_GENERATOR_4 | |
1464 | ||
1465 | ||
1466 | #undef BOOST_OCTONION_MEMBER_DATA_GENERATOR | |
1467 | ||
1468 | #undef BOOST_OCTONION_MEMBER_ASSIGNMENT_GENERATOR | |
1469 | ||
1470 | #undef BOOST_OCTONION_ACCESSOR_GENERATOR | |
1471 | ||
1472 | ||
1473 | // operators | |
1474 | ||
1475 | #define BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) \ | |
1476 | { \ | |
1477 | octonion<T> res(lhs); \ | |
1478 | res op##= rhs; \ | |
1479 | return(res); \ | |
1480 | } | |
1481 | ||
1482 | #define BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \ | |
1483 | template<typename T> \ | |
1484 | inline octonion<T> operator op (T const & lhs, octonion<T> const & rhs) \ | |
1485 | BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) | |
1486 | ||
1487 | #define BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \ | |
1488 | template<typename T> \ | |
1489 | inline octonion<T> operator op (octonion<T> const & lhs, T const & rhs) \ | |
1490 | BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) | |
1491 | ||
1492 | #define BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \ | |
1493 | template<typename T> \ | |
1494 | inline octonion<T> operator op (::std::complex<T> const & lhs, octonion<T> const & rhs) \ | |
1495 | BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) | |
1496 | ||
1497 | #define BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \ | |
1498 | template<typename T> \ | |
1499 | inline octonion<T> operator op (octonion<T> const & lhs, ::std::complex<T> const & rhs) \ | |
1500 | BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) | |
1501 | ||
1502 | #define BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \ | |
1503 | template<typename T> \ | |
1504 | inline octonion<T> operator op (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) \ | |
1505 | BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) | |
1506 | ||
1507 | #define BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \ | |
1508 | template<typename T> \ | |
1509 | inline octonion<T> operator op (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) \ | |
1510 | BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) | |
1511 | ||
1512 | #define BOOST_OCTONION_OPERATOR_GENERATOR_4(op) \ | |
1513 | template<typename T> \ | |
1514 | inline octonion<T> operator op (octonion<T> const & lhs, octonion<T> const & rhs) \ | |
1515 | BOOST_OCTONION_OPERATOR_GENERATOR_BODY(op) | |
1516 | ||
1517 | #define BOOST_OCTONION_OPERATOR_GENERATOR(op) \ | |
1518 | BOOST_OCTONION_OPERATOR_GENERATOR_1_L(op) \ | |
1519 | BOOST_OCTONION_OPERATOR_GENERATOR_1_R(op) \ | |
1520 | BOOST_OCTONION_OPERATOR_GENERATOR_2_L(op) \ | |
1521 | BOOST_OCTONION_OPERATOR_GENERATOR_2_R(op) \ | |
1522 | BOOST_OCTONION_OPERATOR_GENERATOR_3_L(op) \ | |
1523 | BOOST_OCTONION_OPERATOR_GENERATOR_3_R(op) \ | |
1524 | BOOST_OCTONION_OPERATOR_GENERATOR_4(op) | |
1525 | ||
1526 | ||
1527 | BOOST_OCTONION_OPERATOR_GENERATOR(+) | |
1528 | BOOST_OCTONION_OPERATOR_GENERATOR(-) | |
1529 | BOOST_OCTONION_OPERATOR_GENERATOR(*) | |
1530 | BOOST_OCTONION_OPERATOR_GENERATOR(/) | |
1531 | ||
1532 | ||
1533 | #undef BOOST_OCTONION_OPERATOR_GENERATOR | |
1534 | ||
1535 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_L | |
1536 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_1_R | |
1537 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_L | |
1538 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_2_R | |
1539 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_L | |
1540 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_3_R | |
1541 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_4 | |
1542 | ||
1543 | #undef BOOST_OCTONION_OPERATOR_GENERATOR_BODY | |
1544 | ||
1545 | ||
1546 | template<typename T> | |
1547 | inline octonion<T> operator + (octonion<T> const & o) | |
1548 | { | |
1549 | return(o); | |
1550 | } | |
1551 | ||
1552 | ||
1553 | template<typename T> | |
1554 | inline octonion<T> operator - (octonion<T> const & o) | |
1555 | { | |
1556 | 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())); | |
1557 | } | |
1558 | ||
1559 | ||
1560 | template<typename T> | |
1561 | inline bool operator == (T const & lhs, octonion<T> const & rhs) | |
1562 | { | |
1563 | return( | |
1564 | (rhs.R_component_1() == lhs)&& | |
1565 | (rhs.R_component_2() == static_cast<T>(0))&& | |
1566 | (rhs.R_component_3() == static_cast<T>(0))&& | |
1567 | (rhs.R_component_4() == static_cast<T>(0))&& | |
1568 | (rhs.R_component_5() == static_cast<T>(0))&& | |
1569 | (rhs.R_component_6() == static_cast<T>(0))&& | |
1570 | (rhs.R_component_7() == static_cast<T>(0))&& | |
1571 | (rhs.R_component_8() == static_cast<T>(0)) | |
1572 | ); | |
1573 | } | |
1574 | ||
1575 | ||
1576 | template<typename T> | |
1577 | inline bool operator == (octonion<T> const & lhs, T const & rhs) | |
1578 | { | |
1579 | return( | |
1580 | (lhs.R_component_1() == rhs)&& | |
1581 | (lhs.R_component_2() == static_cast<T>(0))&& | |
1582 | (lhs.R_component_3() == static_cast<T>(0))&& | |
1583 | (lhs.R_component_4() == static_cast<T>(0))&& | |
1584 | (lhs.R_component_5() == static_cast<T>(0))&& | |
1585 | (lhs.R_component_6() == static_cast<T>(0))&& | |
1586 | (lhs.R_component_7() == static_cast<T>(0))&& | |
1587 | (lhs.R_component_8() == static_cast<T>(0)) | |
1588 | ); | |
1589 | } | |
1590 | ||
1591 | ||
1592 | template<typename T> | |
1593 | inline bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs) | |
1594 | { | |
1595 | return( | |
1596 | (rhs.R_component_1() == lhs.real())&& | |
1597 | (rhs.R_component_2() == lhs.imag())&& | |
1598 | (rhs.R_component_3() == static_cast<T>(0))&& | |
1599 | (rhs.R_component_4() == static_cast<T>(0))&& | |
1600 | (rhs.R_component_5() == static_cast<T>(0))&& | |
1601 | (rhs.R_component_6() == static_cast<T>(0))&& | |
1602 | (rhs.R_component_7() == static_cast<T>(0))&& | |
1603 | (rhs.R_component_8() == static_cast<T>(0)) | |
1604 | ); | |
1605 | } | |
1606 | ||
1607 | ||
1608 | template<typename T> | |
1609 | inline bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs) | |
1610 | { | |
1611 | return( | |
1612 | (lhs.R_component_1() == rhs.real())&& | |
1613 | (lhs.R_component_2() == rhs.imag())&& | |
1614 | (lhs.R_component_3() == static_cast<T>(0))&& | |
1615 | (lhs.R_component_4() == static_cast<T>(0))&& | |
1616 | (lhs.R_component_5() == static_cast<T>(0))&& | |
1617 | (lhs.R_component_6() == static_cast<T>(0))&& | |
1618 | (lhs.R_component_7() == static_cast<T>(0))&& | |
1619 | (lhs.R_component_8() == static_cast<T>(0)) | |
1620 | ); | |
1621 | } | |
1622 | ||
1623 | ||
1624 | template<typename T> | |
1625 | inline bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) | |
1626 | { | |
1627 | return( | |
1628 | (rhs.R_component_1() == lhs.R_component_1())&& | |
1629 | (rhs.R_component_2() == lhs.R_component_2())&& | |
1630 | (rhs.R_component_3() == lhs.R_component_3())&& | |
1631 | (rhs.R_component_4() == lhs.R_component_4())&& | |
1632 | (rhs.R_component_5() == static_cast<T>(0))&& | |
1633 | (rhs.R_component_6() == static_cast<T>(0))&& | |
1634 | (rhs.R_component_7() == static_cast<T>(0))&& | |
1635 | (rhs.R_component_8() == static_cast<T>(0)) | |
1636 | ); | |
1637 | } | |
1638 | ||
1639 | ||
1640 | template<typename T> | |
1641 | inline bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) | |
1642 | { | |
1643 | return( | |
1644 | (lhs.R_component_1() == rhs.R_component_1())&& | |
1645 | (lhs.R_component_2() == rhs.R_component_2())&& | |
1646 | (lhs.R_component_3() == rhs.R_component_3())&& | |
1647 | (lhs.R_component_4() == rhs.R_component_4())&& | |
1648 | (lhs.R_component_5() == static_cast<T>(0))&& | |
1649 | (lhs.R_component_6() == static_cast<T>(0))&& | |
1650 | (lhs.R_component_7() == static_cast<T>(0))&& | |
1651 | (lhs.R_component_8() == static_cast<T>(0)) | |
1652 | ); | |
1653 | } | |
1654 | ||
1655 | ||
1656 | template<typename T> | |
1657 | inline bool operator == (octonion<T> const & lhs, octonion<T> const & rhs) | |
1658 | { | |
1659 | return( | |
1660 | (rhs.R_component_1() == lhs.R_component_1())&& | |
1661 | (rhs.R_component_2() == lhs.R_component_2())&& | |
1662 | (rhs.R_component_3() == lhs.R_component_3())&& | |
1663 | (rhs.R_component_4() == lhs.R_component_4())&& | |
1664 | (rhs.R_component_5() == lhs.R_component_5())&& | |
1665 | (rhs.R_component_6() == lhs.R_component_6())&& | |
1666 | (rhs.R_component_7() == lhs.R_component_7())&& | |
1667 | (rhs.R_component_8() == lhs.R_component_8()) | |
1668 | ); | |
1669 | } | |
1670 | ||
1671 | ||
1672 | #define BOOST_OCTONION_NOT_EQUAL_GENERATOR \ | |
1673 | { \ | |
1674 | return(!(lhs == rhs)); \ | |
1675 | } | |
1676 | ||
1677 | template<typename T> | |
1678 | inline bool operator != (T const & lhs, octonion<T> const & rhs) | |
1679 | BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1680 | ||
1681 | template<typename T> | |
1682 | inline bool operator != (octonion<T> const & lhs, T const & rhs) | |
1683 | BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1684 | ||
1685 | template<typename T> | |
1686 | inline bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs) | |
1687 | BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1688 | ||
1689 | template<typename T> | |
1690 | inline bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs) | |
1691 | BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1692 | ||
1693 | template<typename T> | |
1694 | inline bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs) | |
1695 | BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1696 | ||
1697 | template<typename T> | |
1698 | inline bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs) | |
1699 | BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1700 | ||
1701 | template<typename T> | |
1702 | inline bool operator != (octonion<T> const & lhs, octonion<T> const & rhs) | |
1703 | BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1704 | ||
1705 | #undef BOOST_OCTONION_NOT_EQUAL_GENERATOR | |
1706 | ||
1707 | ||
1708 | // Note: the default values in the constructors of the complex and quaternions make for | |
1709 | // a very complex and ambiguous situation; we have made choices to disambiguate. | |
1710 | template<typename T, typename charT, class traits> | |
1711 | ::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is, | |
1712 | octonion<T> & o) | |
1713 | { | |
1714 | #ifdef BOOST_NO_STD_LOCALE | |
1715 | #else | |
1716 | const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc()); | |
1717 | #endif /* BOOST_NO_STD_LOCALE */ | |
1718 | ||
1719 | T a = T(); | |
1720 | T b = T(); | |
1721 | T c = T(); | |
1722 | T d = T(); | |
1723 | T e = T(); | |
1724 | T f = T(); | |
1725 | T g = T(); | |
1726 | T h = T(); | |
1727 | ||
1728 | ::std::complex<T> u = ::std::complex<T>(); | |
1729 | ::std::complex<T> v = ::std::complex<T>(); | |
1730 | ::std::complex<T> x = ::std::complex<T>(); | |
1731 | ::std::complex<T> y = ::std::complex<T>(); | |
1732 | ||
1733 | ::boost::math::quaternion<T> p = ::boost::math::quaternion<T>(); | |
1734 | ::boost::math::quaternion<T> q = ::boost::math::quaternion<T>(); | |
1735 | ||
1736 | charT ch = charT(); | |
1737 | char cc; | |
1738 | ||
1739 | is >> ch; // get the first lexeme | |
1740 | ||
1741 | if (!is.good()) goto finish; | |
1742 | ||
1743 | #ifdef BOOST_NO_STD_LOCALE | |
1744 | cc = ch; | |
1745 | #else | |
1746 | cc = ct.narrow(ch, char()); | |
1747 | #endif /* BOOST_NO_STD_LOCALE */ | |
1748 | ||
1749 | if (cc == '(') // read "(" | |
1750 | { | |
1751 | is >> ch; // get the second lexeme | |
1752 | ||
1753 | if (!is.good()) goto finish; | |
1754 | ||
1755 | #ifdef BOOST_NO_STD_LOCALE | |
1756 | cc = ch; | |
1757 | #else | |
1758 | cc = ct.narrow(ch, char()); | |
1759 | #endif /* BOOST_NO_STD_LOCALE */ | |
1760 | ||
1761 | if (cc == '(') // read "((" | |
1762 | { | |
1763 | is >> ch; // get the third lexeme | |
1764 | ||
1765 | if (!is.good()) goto finish; | |
1766 | ||
1767 | #ifdef BOOST_NO_STD_LOCALE | |
1768 | cc = ch; | |
1769 | #else | |
1770 | cc = ct.narrow(ch, char()); | |
1771 | #endif /* BOOST_NO_STD_LOCALE */ | |
1772 | ||
1773 | if (cc == '(') // read "(((" | |
1774 | { | |
1775 | is.putback(ch); | |
1776 | ||
1777 | is >> u; // read "((u" | |
1778 | ||
1779 | if (!is.good()) goto finish; | |
1780 | ||
1781 | is >> ch; // get the next lexeme | |
1782 | ||
1783 | if (!is.good()) goto finish; | |
1784 | ||
1785 | #ifdef BOOST_NO_STD_LOCALE | |
1786 | cc = ch; | |
1787 | #else | |
1788 | cc = ct.narrow(ch, char()); | |
1789 | #endif /* BOOST_NO_STD_LOCALE */ | |
1790 | ||
1791 | if (cc == ')') // read "((u)" | |
1792 | { | |
1793 | is >> ch; // get the next lexeme | |
1794 | ||
1795 | if (!is.good()) goto finish; | |
1796 | ||
1797 | #ifdef BOOST_NO_STD_LOCALE | |
1798 | cc = ch; | |
1799 | #else | |
1800 | cc = ct.narrow(ch, char()); | |
1801 | #endif /* BOOST_NO_STD_LOCALE */ | |
1802 | ||
1803 | if (cc == ')') // format: (((a))), (((a,b))) | |
1804 | { | |
1805 | o = octonion<T>(u); | |
1806 | } | |
1807 | else if (cc == ',') // read "((u)," | |
1808 | { | |
1809 | p = ::boost::math::quaternion<T>(u); | |
1810 | ||
1811 | is >> q; // read "((u),q" | |
1812 | ||
1813 | if (!is.good()) goto finish; | |
1814 | ||
1815 | is >> ch; // get the next lexeme | |
1816 | ||
1817 | if (!is.good()) goto finish; | |
1818 | ||
1819 | #ifdef BOOST_NO_STD_LOCALE | |
1820 | cc = ch; | |
1821 | #else | |
1822 | cc = ct.narrow(ch, char()); | |
1823 | #endif /* BOOST_NO_STD_LOCALE */ | |
1824 | ||
1825 | if (cc == ')') // format: (((a)),q), (((a,b)),q) | |
1826 | { | |
1827 | o = octonion<T>(p,q); | |
1828 | } | |
1829 | else // error | |
1830 | { | |
1831 | is.setstate(::std::ios_base::failbit); | |
1832 | } | |
1833 | } | |
1834 | else // error | |
1835 | { | |
1836 | is.setstate(::std::ios_base::failbit); | |
1837 | } | |
1838 | } | |
1839 | else if (cc ==',') // read "((u," | |
1840 | { | |
1841 | is >> v; // read "((u,v" | |
1842 | ||
1843 | if (!is.good()) goto finish; | |
1844 | ||
1845 | is >> ch; // get the next lexeme | |
1846 | ||
1847 | if (!is.good()) goto finish; | |
1848 | ||
1849 | #ifdef BOOST_NO_STD_LOCALE | |
1850 | cc = ch; | |
1851 | #else | |
1852 | cc = ct.narrow(ch, char()); | |
1853 | #endif /* BOOST_NO_STD_LOCALE */ | |
1854 | ||
1855 | if (cc == ')') // read "((u,v)" | |
1856 | { | |
1857 | p = ::boost::math::quaternion<T>(u,v); | |
1858 | ||
1859 | is >> ch; // get the next lexeme | |
1860 | ||
1861 | if (!is.good()) goto finish; | |
1862 | ||
1863 | #ifdef BOOST_NO_STD_LOCALE | |
1864 | cc = ch; | |
1865 | #else | |
1866 | cc = ct.narrow(ch, char()); | |
1867 | #endif /* BOOST_NO_STD_LOCALE */ | |
1868 | ||
1869 | if (cc == ')') // format: (((a),v)), (((a,b),v)) | |
1870 | { | |
1871 | o = octonion<T>(p); | |
1872 | } | |
1873 | else if (cc == ',') // read "((u,v)," | |
1874 | { | |
1875 | is >> q; // read "(p,q" | |
1876 | ||
1877 | if (!is.good()) goto finish; | |
1878 | ||
1879 | is >> ch; // get the next lexeme | |
1880 | ||
1881 | if (!is.good()) goto finish; | |
1882 | ||
1883 | #ifdef BOOST_NO_STD_LOCALE | |
1884 | cc = ch; | |
1885 | #else | |
1886 | cc = ct.narrow(ch, char()); | |
1887 | #endif /* BOOST_NO_STD_LOCALE */ | |
1888 | ||
1889 | if (cc == ')') // format: (((a),v),q), (((a,b),v),q) | |
1890 | { | |
1891 | o = octonion<T>(p,q); | |
1892 | } | |
1893 | else // error | |
1894 | { | |
1895 | is.setstate(::std::ios_base::failbit); | |
1896 | } | |
1897 | } | |
1898 | else // error | |
1899 | { | |
1900 | is.setstate(::std::ios_base::failbit); | |
1901 | } | |
1902 | } | |
1903 | else // error | |
1904 | { | |
1905 | is.setstate(::std::ios_base::failbit); | |
1906 | } | |
1907 | } | |
1908 | else // error | |
1909 | { | |
1910 | is.setstate(::std::ios_base::failbit); | |
1911 | } | |
1912 | } | |
1913 | else // read "((a" | |
1914 | { | |
1915 | is.putback(ch); | |
1916 | ||
1917 | is >> a; // we extract the first component | |
1918 | ||
1919 | if (!is.good()) goto finish; | |
1920 | ||
1921 | is >> ch; // get the next lexeme | |
1922 | ||
1923 | if (!is.good()) goto finish; | |
1924 | ||
1925 | #ifdef BOOST_NO_STD_LOCALE | |
1926 | cc = ch; | |
1927 | #else | |
1928 | cc = ct.narrow(ch, char()); | |
1929 | #endif /* BOOST_NO_STD_LOCALE */ | |
1930 | ||
1931 | if (cc == ')') // read "((a)" | |
1932 | { | |
1933 | is >> ch; // get the next lexeme | |
1934 | ||
1935 | if (!is.good()) goto finish; | |
1936 | ||
1937 | #ifdef BOOST_NO_STD_LOCALE | |
1938 | cc = ch; | |
1939 | #else | |
1940 | cc = ct.narrow(ch, char()); | |
1941 | #endif /* BOOST_NO_STD_LOCALE */ | |
1942 | ||
1943 | if (cc == ')') // read "((a))" | |
1944 | { | |
1945 | o = octonion<T>(a); | |
1946 | } | |
1947 | else if (cc == ',') // read "((a)," | |
1948 | { | |
1949 | is >> ch; // get the next lexeme | |
1950 | ||
1951 | if (!is.good()) goto finish; | |
1952 | ||
1953 | #ifdef BOOST_NO_STD_LOCALE | |
1954 | cc = ch; | |
1955 | #else | |
1956 | cc = ct.narrow(ch, char()); | |
1957 | #endif /* BOOST_NO_STD_LOCALE */ | |
1958 | ||
1959 | if (cc == '(') // read "((a),(" | |
1960 | { | |
1961 | is >> ch; // get the next lexeme | |
1962 | ||
1963 | if (!is.good()) goto finish; | |
1964 | ||
1965 | #ifdef BOOST_NO_STD_LOCALE | |
1966 | cc = ch; | |
1967 | #else | |
1968 | cc = ct.narrow(ch, char()); | |
1969 | #endif /* BOOST_NO_STD_LOCALE */ | |
1970 | ||
1971 | if (cc == '(') // read "((a),((" | |
1972 | { | |
1973 | is.putback(ch); | |
1974 | ||
1975 | is.putback(ch); // we backtrack twice, with the same value! | |
1976 | ||
1977 | is >> q; // read "((a),q" | |
1978 | ||
1979 | if (!is.good()) goto finish; | |
1980 | ||
1981 | is >> ch; // get the next lexeme | |
1982 | ||
1983 | if (!is.good()) goto finish; | |
1984 | ||
1985 | #ifdef BOOST_NO_STD_LOCALE | |
1986 | cc = ch; | |
1987 | #else | |
1988 | cc = ct.narrow(ch, char()); | |
1989 | #endif /* BOOST_NO_STD_LOCALE */ | |
1990 | ||
1991 | if (cc == ')') // read "((a),q)" | |
1992 | { | |
1993 | p = ::boost::math::quaternion<T>(a); | |
1994 | ||
1995 | o = octonion<T>(p,q); | |
1996 | } | |
1997 | else // error | |
1998 | { | |
1999 | is.setstate(::std::ios_base::failbit); | |
2000 | } | |
2001 | } | |
2002 | else // read "((a),(c" or "((a),(e" | |
2003 | { | |
2004 | is.putback(ch); | |
2005 | ||
2006 | is >> c; | |
2007 | ||
2008 | if (!is.good()) goto finish; | |
2009 | ||
2010 | is >> ch; // get the next lexeme | |
2011 | ||
2012 | if (!is.good()) goto finish; | |
2013 | ||
2014 | #ifdef BOOST_NO_STD_LOCALE | |
2015 | cc = ch; | |
2016 | #else | |
2017 | cc = ct.narrow(ch, char()); | |
2018 | #endif /* BOOST_NO_STD_LOCALE */ | |
2019 | ||
2020 | if (cc == ')') // read "((a),(c)" (ambiguity resolution) | |
2021 | { | |
2022 | is >> ch; // get the next lexeme | |
2023 | ||
2024 | if (!is.good()) goto finish; | |
2025 | ||
2026 | #ifdef BOOST_NO_STD_LOCALE | |
2027 | cc = ch; | |
2028 | #else | |
2029 | cc = ct.narrow(ch, char()); | |
2030 | #endif /* BOOST_NO_STD_LOCALE */ | |
2031 | ||
2032 | if (cc == ')') // read "((a),(c))" | |
2033 | { | |
2034 | o = octonion<T>(a,b,c); | |
2035 | } | |
2036 | else if (cc == ',') // read "((a),(c)," | |
2037 | { | |
2038 | u = ::std::complex<T>(a); | |
2039 | ||
2040 | v = ::std::complex<T>(c); | |
2041 | ||
2042 | is >> x; // read "((a),(c),x" | |
2043 | ||
2044 | if (!is.good()) goto finish; | |
2045 | ||
2046 | is >> ch; // get the next lexeme | |
2047 | ||
2048 | if (!is.good()) goto finish; | |
2049 | ||
2050 | #ifdef BOOST_NO_STD_LOCALE | |
2051 | cc = ch; | |
2052 | #else | |
2053 | cc = ct.narrow(ch, char()); | |
2054 | #endif /* BOOST_NO_STD_LOCALE */ | |
2055 | ||
2056 | if (cc == ')') // read "((a),(c),x)" | |
2057 | { | |
2058 | o = octonion<T>(u,v,x); | |
2059 | } | |
2060 | else if (cc == ',') // read "((a),(c),x," | |
2061 | { | |
2062 | is >> y; // read "((a),(c),x,y" | |
2063 | ||
2064 | if (!is.good()) goto finish; | |
2065 | ||
2066 | is >> ch; // get the next lexeme | |
2067 | ||
2068 | if (!is.good()) goto finish; | |
2069 | ||
2070 | #ifdef BOOST_NO_STD_LOCALE | |
2071 | cc = ch; | |
2072 | #else | |
2073 | cc = ct.narrow(ch, char()); | |
2074 | #endif /* BOOST_NO_STD_LOCALE */ | |
2075 | ||
2076 | if (cc == ')') // read "((a),(c),x,y)" | |
2077 | { | |
2078 | o = octonion<T>(u,v,x,y); | |
2079 | } | |
2080 | else // error | |
2081 | { | |
2082 | is.setstate(::std::ios_base::failbit); | |
2083 | } | |
2084 | } | |
2085 | else // error | |
2086 | { | |
2087 | is.setstate(::std::ios_base::failbit); | |
2088 | } | |
2089 | } | |
2090 | else // error | |
2091 | { | |
2092 | is.setstate(::std::ios_base::failbit); | |
2093 | } | |
2094 | } | |
2095 | else if (cc == ',') // read "((a),(c," or "((a),(e," | |
2096 | { | |
2097 | is >> ch; // get the next lexeme | |
2098 | ||
2099 | if (!is.good()) goto finish; | |
2100 | ||
2101 | #ifdef BOOST_NO_STD_LOCALE | |
2102 | cc = ch; | |
2103 | #else | |
2104 | cc = ct.narrow(ch, char()); | |
2105 | #endif /* BOOST_NO_STD_LOCALE */ | |
2106 | ||
2107 | if (cc == '(') // read "((a),(e,(" (ambiguity resolution) | |
2108 | { | |
2109 | p = ::boost::math::quaternion<T>(a); | |
2110 | ||
2111 | x = ::std::complex<T>(c); // "c" was actually "e" | |
2112 | ||
2113 | is.putback(ch); // we can only backtrace once | |
2114 | ||
2115 | is >> y; // read "((a),(e,y" | |
2116 | ||
2117 | if (!is.good()) goto finish; | |
2118 | ||
2119 | is >> ch; // get the next lexeme | |
2120 | ||
2121 | #ifdef BOOST_NO_STD_LOCALE | |
2122 | cc = ch; | |
2123 | #else | |
2124 | cc = ct.narrow(ch, char()); | |
2125 | #endif /* BOOST_NO_STD_LOCALE */ | |
2126 | ||
2127 | if (cc == ')') // read "((a),(e,y)" | |
2128 | { | |
2129 | q = ::boost::math::quaternion<T>(x,y); | |
2130 | ||
2131 | is >> ch; // get the next lexeme | |
2132 | ||
2133 | #ifdef BOOST_NO_STD_LOCALE | |
2134 | cc = ch; | |
2135 | #else | |
2136 | cc = ct.narrow(ch, char()); | |
2137 | #endif /* BOOST_NO_STD_LOCALE */ | |
2138 | ||
2139 | if (cc == ')') // read "((a),(e,y))" | |
2140 | { | |
2141 | o = octonion<T>(p,q); | |
2142 | } | |
2143 | else // error | |
2144 | { | |
2145 | is.setstate(::std::ios_base::failbit); | |
2146 | } | |
2147 | } | |
2148 | else // error | |
2149 | { | |
2150 | is.setstate(::std::ios_base::failbit); | |
2151 | } | |
2152 | } | |
2153 | else // read "((a),(c,d" or "((a),(e,f" | |
2154 | { | |
2155 | is.putback(ch); | |
2156 | ||
2157 | is >> d; | |
2158 | ||
2159 | if (!is.good()) goto finish; | |
2160 | ||
2161 | is >> ch; // get the next lexeme | |
2162 | ||
2163 | if (!is.good()) goto finish; | |
2164 | ||
2165 | #ifdef BOOST_NO_STD_LOCALE | |
2166 | cc = ch; | |
2167 | #else | |
2168 | cc = ct.narrow(ch, char()); | |
2169 | #endif /* BOOST_NO_STD_LOCALE */ | |
2170 | ||
2171 | if (cc == ')') // read "((a),(c,d)" (ambiguity resolution) | |
2172 | { | |
2173 | is >> ch; // get the next lexeme | |
2174 | ||
2175 | if (!is.good()) goto finish; | |
2176 | ||
2177 | #ifdef BOOST_NO_STD_LOCALE | |
2178 | cc = ch; | |
2179 | #else | |
2180 | cc = ct.narrow(ch, char()); | |
2181 | #endif /* BOOST_NO_STD_LOCALE */ | |
2182 | ||
2183 | if (cc == ')') // read "((a),(c,d))" | |
2184 | { | |
2185 | o = octonion<T>(a,b,c,d); | |
2186 | } | |
2187 | else if (cc == ',') // read "((a),(c,d)," | |
2188 | { | |
2189 | u = ::std::complex<T>(a); | |
2190 | ||
2191 | v = ::std::complex<T>(c,d); | |
2192 | ||
2193 | is >> x; // read "((a),(c,d),x" | |
2194 | ||
2195 | if (!is.good()) goto finish; | |
2196 | ||
2197 | is >> ch; // get the next lexeme | |
2198 | ||
2199 | if (!is.good()) goto finish; | |
2200 | ||
2201 | #ifdef BOOST_NO_STD_LOCALE | |
2202 | cc = ch; | |
2203 | #else | |
2204 | cc = ct.narrow(ch, char()); | |
2205 | #endif /* BOOST_NO_STD_LOCALE */ | |
2206 | ||
2207 | if (cc == ')') // read "((a),(c,d),x)" | |
2208 | { | |
2209 | o = octonion<T>(u,v,x); | |
2210 | } | |
2211 | else if (cc == ',') // read "((a),(c,d),x," | |
2212 | { | |
2213 | is >> y; // read "((a),(c,d),x,y" | |
2214 | ||
2215 | if (!is.good()) goto finish; | |
2216 | ||
2217 | is >> ch; // get the next lexeme | |
2218 | ||
2219 | if (!is.good()) goto finish; | |
2220 | ||
2221 | #ifdef BOOST_NO_STD_LOCALE | |
2222 | cc = ch; | |
2223 | #else | |
2224 | cc = ct.narrow(ch, char()); | |
2225 | #endif /* BOOST_NO_STD_LOCALE */ | |
2226 | ||
2227 | if (cc == ')') // read "((a),(c,d),x,y)" | |
2228 | { | |
2229 | o = octonion<T>(u,v,x,y); | |
2230 | } | |
2231 | else // error | |
2232 | { | |
2233 | is.setstate(::std::ios_base::failbit); | |
2234 | } | |
2235 | } | |
2236 | else // error | |
2237 | { | |
2238 | is.setstate(::std::ios_base::failbit); | |
2239 | } | |
2240 | } | |
2241 | else // error | |
2242 | { | |
2243 | is.setstate(::std::ios_base::failbit); | |
2244 | } | |
2245 | } | |
2246 | else if (cc == ',') // read "((a),(e,f," (ambiguity resolution) | |
2247 | { | |
2248 | p = ::boost::math::quaternion<T>(a); | |
2249 | ||
2250 | is >> g; // read "((a),(e,f,g" (too late to backtrack) | |
2251 | ||
2252 | if (!is.good()) goto finish; | |
2253 | ||
2254 | is >> ch; // get the next lexeme | |
2255 | ||
2256 | if (!is.good()) goto finish; | |
2257 | ||
2258 | #ifdef BOOST_NO_STD_LOCALE | |
2259 | cc = ch; | |
2260 | #else | |
2261 | cc = ct.narrow(ch, char()); | |
2262 | #endif /* BOOST_NO_STD_LOCALE */ | |
2263 | ||
2264 | if (cc == ')') // read "((a),(e,f,g)" | |
2265 | { | |
2266 | q = ::boost::math::quaternion<T>(c,d,g); // "c" was actually "e", and "d" was actually "f" | |
2267 | ||
2268 | is >> ch; // get the next lexeme | |
2269 | ||
2270 | if (!is.good()) goto finish; | |
2271 | ||
2272 | #ifdef BOOST_NO_STD_LOCALE | |
2273 | cc = ch; | |
2274 | #else | |
2275 | cc = ct.narrow(ch, char()); | |
2276 | #endif /* BOOST_NO_STD_LOCALE */ | |
2277 | ||
2278 | if (cc == ')') // read "((a),(e,f,g))" | |
2279 | { | |
2280 | o = octonion<T>(p,q); | |
2281 | } | |
2282 | else // error | |
2283 | { | |
2284 | is.setstate(::std::ios_base::failbit); | |
2285 | } | |
2286 | } | |
2287 | else if (cc == ',') // read "((a),(e,f,g," | |
2288 | { | |
2289 | is >> h; // read "((a),(e,f,g,h" | |
2290 | ||
2291 | if (!is.good()) goto finish; | |
2292 | ||
2293 | is >> ch; // get the next lexeme | |
2294 | ||
2295 | if (!is.good()) goto finish; | |
2296 | ||
2297 | #ifdef BOOST_NO_STD_LOCALE | |
2298 | cc = ch; | |
2299 | #else | |
2300 | cc = ct.narrow(ch, char()); | |
2301 | #endif /* BOOST_NO_STD_LOCALE */ | |
2302 | ||
2303 | if (cc == ')') // read "((a),(e,f,g,h)" | |
2304 | { | |
2305 | q = ::boost::math::quaternion<T>(c,d,g,h); // "c" was actually "e", and "d" was actually "f" | |
2306 | ||
2307 | is >> ch; // get the next lexeme | |
2308 | ||
2309 | if (!is.good()) goto finish; | |
2310 | ||
2311 | #ifdef BOOST_NO_STD_LOCALE | |
2312 | cc = ch; | |
2313 | #else | |
2314 | cc = ct.narrow(ch, char()); | |
2315 | #endif /* BOOST_NO_STD_LOCALE */ | |
2316 | ||
2317 | if (cc == ')') // read "((a),(e,f,g,h))" | |
2318 | { | |
2319 | o = octonion<T>(p,q); | |
2320 | } | |
2321 | else // error | |
2322 | { | |
2323 | is.setstate(::std::ios_base::failbit); | |
2324 | } | |
2325 | } | |
2326 | else // error | |
2327 | { | |
2328 | is.setstate(::std::ios_base::failbit); | |
2329 | } | |
2330 | } | |
2331 | else // error | |
2332 | { | |
2333 | is.setstate(::std::ios_base::failbit); | |
2334 | } | |
2335 | } | |
2336 | else // error | |
2337 | { | |
2338 | is.setstate(::std::ios_base::failbit); | |
2339 | } | |
2340 | } | |
2341 | } | |
2342 | else // error | |
2343 | { | |
2344 | is.setstate(::std::ios_base::failbit); | |
2345 | } | |
2346 | } | |
2347 | } | |
2348 | else // read "((a),c" (ambiguity resolution) | |
2349 | { | |
2350 | is.putback(ch); | |
2351 | ||
2352 | is >> c; // we extract the third component | |
2353 | ||
2354 | if (!is.good()) goto finish; | |
2355 | ||
2356 | is >> ch; // get the next lexeme | |
2357 | ||
2358 | if (!is.good()) goto finish; | |
2359 | ||
2360 | #ifdef BOOST_NO_STD_LOCALE | |
2361 | cc = ch; | |
2362 | #else | |
2363 | cc = ct.narrow(ch, char()); | |
2364 | #endif /* BOOST_NO_STD_LOCALE */ | |
2365 | ||
2366 | if (cc == ')') // read "((a),c)" | |
2367 | { | |
2368 | o = octonion<T>(a,b,c); | |
2369 | } | |
2370 | else if (cc == ',') // read "((a),c," | |
2371 | { | |
2372 | is >> x; // read "((a),c,x" | |
2373 | ||
2374 | if (!is.good()) goto finish; | |
2375 | ||
2376 | is >> ch; // get the next lexeme | |
2377 | ||
2378 | if (!is.good()) goto finish; | |
2379 | ||
2380 | #ifdef BOOST_NO_STD_LOCALE | |
2381 | cc = ch; | |
2382 | #else | |
2383 | cc = ct.narrow(ch, char()); | |
2384 | #endif /* BOOST_NO_STD_LOCALE */ | |
2385 | ||
2386 | if (cc == ')') // read "((a),c,x)" | |
2387 | { | |
2388 | o = octonion<T>(a,b,c,d,x.real(),x.imag()); | |
2389 | } | |
2390 | else if (cc == ',') // read "((a),c,x," | |
2391 | { | |
2392 | is >> y;if (!is.good()) goto finish; // read "((a),c,x,y" | |
2393 | ||
2394 | is >> ch; // get the next lexeme | |
2395 | ||
2396 | if (!is.good()) goto finish; | |
2397 | ||
2398 | #ifdef BOOST_NO_STD_LOCALE | |
2399 | cc = ch; | |
2400 | #else | |
2401 | cc = ct.narrow(ch, char()); | |
2402 | #endif /* BOOST_NO_STD_LOCALE */ | |
2403 | ||
2404 | if (cc == ')') // read "((a),c,x,y)" | |
2405 | { | |
2406 | o = octonion<T>(a,b,c,d,x.real(),x.imag(),y.real(),y.imag()); | |
2407 | } | |
2408 | else // error | |
2409 | { | |
2410 | is.setstate(::std::ios_base::failbit); | |
2411 | } | |
2412 | } | |
2413 | else // error | |
2414 | { | |
2415 | is.setstate(::std::ios_base::failbit); | |
2416 | } | |
2417 | } | |
2418 | else // error | |
2419 | { | |
2420 | is.setstate(::std::ios_base::failbit); | |
2421 | } | |
2422 | } | |
2423 | } | |
2424 | else // error | |
2425 | { | |
2426 | is.setstate(::std::ios_base::failbit); | |
2427 | } | |
2428 | } | |
2429 | else if (cc ==',') // read "((a," | |
2430 | { | |
2431 | is >> ch; // get the next lexeme | |
2432 | ||
2433 | if (!is.good()) goto finish; | |
2434 | ||
2435 | #ifdef BOOST_NO_STD_LOCALE | |
2436 | cc = ch; | |
2437 | #else | |
2438 | cc = ct.narrow(ch, char()); | |
2439 | #endif /* BOOST_NO_STD_LOCALE */ | |
2440 | ||
2441 | if (cc == '(') // read "((a,(" | |
2442 | { | |
2443 | u = ::std::complex<T>(a); | |
2444 | ||
2445 | is.putback(ch); // can only backtrack so much | |
2446 | ||
2447 | is >> v; // read "((a,v" | |
2448 | ||
2449 | if (!is.good()) goto finish; | |
2450 | ||
2451 | is >> ch; // get the next lexeme | |
2452 | ||
2453 | if (!is.good()) goto finish; | |
2454 | ||
2455 | #ifdef BOOST_NO_STD_LOCALE | |
2456 | cc = ch; | |
2457 | #else | |
2458 | cc = ct.narrow(ch, char()); | |
2459 | #endif /* BOOST_NO_STD_LOCALE */ | |
2460 | ||
2461 | if (cc == ')') // read "((a,v)" | |
2462 | { | |
2463 | is >> ch; // get the next lexeme | |
2464 | ||
2465 | if (!is.good()) goto finish; | |
2466 | ||
2467 | #ifdef BOOST_NO_STD_LOCALE | |
2468 | cc = ch; | |
2469 | #else | |
2470 | cc = ct.narrow(ch, char()); | |
2471 | #endif /* BOOST_NO_STD_LOCALE */ | |
2472 | ||
2473 | if (cc == ')') // read "((a,v))" | |
2474 | { | |
2475 | o = octonion<T>(u,v); | |
2476 | } | |
2477 | else if (cc == ',') // read "((a,v)," | |
2478 | { | |
2479 | p = ::boost::math::quaternion<T>(u,v); | |
2480 | ||
2481 | is >> q; // read "((a,v),q" | |
2482 | ||
2483 | if (!is.good()) goto finish; | |
2484 | ||
2485 | is >> ch; // get the next lexeme | |
2486 | ||
2487 | if (!is.good()) goto finish; | |
2488 | ||
2489 | #ifdef BOOST_NO_STD_LOCALE | |
2490 | cc = ch; | |
2491 | #else | |
2492 | cc = ct.narrow(ch, char()); | |
2493 | #endif /* BOOST_NO_STD_LOCALE */ | |
2494 | ||
2495 | if (cc == ')') // read "((a,v),q)" | |
2496 | { | |
2497 | o = octonion<T>(p,q); | |
2498 | } | |
2499 | else // error | |
2500 | { | |
2501 | is.setstate(::std::ios_base::failbit); | |
2502 | } | |
2503 | } | |
2504 | else // error | |
2505 | { | |
2506 | is.setstate(::std::ios_base::failbit); | |
2507 | } | |
2508 | } | |
2509 | else // error | |
2510 | { | |
2511 | is.setstate(::std::ios_base::failbit); | |
2512 | } | |
2513 | } | |
2514 | else | |
2515 | { | |
2516 | is.putback(ch); | |
2517 | ||
2518 | is >> b; // read "((a,b" | |
2519 | ||
2520 | if (!is.good()) goto finish; | |
2521 | ||
2522 | is >> ch; // get the next lexeme | |
2523 | ||
2524 | if (!is.good()) goto finish; | |
2525 | ||
2526 | #ifdef BOOST_NO_STD_LOCALE | |
2527 | cc = ch; | |
2528 | #else | |
2529 | cc = ct.narrow(ch, char()); | |
2530 | #endif /* BOOST_NO_STD_LOCALE */ | |
2531 | ||
2532 | if (cc == ')') // read "((a,b)" | |
2533 | { | |
2534 | is >> ch; // get the next lexeme | |
2535 | ||
2536 | if (!is.good()) goto finish; | |
2537 | ||
2538 | #ifdef BOOST_NO_STD_LOCALE | |
2539 | cc = ch; | |
2540 | #else | |
2541 | cc = ct.narrow(ch, char()); | |
2542 | #endif /* BOOST_NO_STD_LOCALE */ | |
2543 | ||
2544 | if (cc == ')') // read "((a,b))" | |
2545 | { | |
2546 | o = octonion<T>(a,b); | |
2547 | } | |
2548 | else if (cc == ',') // read "((a,b)," | |
2549 | { | |
2550 | is >> ch; // get the next lexeme | |
2551 | ||
2552 | if (!is.good()) goto finish; | |
2553 | ||
2554 | #ifdef BOOST_NO_STD_LOCALE | |
2555 | cc = ch; | |
2556 | #else | |
2557 | cc = ct.narrow(ch, char()); | |
2558 | #endif /* BOOST_NO_STD_LOCALE */ | |
2559 | ||
2560 | if (cc == '(') // read "((a,b),(" | |
2561 | { | |
2562 | is >> ch; // get the next lexeme | |
2563 | ||
2564 | if (!is.good()) goto finish; | |
2565 | ||
2566 | #ifdef BOOST_NO_STD_LOCALE | |
2567 | cc = ch; | |
2568 | #else | |
2569 | cc = ct.narrow(ch, char()); | |
2570 | #endif /* BOOST_NO_STD_LOCALE */ | |
2571 | ||
2572 | if (cc == '(') // read "((a,b),((" | |
2573 | { | |
2574 | p = ::boost::math::quaternion<T>(a,b); | |
2575 | ||
2576 | is.putback(ch); | |
2577 | ||
2578 | is.putback(ch); // we backtrack twice, with the same value | |
2579 | ||
2580 | is >> q; // read "((a,b),q" | |
2581 | ||
2582 | if (!is.good()) goto finish; | |
2583 | ||
2584 | is >> ch; // get the next lexeme | |
2585 | ||
2586 | if (!is.good()) goto finish; | |
2587 | ||
2588 | #ifdef BOOST_NO_STD_LOCALE | |
2589 | cc = ch; | |
2590 | #else | |
2591 | cc = ct.narrow(ch, char()); | |
2592 | #endif /* BOOST_NO_STD_LOCALE */ | |
2593 | ||
2594 | if (cc == ')') // read "((a,b),q)" | |
2595 | { | |
2596 | o = octonion<T>(p,q); | |
2597 | } | |
2598 | else // error | |
2599 | { | |
2600 | is.setstate(::std::ios_base::failbit); | |
2601 | } | |
2602 | } | |
2603 | else // read "((a,b),(c" or "((a,b),(e" | |
2604 | { | |
2605 | is.putback(ch); | |
2606 | ||
2607 | is >> c; | |
2608 | ||
2609 | if (!is.good()) goto finish; | |
2610 | ||
2611 | is >> ch; // get the next lexeme | |
2612 | ||
2613 | if (!is.good()) goto finish; | |
2614 | ||
2615 | #ifdef BOOST_NO_STD_LOCALE | |
2616 | cc = ch; | |
2617 | #else | |
2618 | cc = ct.narrow(ch, char()); | |
2619 | #endif /* BOOST_NO_STD_LOCALE */ | |
2620 | ||
2621 | if (cc == ')') // read "((a,b),(c)" (ambiguity resolution) | |
2622 | { | |
2623 | is >> ch; // get the next lexeme | |
2624 | ||
2625 | if (!is.good()) goto finish; | |
2626 | ||
2627 | #ifdef BOOST_NO_STD_LOCALE | |
2628 | cc = ch; | |
2629 | #else | |
2630 | cc = ct.narrow(ch, char()); | |
2631 | #endif /* BOOST_NO_STD_LOCALE */ | |
2632 | ||
2633 | if (cc == ')') // read "((a,b),(c))" | |
2634 | { | |
2635 | o = octonion<T>(a,b,c); | |
2636 | } | |
2637 | else if (cc == ',') // read "((a,b),(c)," | |
2638 | { | |
2639 | u = ::std::complex<T>(a,b); | |
2640 | ||
2641 | v = ::std::complex<T>(c); | |
2642 | ||
2643 | is >> x; // read "((a,b),(c),x" | |
2644 | ||
2645 | if (!is.good()) goto finish; | |
2646 | ||
2647 | is >> ch; // get the next lexeme | |
2648 | ||
2649 | if (!is.good()) goto finish; | |
2650 | ||
2651 | #ifdef BOOST_NO_STD_LOCALE | |
2652 | cc = ch; | |
2653 | #else | |
2654 | cc = ct.narrow(ch, char()); | |
2655 | #endif /* BOOST_NO_STD_LOCALE */ | |
2656 | ||
2657 | if (cc == ')') // read "((a,b),(c),x)" | |
2658 | { | |
2659 | o = octonion<T>(u,v,x); | |
2660 | } | |
2661 | else if (cc == ',') // read "((a,b),(c),x," | |
2662 | { | |
2663 | is >> y; // read "((a,b),(c),x,y" | |
2664 | ||
2665 | if (!is.good()) goto finish; | |
2666 | ||
2667 | is >> ch; // get the next lexeme | |
2668 | ||
2669 | if (!is.good()) goto finish; | |
2670 | ||
2671 | #ifdef BOOST_NO_STD_LOCALE | |
2672 | cc = ch; | |
2673 | #else | |
2674 | cc = ct.narrow(ch, char()); | |
2675 | #endif /* BOOST_NO_STD_LOCALE */ | |
2676 | ||
2677 | if (cc == ')') // read "((a,b),(c),x,y)" | |
2678 | { | |
2679 | o = octonion<T>(u,v,x,y); | |
2680 | } | |
2681 | else // error | |
2682 | { | |
2683 | is.setstate(::std::ios_base::failbit); | |
2684 | } | |
2685 | } | |
2686 | else // error | |
2687 | { | |
2688 | is.setstate(::std::ios_base::failbit); | |
2689 | } | |
2690 | } | |
2691 | else // error | |
2692 | { | |
2693 | is.setstate(::std::ios_base::failbit); | |
2694 | } | |
2695 | } | |
2696 | else if (cc == ',') // read "((a,b),(c," or "((a,b),(e," | |
2697 | { | |
2698 | is >> ch; // get the next lexeme | |
2699 | ||
2700 | if (!is.good()) goto finish; | |
2701 | ||
2702 | #ifdef BOOST_NO_STD_LOCALE | |
2703 | cc = ch; | |
2704 | #else | |
2705 | cc = ct.narrow(ch, char()); | |
2706 | #endif /* BOOST_NO_STD_LOCALE */ | |
2707 | ||
2708 | if (cc == '(') // read "((a,b),(e,(" (ambiguity resolution) | |
2709 | { | |
2710 | u = ::std::complex<T>(a,b); | |
2711 | ||
2712 | x = ::std::complex<T>(c); // "c" is actually "e" | |
2713 | ||
2714 | is.putback(ch); | |
2715 | ||
2716 | is >> y; // read "((a,b),(e,y" | |
2717 | ||
2718 | if (!is.good()) goto finish; | |
2719 | ||
2720 | is >> ch; // get the next lexeme | |
2721 | ||
2722 | if (!is.good()) goto finish; | |
2723 | ||
2724 | #ifdef BOOST_NO_STD_LOCALE | |
2725 | cc = ch; | |
2726 | #else | |
2727 | cc = ct.narrow(ch, char()); | |
2728 | #endif /* BOOST_NO_STD_LOCALE */ | |
2729 | ||
2730 | if (cc == ')') // read "((a,b),(e,y)" | |
2731 | { | |
2732 | is >> ch; // get the next lexeme | |
2733 | ||
2734 | if (!is.good()) goto finish; | |
2735 | ||
2736 | #ifdef BOOST_NO_STD_LOCALE | |
2737 | cc = ch; | |
2738 | #else | |
2739 | cc = ct.narrow(ch, char()); | |
2740 | #endif /* BOOST_NO_STD_LOCALE */ | |
2741 | ||
2742 | if (cc == ')') // read "((a,b),(e,y))" | |
2743 | { | |
2744 | o = octonion<T>(u,v,x,y); | |
2745 | } | |
2746 | else // error | |
2747 | { | |
2748 | is.setstate(::std::ios_base::failbit); | |
2749 | } | |
2750 | } | |
2751 | else // error | |
2752 | { | |
2753 | is.setstate(::std::ios_base::failbit); | |
2754 | } | |
2755 | } | |
2756 | else // read "((a,b),(c,d" or "((a,b),(e,f" | |
2757 | { | |
2758 | is.putback(ch); | |
2759 | ||
2760 | is >> d; | |
2761 | ||
2762 | if (!is.good()) goto finish; | |
2763 | ||
2764 | is >> ch; // get the next lexeme | |
2765 | ||
2766 | if (!is.good()) goto finish; | |
2767 | ||
2768 | #ifdef BOOST_NO_STD_LOCALE | |
2769 | cc = ch; | |
2770 | #else | |
2771 | cc = ct.narrow(ch, char()); | |
2772 | #endif /* BOOST_NO_STD_LOCALE */ | |
2773 | ||
2774 | if (cc == ')') // read "((a,b),(c,d)" (ambiguity resolution) | |
2775 | { | |
2776 | u = ::std::complex<T>(a,b); | |
2777 | ||
2778 | v = ::std::complex<T>(c,d); | |
2779 | ||
2780 | is >> ch; // get the next lexeme | |
2781 | ||
2782 | if (!is.good()) goto finish; | |
2783 | ||
2784 | #ifdef BOOST_NO_STD_LOCALE | |
2785 | cc = ch; | |
2786 | #else | |
2787 | cc = ct.narrow(ch, char()); | |
2788 | #endif /* BOOST_NO_STD_LOCALE */ | |
2789 | ||
2790 | if (cc == ')') // read "((a,b),(c,d))" | |
2791 | { | |
2792 | o = octonion<T>(u,v); | |
2793 | } | |
2794 | else if (cc == ',') // read "((a,b),(c,d)," | |
2795 | { | |
2796 | is >> x; // read "((a,b),(c,d),x | |
2797 | ||
2798 | if (!is.good()) goto finish; | |
2799 | ||
2800 | is >> ch; // get the next lexeme | |
2801 | ||
2802 | if (!is.good()) goto finish; | |
2803 | ||
2804 | #ifdef BOOST_NO_STD_LOCALE | |
2805 | cc = ch; | |
2806 | #else | |
2807 | cc = ct.narrow(ch, char()); | |
2808 | #endif /* BOOST_NO_STD_LOCALE */ | |
2809 | ||
2810 | if (cc == ')') // read "((a,b),(c,d),x)" | |
2811 | { | |
2812 | o = octonion<T>(u,v,x); | |
2813 | } | |
2814 | else if (cc == ',') // read "((a,b),(c,d),x," | |
2815 | { | |
2816 | is >> y; // read "((a,b),(c,d),x,y" | |
2817 | ||
2818 | if (!is.good()) goto finish; | |
2819 | ||
2820 | is >> ch; // get the next lexeme | |
2821 | ||
2822 | if (!is.good()) goto finish; | |
2823 | ||
2824 | #ifdef BOOST_NO_STD_LOCALE | |
2825 | cc = ch; | |
2826 | #else | |
2827 | cc = ct.narrow(ch, char()); | |
2828 | #endif /* BOOST_NO_STD_LOCALE */ | |
2829 | ||
2830 | if (cc == ')') // read "((a,b),(c,d),x,y)" | |
2831 | { | |
2832 | o = octonion<T>(u,v,x,y); | |
2833 | } | |
2834 | else // error | |
2835 | { | |
2836 | is.setstate(::std::ios_base::failbit); | |
2837 | } | |
2838 | } | |
2839 | else // error | |
2840 | { | |
2841 | is.setstate(::std::ios_base::failbit); | |
2842 | } | |
2843 | } | |
2844 | else // error | |
2845 | { | |
2846 | is.setstate(::std::ios_base::failbit); | |
2847 | } | |
2848 | } | |
2849 | else if (cc == ',') // read "((a,b),(e,f," (ambiguity resolution) | |
2850 | { | |
2851 | p = ::boost::math::quaternion<T>(a,b); // too late to backtrack | |
2852 | ||
2853 | is >> g; // read "((a,b),(e,f,g" | |
2854 | ||
2855 | if (!is.good()) goto finish; | |
2856 | ||
2857 | is >> ch; // get the next lexeme | |
2858 | ||
2859 | if (!is.good()) goto finish; | |
2860 | ||
2861 | #ifdef BOOST_NO_STD_LOCALE | |
2862 | cc = ch; | |
2863 | #else | |
2864 | cc = ct.narrow(ch, char()); | |
2865 | #endif /* BOOST_NO_STD_LOCALE */ | |
2866 | ||
2867 | if (cc == ')') // read "((a,b),(e,f,g)" | |
2868 | { | |
2869 | is >> ch; // get the next lexeme | |
2870 | ||
2871 | if (!is.good()) goto finish; | |
2872 | ||
2873 | #ifdef BOOST_NO_STD_LOCALE | |
2874 | cc = ch; | |
2875 | #else | |
2876 | cc = ct.narrow(ch, char()); | |
2877 | #endif /* BOOST_NO_STD_LOCALE */ | |
2878 | ||
2879 | if (cc == ')') // read "((a,b),(e,f,g))" | |
2880 | { | |
2881 | q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f" | |
2882 | ||
2883 | o = octonion<T>(p,q); | |
2884 | } | |
2885 | else // error | |
2886 | { | |
2887 | is.setstate(::std::ios_base::failbit); | |
2888 | } | |
2889 | } | |
2890 | else if (cc == ',') // read "((a,b),(e,f,g," | |
2891 | { | |
2892 | is >> h; // read "((a,b),(e,f,g,h" | |
2893 | ||
2894 | if (!is.good()) goto finish; | |
2895 | ||
2896 | is >> ch; // get the next lexeme | |
2897 | ||
2898 | if (!is.good()) goto finish; | |
2899 | ||
2900 | #ifdef BOOST_NO_STD_LOCALE | |
2901 | cc = ch; | |
2902 | #else | |
2903 | cc = ct.narrow(ch, char()); | |
2904 | #endif /* BOOST_NO_STD_LOCALE */ | |
2905 | ||
2906 | if (cc == ')') // read "((a,b),(e,f,g,h)" | |
2907 | { | |
2908 | is >> ch; // get the next lexeme | |
2909 | ||
2910 | if (!is.good()) goto finish; | |
2911 | ||
2912 | #ifdef BOOST_NO_STD_LOCALE | |
2913 | cc = ch; | |
2914 | #else | |
2915 | cc = ct.narrow(ch, char()); | |
2916 | #endif /* BOOST_NO_STD_LOCALE */ | |
2917 | ||
2918 | if (cc == ')') // read ((a,b),(e,f,g,h))" | |
2919 | { | |
2920 | q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f" | |
2921 | ||
2922 | o = octonion<T>(p,q); | |
2923 | } | |
2924 | else // error | |
2925 | { | |
2926 | is.setstate(::std::ios_base::failbit); | |
2927 | } | |
2928 | } | |
2929 | else // error | |
2930 | { | |
2931 | is.setstate(::std::ios_base::failbit); | |
2932 | } | |
2933 | } | |
2934 | else // error | |
2935 | { | |
2936 | is.setstate(::std::ios_base::failbit); | |
2937 | } | |
2938 | } | |
2939 | else // error | |
2940 | { | |
2941 | is.setstate(::std::ios_base::failbit); | |
2942 | } | |
2943 | } | |
2944 | } | |
2945 | else // error | |
2946 | { | |
2947 | is.setstate(::std::ios_base::failbit); | |
2948 | } | |
2949 | } | |
2950 | } | |
2951 | else // error | |
2952 | { | |
2953 | is.setstate(::std::ios_base::failbit); | |
2954 | } | |
2955 | } | |
2956 | else // error | |
2957 | { | |
2958 | is.setstate(::std::ios_base::failbit); | |
2959 | } | |
2960 | } | |
2961 | else if (cc == ',') // read "((a,b," | |
2962 | { | |
2963 | is >> c; // read "((a,b,c" | |
2964 | ||
2965 | if (!is.good()) goto finish; | |
2966 | ||
2967 | is >> ch; // get the next lexeme | |
2968 | ||
2969 | if (!is.good()) goto finish; | |
2970 | ||
2971 | #ifdef BOOST_NO_STD_LOCALE | |
2972 | cc = ch; | |
2973 | #else | |
2974 | cc = ct.narrow(ch, char()); | |
2975 | #endif /* BOOST_NO_STD_LOCALE */ | |
2976 | ||
2977 | if (cc == ')') // read "((a,b,c)" | |
2978 | { | |
2979 | is >> ch; // get the next lexeme | |
2980 | ||
2981 | if (!is.good()) goto finish; | |
2982 | ||
2983 | #ifdef BOOST_NO_STD_LOCALE | |
2984 | cc = ch; | |
2985 | #else | |
2986 | cc = ct.narrow(ch, char()); | |
2987 | #endif /* BOOST_NO_STD_LOCALE */ | |
2988 | ||
2989 | if (cc == ')') // read "((a,b,c))" | |
2990 | { | |
2991 | o = octonion<T>(a,b,c); | |
2992 | } | |
2993 | else if (cc == ',') // read "((a,b,c)," | |
2994 | { | |
2995 | p = ::boost::math::quaternion<T>(a,b,c); | |
2996 | ||
2997 | is >> q; // read "((a,b,c),q" | |
2998 | ||
2999 | if (!is.good()) goto finish; | |
3000 | ||
3001 | is >> ch; // get the next lexeme | |
3002 | ||
3003 | if (!is.good()) goto finish; | |
3004 | ||
3005 | #ifdef BOOST_NO_STD_LOCALE | |
3006 | cc = ch; | |
3007 | #else | |
3008 | cc = ct.narrow(ch, char()); | |
3009 | #endif /* BOOST_NO_STD_LOCALE */ | |
3010 | ||
3011 | if (cc == ')') // read "((a,b,c),q)" | |
3012 | { | |
3013 | o = octonion<T>(p,q); | |
3014 | } | |
3015 | else // error | |
3016 | { | |
3017 | is.setstate(::std::ios_base::failbit); | |
3018 | } | |
3019 | } | |
3020 | else // error | |
3021 | { | |
3022 | is.setstate(::std::ios_base::failbit); | |
3023 | } | |
3024 | } | |
3025 | else if (cc == ',') // read "((a,b,c," | |
3026 | { | |
3027 | is >> d; // read "((a,b,c,d" | |
3028 | ||
3029 | if (!is.good()) goto finish; | |
3030 | ||
3031 | is >> ch; // get the next lexeme | |
3032 | ||
3033 | if (!is.good()) goto finish; | |
3034 | ||
3035 | #ifdef BOOST_NO_STD_LOCALE | |
3036 | cc = ch; | |
3037 | #else | |
3038 | cc = ct.narrow(ch, char()); | |
3039 | #endif /* BOOST_NO_STD_LOCALE */ | |
3040 | ||
3041 | if (cc == ')') // read "((a,b,c,d)" | |
3042 | { | |
3043 | is >> ch; // get the next lexeme | |
3044 | ||
3045 | if (!is.good()) goto finish; | |
3046 | ||
3047 | #ifdef BOOST_NO_STD_LOCALE | |
3048 | cc = ch; | |
3049 | #else | |
3050 | cc = ct.narrow(ch, char()); | |
3051 | #endif /* BOOST_NO_STD_LOCALE */ | |
3052 | ||
3053 | if (cc == ')') // read "((a,b,c,d))" | |
3054 | { | |
3055 | o = octonion<T>(a,b,c,d); | |
3056 | } | |
3057 | else if (cc == ',') // read "((a,b,c,d)," | |
3058 | { | |
3059 | p = ::boost::math::quaternion<T>(a,b,c,d); | |
3060 | ||
3061 | is >> q; // read "((a,b,c,d),q" | |
3062 | ||
3063 | if (!is.good()) goto finish; | |
3064 | ||
3065 | is >> ch; // get the next lexeme | |
3066 | ||
3067 | if (!is.good()) goto finish; | |
3068 | ||
3069 | #ifdef BOOST_NO_STD_LOCALE | |
3070 | cc = ch; | |
3071 | #else | |
3072 | cc = ct.narrow(ch, char()); | |
3073 | #endif /* BOOST_NO_STD_LOCALE */ | |
3074 | ||
3075 | if (cc == ')') // read "((a,b,c,d),q)" | |
3076 | { | |
3077 | o = octonion<T>(p,q); | |
3078 | } | |
3079 | else // error | |
3080 | { | |
3081 | is.setstate(::std::ios_base::failbit); | |
3082 | } | |
3083 | } | |
3084 | else // error | |
3085 | { | |
3086 | is.setstate(::std::ios_base::failbit); | |
3087 | } | |
3088 | } | |
3089 | else // error | |
3090 | { | |
3091 | is.setstate(::std::ios_base::failbit); | |
3092 | } | |
3093 | } | |
3094 | else // error | |
3095 | { | |
3096 | is.setstate(::std::ios_base::failbit); | |
3097 | } | |
3098 | } | |
3099 | else // error | |
3100 | { | |
3101 | is.setstate(::std::ios_base::failbit); | |
3102 | } | |
3103 | } | |
3104 | } | |
3105 | else // error | |
3106 | { | |
3107 | is.setstate(::std::ios_base::failbit); | |
3108 | } | |
3109 | } | |
3110 | } | |
3111 | else // read "(a" | |
3112 | { | |
3113 | is.putback(ch); | |
3114 | ||
3115 | is >> a; // we extract the first component | |
3116 | ||
3117 | if (!is.good()) goto finish; | |
3118 | ||
3119 | is >> ch; // get the next lexeme | |
3120 | ||
3121 | if (!is.good()) goto finish; | |
3122 | ||
3123 | #ifdef BOOST_NO_STD_LOCALE | |
3124 | cc = ch; | |
3125 | #else | |
3126 | cc = ct.narrow(ch, char()); | |
3127 | #endif /* BOOST_NO_STD_LOCALE */ | |
3128 | ||
3129 | if (cc == ')') // read "(a)" | |
3130 | { | |
3131 | o = octonion<T>(a); | |
3132 | } | |
3133 | else if (cc == ',') // read "(a," | |
3134 | { | |
3135 | is >> ch; // get the next lexeme | |
3136 | ||
3137 | if (!is.good()) goto finish; | |
3138 | ||
3139 | #ifdef BOOST_NO_STD_LOCALE | |
3140 | cc = ch; | |
3141 | #else | |
3142 | cc = ct.narrow(ch, char()); | |
3143 | #endif /* BOOST_NO_STD_LOCALE */ | |
3144 | ||
3145 | if (cc == '(') // read "(a,(" | |
3146 | { | |
3147 | is >> ch; // get the next lexeme | |
3148 | ||
3149 | if (!is.good()) goto finish; | |
3150 | ||
3151 | #ifdef BOOST_NO_STD_LOCALE | |
3152 | cc = ch; | |
3153 | #else | |
3154 | cc = ct.narrow(ch, char()); | |
3155 | #endif /* BOOST_NO_STD_LOCALE */ | |
3156 | ||
3157 | if (cc == '(') // read "(a,((" | |
3158 | { | |
3159 | p = ::boost::math::quaternion<T>(a); | |
3160 | ||
3161 | is.putback(ch); | |
3162 | ||
3163 | is.putback(ch); // we backtrack twice, with the same value | |
3164 | ||
3165 | is >> q; // read "(a,q" | |
3166 | ||
3167 | if (!is.good()) goto finish; | |
3168 | ||
3169 | is >> ch; // get the next lexeme | |
3170 | ||
3171 | if (!is.good()) goto finish; | |
3172 | ||
3173 | #ifdef BOOST_NO_STD_LOCALE | |
3174 | cc = ch; | |
3175 | #else | |
3176 | cc = ct.narrow(ch, char()); | |
3177 | #endif /* BOOST_NO_STD_LOCALE */ | |
3178 | ||
3179 | if (cc == ')') // read "(a,q)" | |
3180 | { | |
3181 | o = octonion<T>(p,q); | |
3182 | } | |
3183 | else // error | |
3184 | { | |
3185 | is.setstate(::std::ios_base::failbit); | |
3186 | } | |
3187 | } | |
3188 | else // read "(a,(c" or "(a,(e" | |
3189 | { | |
3190 | is.putback(ch); | |
3191 | ||
3192 | is >> c; | |
3193 | ||
3194 | if (!is.good()) goto finish; | |
3195 | ||
3196 | is >> ch; // get the next lexeme | |
3197 | ||
3198 | if (!is.good()) goto finish; | |
3199 | ||
3200 | #ifdef BOOST_NO_STD_LOCALE | |
3201 | cc = ch; | |
3202 | #else | |
3203 | cc = ct.narrow(ch, char()); | |
3204 | #endif /* BOOST_NO_STD_LOCALE */ | |
3205 | ||
3206 | if (cc == ')') // read "(a,(c)" (ambiguity resolution) | |
3207 | { | |
3208 | is >> ch; // get the next lexeme | |
3209 | ||
3210 | if (!is.good()) goto finish; | |
3211 | ||
3212 | #ifdef BOOST_NO_STD_LOCALE | |
3213 | cc = ch; | |
3214 | #else | |
3215 | cc = ct.narrow(ch, char()); | |
3216 | #endif /* BOOST_NO_STD_LOCALE */ | |
3217 | ||
3218 | if (cc == ')') // read "(a,(c))" | |
3219 | { | |
3220 | o = octonion<T>(a,b,c); | |
3221 | } | |
3222 | else if (cc == ',') // read "(a,(c)," | |
3223 | { | |
3224 | u = ::std::complex<T>(a); | |
3225 | ||
3226 | v = ::std::complex<T>(c); | |
3227 | ||
3228 | is >> x; // read "(a,(c),x" | |
3229 | ||
3230 | if (!is.good()) goto finish; | |
3231 | ||
3232 | is >> ch; // get the next lexeme | |
3233 | ||
3234 | if (!is.good()) goto finish; | |
3235 | ||
3236 | #ifdef BOOST_NO_STD_LOCALE | |
3237 | cc = ch; | |
3238 | #else | |
3239 | cc = ct.narrow(ch, char()); | |
3240 | #endif /* BOOST_NO_STD_LOCALE */ | |
3241 | ||
3242 | if (cc == ')') // read "(a,(c),x)" | |
3243 | { | |
3244 | o = octonion<T>(u,v,x); | |
3245 | } | |
3246 | else if (cc == ',') // read "(a,(c),x," | |
3247 | { | |
3248 | is >> y; // read "(a,(c),x,y" | |
3249 | ||
3250 | if (!is.good()) goto finish; | |
3251 | ||
3252 | is >> ch; // get the next lexeme | |
3253 | ||
3254 | if (!is.good()) goto finish; | |
3255 | ||
3256 | #ifdef BOOST_NO_STD_LOCALE | |
3257 | cc = ch; | |
3258 | #else | |
3259 | cc = ct.narrow(ch, char()); | |
3260 | #endif /* BOOST_NO_STD_LOCALE */ | |
3261 | ||
3262 | if (cc == ')') // read "(a,(c),x,y)" | |
3263 | { | |
3264 | o = octonion<T>(u,v,x,y); | |
3265 | } | |
3266 | else // error | |
3267 | { | |
3268 | is.setstate(::std::ios_base::failbit); | |
3269 | } | |
3270 | } | |
3271 | else // error | |
3272 | { | |
3273 | is.setstate(::std::ios_base::failbit); | |
3274 | } | |
3275 | } | |
3276 | else // error | |
3277 | { | |
3278 | is.setstate(::std::ios_base::failbit); | |
3279 | } | |
3280 | } | |
3281 | else if (cc == ',') // read "(a,(c," or "(a,(e," | |
3282 | { | |
3283 | is >> ch; // get the next lexeme | |
3284 | ||
3285 | if (!is.good()) goto finish; | |
3286 | ||
3287 | #ifdef BOOST_NO_STD_LOCALE | |
3288 | cc = ch; | |
3289 | #else | |
3290 | cc = ct.narrow(ch, char()); | |
3291 | #endif /* BOOST_NO_STD_LOCALE */ | |
3292 | ||
3293 | if (cc == '(') // read "(a,(e,(" (ambiguity resolution) | |
3294 | { | |
3295 | u = ::std::complex<T>(a); | |
3296 | ||
3297 | x = ::std::complex<T>(c); // "c" is actually "e" | |
3298 | ||
3299 | is.putback(ch); // we backtrack | |
3300 | ||
3301 | is >> y; // read "(a,(e,y" | |
3302 | ||
3303 | if (!is.good()) goto finish; | |
3304 | ||
3305 | is >> ch; // get the next lexeme | |
3306 | ||
3307 | if (!is.good()) goto finish; | |
3308 | ||
3309 | #ifdef BOOST_NO_STD_LOCALE | |
3310 | cc = ch; | |
3311 | #else | |
3312 | cc = ct.narrow(ch, char()); | |
3313 | #endif /* BOOST_NO_STD_LOCALE */ | |
3314 | ||
3315 | if (cc == ')') // read "(a,(e,y)" | |
3316 | { | |
3317 | is >> ch; // get the next lexeme | |
3318 | ||
3319 | if (!is.good()) goto finish; | |
3320 | ||
3321 | #ifdef BOOST_NO_STD_LOCALE | |
3322 | cc = ch; | |
3323 | #else | |
3324 | cc = ct.narrow(ch, char()); | |
3325 | #endif /* BOOST_NO_STD_LOCALE */ | |
3326 | ||
3327 | if (cc == ')') // read "(a,(e,y))" | |
3328 | { | |
3329 | o = octonion<T>(u,v,x,y); | |
3330 | } | |
3331 | else // error | |
3332 | { | |
3333 | is.setstate(::std::ios_base::failbit); | |
3334 | } | |
3335 | } | |
3336 | else // error | |
3337 | { | |
3338 | is.setstate(::std::ios_base::failbit); | |
3339 | } | |
3340 | } | |
3341 | else // read "(a,(c,d" or "(a,(e,f" | |
3342 | { | |
3343 | is.putback(ch); | |
3344 | ||
3345 | is >> d; | |
3346 | ||
3347 | if (!is.good()) goto finish; | |
3348 | ||
3349 | is >> ch; // get the next lexeme | |
3350 | ||
3351 | if (!is.good()) goto finish; | |
3352 | ||
3353 | #ifdef BOOST_NO_STD_LOCALE | |
3354 | cc = ch; | |
3355 | #else | |
3356 | cc = ct.narrow(ch, char()); | |
3357 | #endif /* BOOST_NO_STD_LOCALE */ | |
3358 | ||
3359 | if (cc == ')') // read "(a,(c,d)" (ambiguity resolution) | |
3360 | { | |
3361 | is >> ch; // get the next lexeme | |
3362 | ||
3363 | if (!is.good()) goto finish; | |
3364 | ||
3365 | #ifdef BOOST_NO_STD_LOCALE | |
3366 | cc = ch; | |
3367 | #else | |
3368 | cc = ct.narrow(ch, char()); | |
3369 | #endif /* BOOST_NO_STD_LOCALE */ | |
3370 | ||
3371 | if (cc == ')') // read "(a,(c,d))" | |
3372 | { | |
3373 | o = octonion<T>(a,b,c,d); | |
3374 | } | |
3375 | else if (cc == ',') // read "(a,(c,d)," | |
3376 | { | |
3377 | u = ::std::complex<T>(a); | |
3378 | ||
3379 | v = ::std::complex<T>(c,d); | |
3380 | ||
3381 | is >> x; // read "(a,(c,d),x" | |
3382 | ||
3383 | if (!is.good()) goto finish; | |
3384 | ||
3385 | is >> ch; // get the next lexeme | |
3386 | ||
3387 | if (!is.good()) goto finish; | |
3388 | ||
3389 | #ifdef BOOST_NO_STD_LOCALE | |
3390 | cc = ch; | |
3391 | #else | |
3392 | cc = ct.narrow(ch, char()); | |
3393 | #endif /* BOOST_NO_STD_LOCALE */ | |
3394 | ||
3395 | if (cc == ')') // read "(a,(c,d),x)" | |
3396 | { | |
3397 | o = octonion<T>(u,v,x); | |
3398 | } | |
3399 | else if (cc == ',') // read "(a,(c,d),x," | |
3400 | { | |
3401 | is >> y; // read "(a,(c,d),x,y" | |
3402 | ||
3403 | if (!is.good()) goto finish; | |
3404 | ||
3405 | is >> ch; // get the next lexeme | |
3406 | ||
3407 | if (!is.good()) goto finish; | |
3408 | ||
3409 | #ifdef BOOST_NO_STD_LOCALE | |
3410 | cc = ch; | |
3411 | #else | |
3412 | cc = ct.narrow(ch, char()); | |
3413 | #endif /* BOOST_NO_STD_LOCALE */ | |
3414 | ||
3415 | if (cc == ')') // read "(a,(c,d),x,y)" | |
3416 | { | |
3417 | o = octonion<T>(u,v,x,y); | |
3418 | } | |
3419 | else // error | |
3420 | { | |
3421 | is.setstate(::std::ios_base::failbit); | |
3422 | } | |
3423 | } | |
3424 | else // error | |
3425 | { | |
3426 | is.setstate(::std::ios_base::failbit); | |
3427 | } | |
3428 | } | |
3429 | else // error | |
3430 | { | |
3431 | is.setstate(::std::ios_base::failbit); | |
3432 | } | |
3433 | } | |
3434 | else if (cc == ',') // read "(a,(e,f," (ambiguity resolution) | |
3435 | { | |
3436 | p = ::boost::math::quaternion<T>(a); | |
3437 | ||
3438 | is >> g; // read "(a,(e,f,g" | |
3439 | ||
3440 | if (!is.good()) goto finish; | |
3441 | ||
3442 | is >> ch; // get the next lexeme | |
3443 | ||
3444 | if (!is.good()) goto finish; | |
3445 | ||
3446 | #ifdef BOOST_NO_STD_LOCALE | |
3447 | cc = ch; | |
3448 | #else | |
3449 | cc = ct.narrow(ch, char()); | |
3450 | #endif /* BOOST_NO_STD_LOCALE */ | |
3451 | ||
3452 | if (cc == ')') // read "(a,(e,f,g)" | |
3453 | { | |
3454 | is >> ch; // get the next lexeme | |
3455 | ||
3456 | if (!is.good()) goto finish; | |
3457 | ||
3458 | #ifdef BOOST_NO_STD_LOCALE | |
3459 | cc = ch; | |
3460 | #else | |
3461 | cc = ct.narrow(ch, char()); | |
3462 | #endif /* BOOST_NO_STD_LOCALE */ | |
3463 | ||
3464 | if (cc == ')') // read "(a,(e,f,g))" | |
3465 | { | |
3466 | q = ::boost::math::quaternion<T>(c,d,g); // "c" is actually "e" and "d" is actually "f" | |
3467 | ||
3468 | o = octonion<T>(p,q); | |
3469 | } | |
3470 | else // error | |
3471 | { | |
3472 | is.setstate(::std::ios_base::failbit); | |
3473 | } | |
3474 | } | |
3475 | else if (cc == ',') // read "(a,(e,f,g," | |
3476 | { | |
3477 | is >> h; // read "(a,(e,f,g,h" | |
3478 | ||
3479 | if (!is.good()) goto finish; | |
3480 | ||
3481 | is >> ch; // get the next lexeme | |
3482 | ||
3483 | if (!is.good()) goto finish; | |
3484 | ||
3485 | #ifdef BOOST_NO_STD_LOCALE | |
3486 | cc = ch; | |
3487 | #else | |
3488 | cc = ct.narrow(ch, char()); | |
3489 | #endif /* BOOST_NO_STD_LOCALE */ | |
3490 | ||
3491 | if (cc == ')') // read "(a,(e,f,g,h)" | |
3492 | { | |
3493 | is >> ch; // get the next lexeme | |
3494 | ||
3495 | if (!is.good()) goto finish; | |
3496 | ||
3497 | #ifdef BOOST_NO_STD_LOCALE | |
3498 | cc = ch; | |
3499 | #else | |
3500 | cc = ct.narrow(ch, char()); | |
3501 | #endif /* BOOST_NO_STD_LOCALE */ | |
3502 | ||
3503 | if (cc == ')') // read "(a,(e,f,g,h))" | |
3504 | { | |
3505 | q = ::boost::math::quaternion<T>(c,d,g,h); // "c" is actually "e" and "d" is actually "f" | |
3506 | ||
3507 | o = octonion<T>(p,q); | |
3508 | } | |
3509 | else // error | |
3510 | { | |
3511 | is.setstate(::std::ios_base::failbit); | |
3512 | } | |
3513 | } | |
3514 | else // error | |
3515 | { | |
3516 | is.setstate(::std::ios_base::failbit); | |
3517 | } | |
3518 | } | |
3519 | else // error | |
3520 | { | |
3521 | is.setstate(::std::ios_base::failbit); | |
3522 | } | |
3523 | } | |
3524 | else // error | |
3525 | { | |
3526 | is.setstate(::std::ios_base::failbit); | |
3527 | } | |
3528 | } | |
3529 | } | |
3530 | else // error | |
3531 | { | |
3532 | is.setstate(::std::ios_base::failbit); | |
3533 | } | |
3534 | } | |
3535 | } | |
3536 | else // read "(a,b" or "(a,c" (ambiguity resolution) | |
3537 | { | |
3538 | is.putback(ch); | |
3539 | ||
3540 | is >> b; | |
3541 | ||
3542 | if (!is.good()) goto finish; | |
3543 | ||
3544 | is >> ch; // get the next lexeme | |
3545 | ||
3546 | if (!is.good()) goto finish; | |
3547 | ||
3548 | #ifdef BOOST_NO_STD_LOCALE | |
3549 | cc = ch; | |
3550 | #else | |
3551 | cc = ct.narrow(ch, char()); | |
3552 | #endif /* BOOST_NO_STD_LOCALE */ | |
3553 | ||
3554 | if (cc == ')') // read "(a,b)" (ambiguity resolution) | |
3555 | { | |
3556 | o = octonion<T>(a,b); | |
3557 | } | |
3558 | else if (cc == ',') // read "(a,b," or "(a,c," | |
3559 | { | |
3560 | is >> ch; // get the next lexeme | |
3561 | ||
3562 | if (!is.good()) goto finish; | |
3563 | ||
3564 | #ifdef BOOST_NO_STD_LOCALE | |
3565 | cc = ch; | |
3566 | #else | |
3567 | cc = ct.narrow(ch, char()); | |
3568 | #endif /* BOOST_NO_STD_LOCALE */ | |
3569 | ||
3570 | if (cc == '(') // read "(a,c,(" (ambiguity resolution) | |
3571 | { | |
3572 | u = ::std::complex<T>(a); | |
3573 | ||
3574 | v = ::std::complex<T>(b); // "b" is actually "c" | |
3575 | ||
3576 | is.putback(ch); // we backtrack | |
3577 | ||
3578 | is >> x; // read "(a,c,x" | |
3579 | ||
3580 | if (!is.good()) goto finish; | |
3581 | ||
3582 | is >> ch; // get the next lexeme | |
3583 | ||
3584 | if (!is.good()) goto finish; | |
3585 | ||
3586 | #ifdef BOOST_NO_STD_LOCALE | |
3587 | cc = ch; | |
3588 | #else | |
3589 | cc = ct.narrow(ch, char()); | |
3590 | #endif /* BOOST_NO_STD_LOCALE */ | |
3591 | ||
3592 | if (cc == ')') // read "(a,c,x)" | |
3593 | { | |
3594 | o = octonion<T>(u,v,x); | |
3595 | } | |
3596 | else if (cc == ',') // read "(a,c,x," | |
3597 | { | |
3598 | is >> y; // read "(a,c,x,y" // read "(a,c,x" | |
3599 | ||
3600 | if (!is.good()) goto finish; | |
3601 | ||
3602 | is >> ch; // get the next lexeme | |
3603 | ||
3604 | if (!is.good()) goto finish; | |
3605 | ||
3606 | #ifdef BOOST_NO_STD_LOCALE | |
3607 | cc = ch; | |
3608 | #else | |
3609 | cc = ct.narrow(ch, char()); | |
3610 | #endif /* BOOST_NO_STD_LOCALE */ | |
3611 | ||
3612 | if (cc == ')') // read "(a,c,x,y)" | |
3613 | { | |
3614 | o = octonion<T>(u,v,x,y); | |
3615 | } | |
3616 | else // error | |
3617 | { | |
3618 | is.setstate(::std::ios_base::failbit); | |
3619 | } | |
3620 | } | |
3621 | else // error | |
3622 | { | |
3623 | is.setstate(::std::ios_base::failbit); | |
3624 | } | |
3625 | } | |
3626 | else // read "(a,b,c" or "(a,c,e" | |
3627 | { | |
3628 | is.putback(ch); | |
3629 | ||
3630 | is >> c; | |
3631 | ||
3632 | if (!is.good()) goto finish; | |
3633 | ||
3634 | is >> ch; // get the next lexeme | |
3635 | ||
3636 | if (!is.good()) goto finish; | |
3637 | ||
3638 | #ifdef BOOST_NO_STD_LOCALE | |
3639 | cc = ch; | |
3640 | #else | |
3641 | cc = ct.narrow(ch, char()); | |
3642 | #endif /* BOOST_NO_STD_LOCALE */ | |
3643 | ||
3644 | if (cc == ')') // read "(a,b,c)" (ambiguity resolution) | |
3645 | { | |
3646 | o = octonion<T>(a,b,c); | |
3647 | } | |
3648 | else if (cc == ',') // read "(a,b,c," or "(a,c,e," | |
3649 | { | |
3650 | is >> ch; // get the next lexeme | |
3651 | ||
3652 | if (!is.good()) goto finish; | |
3653 | ||
3654 | #ifdef BOOST_NO_STD_LOCALE | |
3655 | cc = ch; | |
3656 | #else | |
3657 | cc = ct.narrow(ch, char()); | |
3658 | #endif /* BOOST_NO_STD_LOCALE */ | |
3659 | ||
3660 | if (cc == '(') // read "(a,c,e,(") (ambiguity resolution) | |
3661 | { | |
3662 | u = ::std::complex<T>(a); | |
3663 | ||
3664 | v = ::std::complex<T>(b); // "b" is actually "c" | |
3665 | ||
3666 | x = ::std::complex<T>(c); // "c" is actually "e" | |
3667 | ||
3668 | is.putback(ch); // we backtrack | |
3669 | ||
3670 | is >> y; // read "(a,c,e,y" | |
3671 | ||
3672 | if (!is.good()) goto finish; | |
3673 | ||
3674 | is >> ch; // get the next lexeme | |
3675 | ||
3676 | if (!is.good()) goto finish; | |
3677 | ||
3678 | #ifdef BOOST_NO_STD_LOCALE | |
3679 | cc = ch; | |
3680 | #else | |
3681 | cc = ct.narrow(ch, char()); | |
3682 | #endif /* BOOST_NO_STD_LOCALE */ | |
3683 | ||
3684 | if (cc == ')') // read "(a,c,e,y)" | |
3685 | { | |
3686 | o = octonion<T>(u,v,x,y); | |
3687 | } | |
3688 | else // error | |
3689 | { | |
3690 | is.setstate(::std::ios_base::failbit); | |
3691 | } | |
3692 | } | |
3693 | else // read "(a,b,c,d" (ambiguity resolution) | |
3694 | { | |
3695 | is.putback(ch); // we backtrack | |
3696 | ||
3697 | is >> d; | |
3698 | ||
3699 | if (!is.good()) goto finish; | |
3700 | ||
3701 | is >> ch; // get the next lexeme | |
3702 | ||
3703 | if (!is.good()) goto finish; | |
3704 | ||
3705 | #ifdef BOOST_NO_STD_LOCALE | |
3706 | cc = ch; | |
3707 | #else | |
3708 | cc = ct.narrow(ch, char()); | |
3709 | #endif /* BOOST_NO_STD_LOCALE */ | |
3710 | ||
3711 | if (cc == ')') // read "(a,b,c,d)" | |
3712 | { | |
3713 | o = octonion<T>(a,b,c,d); | |
3714 | } | |
3715 | else if (cc == ',') // read "(a,b,c,d," | |
3716 | { | |
3717 | is >> e; // read "(a,b,c,d,e" | |
3718 | ||
3719 | if (!is.good()) goto finish; | |
3720 | ||
3721 | is >> ch; // get the next lexeme | |
3722 | ||
3723 | if (!is.good()) goto finish; | |
3724 | ||
3725 | #ifdef BOOST_NO_STD_LOCALE | |
3726 | cc = ch; | |
3727 | #else | |
3728 | cc = ct.narrow(ch, char()); | |
3729 | #endif /* BOOST_NO_STD_LOCALE */ | |
3730 | ||
3731 | if (cc == ')') // read "(a,b,c,d,e)" | |
3732 | { | |
3733 | o = octonion<T>(a,b,c,d,e); | |
3734 | } | |
3735 | else if (cc == ',') // read "(a,b,c,d,e," | |
3736 | { | |
3737 | is >> f; // read "(a,b,c,d,e,f" | |
3738 | ||
3739 | if (!is.good()) goto finish; | |
3740 | ||
3741 | is >> ch; // get the next lexeme | |
3742 | ||
3743 | if (!is.good()) goto finish; | |
3744 | ||
3745 | #ifdef BOOST_NO_STD_LOCALE | |
3746 | cc = ch; | |
3747 | #else | |
3748 | cc = ct.narrow(ch, char()); | |
3749 | #endif /* BOOST_NO_STD_LOCALE */ | |
3750 | ||
3751 | if (cc == ')') // read "(a,b,c,d,e,f)" | |
3752 | { | |
3753 | o = octonion<T>(a,b,c,d,e,f); | |
3754 | } | |
3755 | else if (cc == ',') // read "(a,b,c,d,e,f," | |
3756 | { | |
3757 | is >> g; // read "(a,b,c,d,e,f,g" // read "(a,b,c,d,e,f" | |
3758 | ||
3759 | if (!is.good()) goto finish; | |
3760 | ||
3761 | is >> ch; // get the next lexeme | |
3762 | ||
3763 | if (!is.good()) goto finish; | |
3764 | ||
3765 | #ifdef BOOST_NO_STD_LOCALE | |
3766 | cc = ch; | |
3767 | #else | |
3768 | cc = ct.narrow(ch, char()); | |
3769 | #endif /* BOOST_NO_STD_LOCALE */ | |
3770 | ||
3771 | if (cc == ')') // read "(a,b,c,d,e,f,g)" | |
3772 | { | |
3773 | o = octonion<T>(a,b,c,d,e,f,g); | |
3774 | } | |
3775 | else if (cc == ',') // read "(a,b,c,d,e,f,g," | |
3776 | { | |
3777 | 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" | |
3778 | ||
3779 | if (!is.good()) goto finish; | |
3780 | ||
3781 | is >> ch; // get the next lexeme | |
3782 | ||
3783 | if (!is.good()) goto finish; | |
3784 | ||
3785 | #ifdef BOOST_NO_STD_LOCALE | |
3786 | cc = ch; | |
3787 | #else | |
3788 | cc = ct.narrow(ch, char()); | |
3789 | #endif /* BOOST_NO_STD_LOCALE */ | |
3790 | ||
3791 | if (cc == ')') // read "(a,b,c,d,e,f,g,h)" | |
3792 | { | |
3793 | o = octonion<T>(a,b,c,d,e,f,g,h); | |
3794 | } | |
3795 | else // error | |
3796 | { | |
3797 | is.setstate(::std::ios_base::failbit); | |
3798 | } | |
3799 | } | |
3800 | else // error | |
3801 | { | |
3802 | is.setstate(::std::ios_base::failbit); | |
3803 | } | |
3804 | } | |
3805 | else // error | |
3806 | { | |
3807 | is.setstate(::std::ios_base::failbit); | |
3808 | } | |
3809 | } | |
3810 | else // error | |
3811 | { | |
3812 | is.setstate(::std::ios_base::failbit); | |
3813 | } | |
3814 | } | |
3815 | else // error | |
3816 | { | |
3817 | is.setstate(::std::ios_base::failbit); | |
3818 | } | |
3819 | } | |
3820 | } | |
3821 | else // error | |
3822 | { | |
3823 | is.setstate(::std::ios_base::failbit); | |
3824 | } | |
3825 | } | |
3826 | } | |
3827 | else // error | |
3828 | { | |
3829 | is.setstate(::std::ios_base::failbit); | |
3830 | } | |
3831 | } | |
3832 | } | |
3833 | else // error | |
3834 | { | |
3835 | is.setstate(::std::ios_base::failbit); | |
3836 | } | |
3837 | } | |
3838 | } | |
3839 | else // format: a | |
3840 | { | |
3841 | is.putback(ch); | |
3842 | ||
3843 | is >> a; // we extract the first component | |
3844 | ||
3845 | if (!is.good()) goto finish; | |
3846 | ||
3847 | o = octonion<T>(a); | |
3848 | } | |
3849 | ||
3850 | finish: | |
3851 | return(is); | |
3852 | } | |
3853 | ||
3854 | ||
3855 | template<typename T, typename charT, class traits> | |
3856 | ::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os, | |
3857 | octonion<T> const & o) | |
3858 | { | |
3859 | ::std::basic_ostringstream<charT,traits> s; | |
3860 | ||
3861 | s.flags(os.flags()); | |
3862 | #ifdef BOOST_NO_STD_LOCALE | |
3863 | #else | |
3864 | s.imbue(os.getloc()); | |
3865 | #endif /* BOOST_NO_STD_LOCALE */ | |
3866 | s.precision(os.precision()); | |
3867 | ||
3868 | s << '(' << o.R_component_1() << ',' | |
3869 | << o.R_component_2() << ',' | |
3870 | << o.R_component_3() << ',' | |
3871 | << o.R_component_4() << ',' | |
3872 | << o.R_component_5() << ',' | |
3873 | << o.R_component_6() << ',' | |
3874 | << o.R_component_7() << ',' | |
3875 | << o.R_component_8() << ')'; | |
3876 | ||
3877 | return os << s.str(); | |
3878 | } | |
3879 | ||
3880 | ||
3881 | // values | |
3882 | ||
3883 | template<typename T> | |
3884 | inline T real(octonion<T> const & o) | |
3885 | { | |
3886 | return(o.real()); | |
3887 | } | |
3888 | ||
3889 | ||
3890 | template<typename T> | |
3891 | inline octonion<T> unreal(octonion<T> const & o) | |
3892 | { | |
3893 | return(o.unreal()); | |
3894 | } | |
3895 | ||
3896 | ||
3897 | #define BOOST_OCTONION_VALARRAY_LOADER \ | |
3898 | using ::std::valarray; \ | |
3899 | \ | |
3900 | valarray<T> temp(8); \ | |
3901 | \ | |
3902 | temp[0] = o.R_component_1(); \ | |
3903 | temp[1] = o.R_component_2(); \ | |
3904 | temp[2] = o.R_component_3(); \ | |
3905 | temp[3] = o.R_component_4(); \ | |
3906 | temp[4] = o.R_component_5(); \ | |
3907 | temp[5] = o.R_component_6(); \ | |
3908 | temp[6] = o.R_component_7(); \ | |
3909 | temp[7] = o.R_component_8(); | |
3910 | ||
3911 | ||
3912 | template<typename T> | |
3913 | inline T sup(octonion<T> const & o) | |
3914 | { | |
3915 | #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP | |
3916 | using ::std::abs; | |
3917 | #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ | |
3918 | ||
3919 | BOOST_OCTONION_VALARRAY_LOADER | |
3920 | ||
3921 | return((abs(temp).max)()); | |
3922 | } | |
3923 | ||
3924 | ||
3925 | template<typename T> | |
3926 | inline T l1(octonion<T> const & o) | |
3927 | { | |
3928 | #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP | |
3929 | using ::std::abs; | |
3930 | #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ | |
3931 | ||
3932 | BOOST_OCTONION_VALARRAY_LOADER | |
3933 | ||
3934 | return(abs(temp).sum()); | |
3935 | } | |
3936 | ||
3937 | ||
3938 | template<typename T> | |
3939 | inline T abs(const octonion<T> & o) | |
3940 | { | |
3941 | #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP | |
3942 | using ::std::abs; | |
3943 | #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */ | |
3944 | ||
3945 | using ::std::sqrt; | |
3946 | ||
3947 | BOOST_OCTONION_VALARRAY_LOADER | |
3948 | ||
3949 | T maxim = (abs(temp).max)(); // overflow protection | |
3950 | ||
3951 | if (maxim == static_cast<T>(0)) | |
3952 | { | |
3953 | return(maxim); | |
3954 | } | |
3955 | else | |
3956 | { | |
3957 | T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions | |
3958 | ||
3959 | temp *= mixam; | |
3960 | ||
3961 | temp *= temp; | |
3962 | ||
3963 | return(maxim*sqrt(temp.sum())); | |
3964 | } | |
3965 | ||
3966 | //return(::std::sqrt(norm(o))); | |
3967 | } | |
3968 | ||
3969 | ||
3970 | #undef BOOST_OCTONION_VALARRAY_LOADER | |
3971 | ||
3972 | ||
3973 | // Note: This is the Cayley norm, not the Euclidian norm... | |
3974 | ||
3975 | template<typename T> | |
3976 | inline T norm(octonion<T> const & o) | |
3977 | { | |
3978 | return(real(o*conj(o))); | |
3979 | } | |
3980 | ||
3981 | ||
3982 | template<typename T> | |
3983 | inline octonion<T> conj(octonion<T> const & o) | |
3984 | { | |
3985 | return(octonion<T>( +o.R_component_1(), | |
3986 | -o.R_component_2(), | |
3987 | -o.R_component_3(), | |
3988 | -o.R_component_4(), | |
3989 | -o.R_component_5(), | |
3990 | -o.R_component_6(), | |
3991 | -o.R_component_7(), | |
3992 | -o.R_component_8())); | |
3993 | } | |
3994 | ||
3995 | ||
3996 | // Note: There is little point, for the octonions, to introduce the equivalents | |
3997 | // to the complex "arg" and the quaternionic "cylindropolar". | |
3998 | ||
3999 | ||
4000 | template<typename T> | |
4001 | inline octonion<T> spherical(T const & rho, | |
4002 | T const & theta, | |
4003 | T const & phi1, | |
4004 | T const & phi2, | |
4005 | T const & phi3, | |
4006 | T const & phi4, | |
4007 | T const & phi5, | |
4008 | T const & phi6) | |
4009 | { | |
4010 | using ::std::cos; | |
4011 | using ::std::sin; | |
4012 | ||
4013 | //T a = cos(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); | |
4014 | //T b = sin(theta)*cos(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); | |
4015 | //T c = sin(phi1)*cos(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); | |
4016 | //T d = sin(phi2)*cos(phi3)*cos(phi4)*cos(phi5)*cos(phi6); | |
4017 | //T e = sin(phi3)*cos(phi4)*cos(phi5)*cos(phi6); | |
4018 | //T f = sin(phi4)*cos(phi5)*cos(phi6); | |
4019 | //T g = sin(phi5)*cos(phi6); | |
4020 | //T h = sin(phi6); | |
4021 | ||
4022 | T courrant = static_cast<T>(1); | |
4023 | ||
4024 | T h = sin(phi6); | |
4025 | ||
4026 | courrant *= cos(phi6); | |
4027 | ||
4028 | T g = sin(phi5)*courrant; | |
4029 | ||
4030 | courrant *= cos(phi5); | |
4031 | ||
4032 | T f = sin(phi4)*courrant; | |
4033 | ||
4034 | courrant *= cos(phi4); | |
4035 | ||
4036 | T e = sin(phi3)*courrant; | |
4037 | ||
4038 | courrant *= cos(phi3); | |
4039 | ||
4040 | T d = sin(phi2)*courrant; | |
4041 | ||
4042 | courrant *= cos(phi2); | |
4043 | ||
4044 | T c = sin(phi1)*courrant; | |
4045 | ||
4046 | courrant *= cos(phi1); | |
4047 | ||
4048 | T b = sin(theta)*courrant; | |
4049 | T a = cos(theta)*courrant; | |
4050 | ||
4051 | return(rho*octonion<T>(a,b,c,d,e,f,g,h)); | |
4052 | } | |
4053 | ||
4054 | ||
4055 | template<typename T> | |
4056 | inline octonion<T> multipolar(T const & rho1, | |
4057 | T const & theta1, | |
4058 | T const & rho2, | |
4059 | T const & theta2, | |
4060 | T const & rho3, | |
4061 | T const & theta3, | |
4062 | T const & rho4, | |
4063 | T const & theta4) | |
4064 | { | |
4065 | using ::std::cos; | |
4066 | using ::std::sin; | |
4067 | ||
4068 | T a = rho1*cos(theta1); | |
4069 | T b = rho1*sin(theta1); | |
4070 | T c = rho2*cos(theta2); | |
4071 | T d = rho2*sin(theta2); | |
4072 | T e = rho3*cos(theta3); | |
4073 | T f = rho3*sin(theta3); | |
4074 | T g = rho4*cos(theta4); | |
4075 | T h = rho4*sin(theta4); | |
4076 | ||
4077 | return(octonion<T>(a,b,c,d,e,f,g,h)); | |
4078 | } | |
4079 | ||
4080 | ||
4081 | template<typename T> | |
4082 | inline octonion<T> cylindrical(T const & r, | |
4083 | T const & angle, | |
4084 | T const & h1, | |
4085 | T const & h2, | |
4086 | T const & h3, | |
4087 | T const & h4, | |
4088 | T const & h5, | |
4089 | T const & h6) | |
4090 | { | |
4091 | using ::std::cos; | |
4092 | using ::std::sin; | |
4093 | ||
4094 | T a = r*cos(angle); | |
4095 | T b = r*sin(angle); | |
4096 | ||
4097 | return(octonion<T>(a,b,h1,h2,h3,h4,h5,h6)); | |
4098 | } | |
4099 | ||
4100 | ||
4101 | template<typename T> | |
4102 | inline octonion<T> exp(octonion<T> const & o) | |
4103 | { | |
4104 | using ::std::exp; | |
4105 | using ::std::cos; | |
4106 | ||
4107 | using ::boost::math::sinc_pi; | |
4108 | ||
4109 | T u = exp(real(o)); | |
4110 | ||
4111 | T z = abs(unreal(o)); | |
4112 | ||
4113 | T w = sinc_pi(z); | |
4114 | ||
4115 | return(u*octonion<T>(cos(z), | |
4116 | w*o.R_component_2(), w*o.R_component_3(), | |
4117 | w*o.R_component_4(), w*o.R_component_5(), | |
4118 | w*o.R_component_6(), w*o.R_component_7(), | |
4119 | w*o.R_component_8())); | |
4120 | } | |
4121 | ||
4122 | ||
4123 | template<typename T> | |
4124 | inline octonion<T> cos(octonion<T> const & o) | |
4125 | { | |
4126 | using ::std::sin; | |
4127 | using ::std::cos; | |
4128 | using ::std::cosh; | |
4129 | ||
4130 | using ::boost::math::sinhc_pi; | |
4131 | ||
4132 | T z = abs(unreal(o)); | |
4133 | ||
4134 | T w = -sin(o.real())*sinhc_pi(z); | |
4135 | ||
4136 | return(octonion<T>(cos(o.real())*cosh(z), | |
4137 | w*o.R_component_2(), w*o.R_component_3(), | |
4138 | w*o.R_component_4(), w*o.R_component_5(), | |
4139 | w*o.R_component_6(), w*o.R_component_7(), | |
4140 | w*o.R_component_8())); | |
4141 | } | |
4142 | ||
4143 | ||
4144 | template<typename T> | |
4145 | inline octonion<T> sin(octonion<T> const & o) | |
4146 | { | |
4147 | using ::std::sin; | |
4148 | using ::std::cos; | |
4149 | using ::std::cosh; | |
4150 | ||
4151 | using ::boost::math::sinhc_pi; | |
4152 | ||
4153 | T z = abs(unreal(o)); | |
4154 | ||
4155 | T w = +cos(o.real())*sinhc_pi(z); | |
4156 | ||
4157 | return(octonion<T>(sin(o.real())*cosh(z), | |
4158 | w*o.R_component_2(), w*o.R_component_3(), | |
4159 | w*o.R_component_4(), w*o.R_component_5(), | |
4160 | w*o.R_component_6(), w*o.R_component_7(), | |
4161 | w*o.R_component_8())); | |
4162 | } | |
4163 | ||
4164 | ||
4165 | template<typename T> | |
4166 | inline octonion<T> tan(octonion<T> const & o) | |
4167 | { | |
4168 | return(sin(o)/cos(o)); | |
4169 | } | |
4170 | ||
4171 | ||
4172 | template<typename T> | |
4173 | inline octonion<T> cosh(octonion<T> const & o) | |
4174 | { | |
4175 | return((exp(+o)+exp(-o))/static_cast<T>(2)); | |
4176 | } | |
4177 | ||
4178 | ||
4179 | template<typename T> | |
4180 | inline octonion<T> sinh(octonion<T> const & o) | |
4181 | { | |
4182 | return((exp(+o)-exp(-o))/static_cast<T>(2)); | |
4183 | } | |
4184 | ||
4185 | ||
4186 | template<typename T> | |
4187 | inline octonion<T> tanh(octonion<T> const & o) | |
4188 | { | |
4189 | return(sinh(o)/cosh(o)); | |
4190 | } | |
4191 | ||
4192 | ||
4193 | template<typename T> | |
4194 | octonion<T> pow(octonion<T> const & o, | |
4195 | int n) | |
4196 | { | |
4197 | if (n > 1) | |
4198 | { | |
4199 | int m = n>>1; | |
4200 | ||
4201 | octonion<T> result = pow(o, m); | |
4202 | ||
4203 | result *= result; | |
4204 | ||
4205 | if (n != (m<<1)) | |
4206 | { | |
4207 | result *= o; // n odd | |
4208 | } | |
4209 | ||
4210 | return(result); | |
4211 | } | |
4212 | else if (n == 1) | |
4213 | { | |
4214 | return(o); | |
4215 | } | |
4216 | else if (n == 0) | |
4217 | { | |
4218 | return(octonion<T>(static_cast<T>(1))); | |
4219 | } | |
4220 | else /* n < 0 */ | |
4221 | { | |
4222 | return(pow(octonion<T>(static_cast<T>(1))/o,-n)); | |
4223 | } | |
4224 | } | |
4225 | ||
4226 | ||
4227 | // helper templates for converting copy constructors (definition) | |
4228 | ||
4229 | namespace detail | |
4230 | { | |
4231 | ||
4232 | template< typename T, | |
4233 | typename U | |
4234 | > | |
4235 | octonion<T> octonion_type_converter(octonion<U> const & rhs) | |
4236 | { | |
4237 | return(octonion<T>( static_cast<T>(rhs.R_component_1()), | |
4238 | static_cast<T>(rhs.R_component_2()), | |
4239 | static_cast<T>(rhs.R_component_3()), | |
4240 | static_cast<T>(rhs.R_component_4()), | |
4241 | static_cast<T>(rhs.R_component_5()), | |
4242 | static_cast<T>(rhs.R_component_6()), | |
4243 | static_cast<T>(rhs.R_component_7()), | |
4244 | static_cast<T>(rhs.R_component_8()))); | |
4245 | } | |
4246 | } | |
4247 | } | |
4248 | } | |
4249 | ||
4250 | #endif /* BOOST_OCTONION_HPP */ |