1 // test file for octonion.hpp
2
3 // (C) Copyright Hubert Holin 2001.
4 // Distributed under the Boost Software License, Version 1.0. (See
5 // accompanying file LICENSE_1_0.txt or copy at
6 // http://www.boost.org/LICENSE_1_0.txt)
7
8
9 #include <iomanip>
10
11
12 #include <boost/mpl/list.hpp>
13
14 #include <boost/test/unit_test.hpp>
15 #include <boost/test/unit_test_log.hpp>
16
17 #include <boost/math/octonion.hpp>
18
19
20 template<typename T>
21 struct string_type_name;
22
23 #define DEFINE_TYPE_NAME(Type) \
24 template<> struct string_type_name<Type> \
25 { \
26 static char const * _() \
27 { \
28 return #Type; \
29 } \
30 }
31
32 DEFINE_TYPE_NAME(float);
33 DEFINE_TYPE_NAME(double);
34 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
35 DEFINE_TYPE_NAME(long double);
36 #endif
37
38 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
39 typedef boost::mpl::list<float,double,long double> test_types;
40 #else
41 typedef boost::mpl::list<float,double> test_types;
42 #endif
43
44 // Apple GCC 4.0 uses the "double double" format for its long double,
45 // which means that epsilon is VERY small but useless for
46 // comparisons. So, don't do those comparisons.
47 #if (defined(__APPLE_CC__) && defined(__GNUC__) && __GNUC__ == 4) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
48 typedef boost::mpl::list<float,double> near_eps_test_types;
49 #else
50 typedef boost::mpl::list<float,double,long double> near_eps_test_types;
51 #endif
52
53 #if BOOST_WORKAROUND(__GNUC__, < 3)
54 // gcc 2.x ignores function scope using declarations,
55 // put them in the scope of the enclosing namespace instead:
56 using ::std::sqrt;
57 using ::std::atan;
58 using ::std::log;
59 using ::std::exp;
60 using ::std::cos;
61 using ::std::sin;
62 using ::std::tan;
63 using ::std::cosh;
64 using ::std::sinh;
65 using ::std::tanh;
66
67 using ::std::numeric_limits;
68
69 using ::boost::math::abs;
70 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
71
72
73 #ifdef BOOST_NO_STDC_NAMESPACE
74 using ::sqrt;
75 using ::atan;
76 using ::log;
77 using ::exp;
78 using ::cos;
79 using ::sin;
80 using ::tan;
81 using ::cosh;
82 using ::sinh;
83 using ::tanh;
84 #endif /* BOOST_NO_STDC_NAMESPACE */
85
86 #ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
87 using ::boost::math::real;
88 using ::boost::math::unreal;
89 using ::boost::math::sup;
90 using ::boost::math::l1;
91 using ::boost::math::abs;
92 using ::boost::math::norm;
93 using ::boost::math::conj;
94 using ::boost::math::exp;
95 using ::boost::math::pow;
96 using ::boost::math::cos;
97 using ::boost::math::sin;
98 using ::boost::math::tan;
99 using ::boost::math::cosh;
100 using ::boost::math::sinh;
101 using ::boost::math::tanh;
102 using ::boost::math::sinc_pi;
103 using ::boost::math::sinhc_pi;
104 #endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
105
106 // Provide standard floating point abs() overloads if older Microsoft
107 // library is used with _MSC_EXTENSIONS defined. This code also works
108 // for the Intel compiler using the Microsoft library.
109 #if defined(_MSC_EXTENSIONS) && defined(_MSC_VER) && _MSC_VER < 1310
abs(float v)110 inline float abs(float v)
111 {
112 return(fabs(v));
113 }
114
abs(double v)115 inline double abs(double v)
116 {
117 return(fabs(v));
118 }
119
abs(long double v)120 inline long double abs(long double v)
121 {
122 return(fabs(v));
123 }
124 #endif /* BOOST_WORKAROUND(BOOST_MSVC) */
125
126
127 // explicit (if ludicrous) instanciation
128 #if !BOOST_WORKAROUND(__GNUC__, < 3)
129 template class ::boost::math::octonion<int>;
130 #else
131 // gcc doesn't like the absolutely-qualified namespace
132 template class boost::math::octonion<int>;
133 #endif /* !BOOST_WORKAROUND(__GNUC__) */
134
135
136 namespace
137 {
138 template<typename T>
index_i_element(int idx)139 ::boost::math::octonion<T> index_i_element(int idx)
140 {
141 return(
142 ::boost::math::octonion<T>(
143 (idx == 0) ?
144 static_cast<T>(1) :
145 static_cast<T>(0),
146 (idx == 1) ?
147 static_cast<T>(1) :
148 static_cast<T>(0),
149 (idx == 2) ?
150 static_cast<T>(1) :
151 static_cast<T>(0),
152 (idx == 3) ?
153 static_cast<T>(1) :
154 static_cast<T>(0),
155 (idx == 4) ?
156 static_cast<T>(1) :
157 static_cast<T>(0),
158 (idx == 5) ?
159 static_cast<T>(1) :
160 static_cast<T>(0),
161 (idx == 6) ?
162 static_cast<T>(1) :
163 static_cast<T>(0),
164 (idx == 7) ?
165 static_cast<T>(1) :
166 static_cast<T>(0)
167 ));
168 }
169 }
170
171
172
octonion_manual_test()173 void octonion_manual_test()
174 {
175 // tests for evaluation by humans
176
177
178 // using default constructor
179 ::boost::math::octonion<float> o0;
180
181 ::boost::math::octonion<float> oa[2];
182
183 // using constructor "O seen as R^8"
184 ::boost::math::octonion<float> o1(1,2,3,4,5,6,7,8);
185
186 ::std::complex<double> c0(9,10);
187
188 // using constructor "O seen as C^4"
189 ::boost::math::octonion<double> o2(c0);
190
191 ::boost::math::quaternion<long double> q0(11,12,13,14);
192
193 // using constructor "O seen as H^2"
194 ::boost::math::octonion<long double> o3(q0);
195
196 // using UNtemplated copy constructor
197 ::boost::math::octonion<float> o4(o1);
198
199 // using templated copy constructor
200 ::boost::math::octonion<long double> o5(o2);
201
202 // using UNtemplated assignment operator
203 o5 = o3;
204 oa[0] = o0;
205
206 // using templated assignment operator
207 o5 = o2;
208 oa[1] = o5;
209
210 float f0(15);
211
212 // using converting assignment operator
213 o0 = f0;
214
215 // using converting assignment operator
216 o2 = c0;
217
218 // using converting assignment operator
219 o5 = q0;
220
221 // using += (const T &)
222 o4 += f0;
223
224 // using += (const ::std::complex<T> &)
225 o2 += c0;
226
227 // using += (const ::boost::math::quaternion<T> &)
228 o3 += q0;
229
230 // using += (const quaternion<X> &)
231 o5 += o4;
232
233 // using -= (const T &)
234 o1 -= f0;
235
236 // using -= (const ::std::complex<T> &)
237 o2 -= c0;
238
239 // using -= (const ::boost::math::quaternion<T> &)
240 o5 -= q0;
241
242 // using -= (const octonion<X> &)
243 o3 -= o4;
244
245 double d0(16);
246 ::std::complex<double> c1(17,18);
247 ::boost::math::quaternion<double> q1(19,20,21,22);
248
249 // using *= (const T &)
250 o2 *= d0;
251
252 // using *= (const ::std::complex<T> &)
253 o2 *= c1;
254
255 // using *= (const ::boost::math::quaternion<T> &)
256 o2 *= q1;
257
258 // using *= (const octonion<X> &)
259 o2 *= o4;
260
261 long double l0(23);
262 ::std::complex<long double> c2(24,25);
263
264 // using /= (const T &)
265 o5 /= l0;
266
267 // using /= (const ::std::complex<T> &)
268 o5 /= c2;
269
270 // using /= (const quaternion<X> &)
271 o5 /= q0;
272
273 // using /= (const octonion<X> &)
274 o5 /= o5;
275
276 // using + (const T &, const octonion<T> &)
277 ::boost::math::octonion<float> o6 = f0+o0;
278
279 // using + (const octonion<T> &, const T &)
280 ::boost::math::octonion<float> o7 = o0+f0;
281
282 // using + (const ::std::complex<T> &, const quaternion<T> &)
283 ::boost::math::octonion<double> o8 = c0+o2;
284
285 // using + (const octonion<T> &, const ::std::complex<T> &)
286 ::boost::math::octonion<double> o9 = o2+c0;
287
288 // using + (const ::boost::math::quaternion<T>, const octonion<T> &)
289 ::boost::math::octonion<long double> o10 = q0+o3;
290
291 // using + (const octonion<T> &, const ::boost::math::quaternion<T> &)
292 ::boost::math::octonion<long double> o11 = o3+q0;
293
294 // using + (const quaternion<T> &,const quaternion<T> &)
295 ::boost::math::octonion<float> o12 = o0+o4;
296
297 // using - (const T &, const octonion<T> &)
298 o6 = f0-o0;
299
300 // using - (const octonion<T> &, const T &)
301 o7 = o0-f0;
302
303 // using - (const ::std::complex<T> &, const octonion<T> &)
304 o8 = c0-o2;
305
306 // using - (const octonion<T> &, const ::std::complex<T> &)
307 o9 = o2-c0;
308
309 // using - (const quaternion<T> &,const octonion<T> &)
310 o10 = q0-o3;
311
312 // using - (const octonion<T> &,const quaternion<T> &)
313 o11 = o3-q0;
314
315 // using - (const octonion<T> &,const octonion<T> &)
316 o12 = o0-o4;
317
318 // using * (const T &, const octonion<T> &)
319 o6 = f0*o0;
320
321 // using * (const octonion<T> &, const T &)
322 o7 = o0*f0;
323
324 // using * (const ::std::complex<T> &, const octonion<T> &)
325 o8 = c0*o2;
326
327 // using * (const octonion<T> &, const ::std::complex<T> &)
328 o9 = o2*c0;
329
330 // using * (const quaternion<T> &,const octonion<T> &)
331 o10 = q0*o3;
332
333 // using * (const octonion<T> &,const quaternion<T> &)
334 o11 = o3*q0;
335
336 // using * (const octonion<T> &,const octonion<T> &)
337 o12 = o0*o4;
338
339 // using / (const T &, const octonion<T> &)
340 o6 = f0/o0;
341
342 // using / (const octonion<T> &, const T &)
343 o7 = o0/f0;
344
345 // using / (const ::std::complex<T> &, const octonion<T> &)
346 o8 = c0/o2;
347
348 // using / (const octonion<T> &, const ::std::complex<T> &)
349 o9 = o2/c0;
350
351 // using / (const ::boost::math::quaternion<T> &, const octonion<T> &)
352 o10 = q0/o3;
353
354 // using / (const octonion<T> &, const ::boost::math::quaternion<T> &)
355 o11 = o3/q0;
356
357 // using / (const octonion<T> &,const octonion<T> &)
358 o12 = o0/o4;
359
360 // using + (const octonion<T> &)
361 o4 = +o0;
362
363 // using - (const octonion<T> &)
364 o0 = -o4;
365
366 // using == (const T &, const octonion<T> &)
367 f0 == o0;
368
369 // using == (const octonion<T> &, const T &)
370 o0 == f0;
371
372 // using == (const ::std::complex<T> &, const octonion<T> &)
373 c0 == o2;
374
375 // using == (const octonion<T> &, const ::std::complex<T> &)
376 o2 == c0;
377
378 // using == (const ::boost::math::quaternion<T> &, const octonion<T> &)
379 q0 == o3;
380
381 // using == (const octonion<T> &, const ::boost::math::quaternion<T> &)
382 o3 == q0;
383
384 // using == (const octonion<T> &,const octonion<T> &)
385 o0 == o4;
386
387 // using != (const T &, const octonion<T> &)
388 f0 != o0;
389
390 // using != (const octonion<T> &, const T &)
391 o0 != f0;
392
393 // using != (const ::std::complex<T> &, const octonion<T> &)
394 c0 != o2;
395
396 // using != (const octonion<T> &, const ::std::complex<T> &)
397 o2 != c0;
398
399 // using != (const ::boost::math::quaternion<T> &, const octonion<T> &)
400 q0 != o3;
401
402 // using != (const octonion<T> &, const ::boost::math::quaternion<T> &)
403 o3 != q0;
404
405 // using != (const octonion<T> &,const octonion<T> &)
406 o0 != o4;
407
408 BOOST_TEST_MESSAGE("Please input an octonion...");
409
410 #ifdef BOOST_INTERACTIVE_TEST_INPUT_ITERATOR
411 ::std::cin >> o0;
412
413 if (::std::cin.fail())
414 {
415 BOOST_TEST_MESSAGE("You have entered nonsense!");
416 }
417 else
418 {
419 BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
420 }
421 #else
422 ::std::istringstream bogus("(1,2,3,4,5,6,7,8)");
423
424 bogus >> o0;
425
426 BOOST_TEST_MESSAGE("You have entered the octonion " << o0 << " .");
427 #endif
428
429 BOOST_TEST_MESSAGE("For this octonion:");
430
431 BOOST_TEST_MESSAGE( "the value of the real part is "
432 << real(o0));
433
434 BOOST_TEST_MESSAGE( "the value of the unreal part is "
435 << unreal(o0));
436
437 BOOST_TEST_MESSAGE( "the value of the sup norm is "
438 << sup(o0));
439
440 BOOST_TEST_MESSAGE( "the value of the l1 norm is "
441 << l1(o0));
442
443 BOOST_TEST_MESSAGE( "the value of the magnitude (Euclidean norm) is "
444 << abs(o0));
445
446 BOOST_TEST_MESSAGE( "the value of the (Cayley) norm is "
447 << norm(o0));
448
449 BOOST_TEST_MESSAGE( "the value of the conjugate is "
450 << conj(o0));
451
452 BOOST_TEST_MESSAGE( "the value of the exponential is "
453 << exp(o0));
454
455 BOOST_TEST_MESSAGE( "the value of the cube is "
456 << pow(o0,3));
457
458 BOOST_TEST_MESSAGE( "the value of the cosinus is "
459 << cos(o0));
460
461 BOOST_TEST_MESSAGE( "the value of the sinus is "
462 << sin(o0));
463
464 BOOST_TEST_MESSAGE( "the value of the tangent is "
465 << tan(o0));
466
467 BOOST_TEST_MESSAGE( "the value of the hyperbolic cosinus is "
468 << cosh(o0));
469
470 BOOST_TEST_MESSAGE( "the value of the hyperbolic sinus is "
471 << sinh(o0));
472
473 BOOST_TEST_MESSAGE( "the value of the hyperbolic tangent is "
474 << tanh(o0));
475
476 #ifdef BOOST_NO_TEMPLATE_TEMPLATES
477 BOOST_TEST_MESSAGE( "no template templates, can't compute cardinal functions");
478 #else /* BOOST_NO_TEMPLATE_TEMPLATES */
479 BOOST_TEST_MESSAGE( "the value of the Sinus Cardinal (of index pi) is "
480 << sinc_pi(o0));
481
482 BOOST_TEST_MESSAGE( "the value of "
483 << "the Hyperbolic Sinus Cardinal (of index pi) is "
484 << sinhc_pi(o0));
485 #endif /* BOOST_NO_TEMPLATE_TEMPLATES */
486
487 BOOST_TEST_MESSAGE(" ");
488
489 float rho = ::std::sqrt(4096.0f);
490 float theta = ::std::atan(1.0f);
491 float phi1 = ::std::atan(1.0f);
492 float phi2 = ::std::atan(1.0f);
493 float phi3 = ::std::atan(1.0f);
494 float phi4 = ::std::atan(1.0f);
495 float phi5 = ::std::atan(1.0f);
496 float phi6 = ::std::atan(1.0f);
497
498 BOOST_TEST_MESSAGE( "The value of the octonion represented "
499 << "in spherical form by "
500 << "rho = " << rho << " , theta = " << theta
501 << " , phi1 = " << phi1 << " , phi2 = " << phi2
502 << " , phi3 = " << phi3 << " , phi4 = " << phi4
503 << " , phi5 = " << phi5 << " , phi6 = " << phi6
504 << " is "
505 << ::boost::math::spherical(rho, theta,
506 phi1, phi2, phi3, phi4, phi5, phi6));
507
508 float rho1 = 1;
509 float rho2 = 2;
510 float rho3 = ::std::sqrt(2.0f);
511 float rho4 = ::std::sqrt(8.0f);
512 float theta1 = 0;
513 float theta2 = ::std::atan(1.0f)*2;
514 float theta3 = ::std::atan(1.0f);
515 float theta4 = ::std::atan(::std::sqrt(3.0f));
516
517 BOOST_TEST_MESSAGE( "The value of the octonion represented "
518 << "in multipolar form by "
519 << "rho1 = " << rho1 << " , theta1 = " << theta1
520 << " , rho2 = " << rho2 << " , theta2 = " << theta2
521 << "rho3 = " << rho3 << " , theta3 = " << theta3
522 << " , rho4 = " << rho4 << " , theta4 = " << theta4
523 << " is "
524 << ::boost::math::multipolar(rho1, theta1, rho2, theta2,
525 rho3, theta3, rho4, theta4));
526
527 float r = ::std::sqrt(2.0f);
528 float angle = ::std::atan(1.0f);
529 float h1 = 3;
530 float h2 = 4;
531 float h3 = 5;
532 float h4 = 6;
533 float h5 = 7;
534 float h6 = 8;
535
536 BOOST_TEST_MESSAGE( "The value of the octonion represented "
537 << "in cylindrical form by "
538 << "r = " << r << " , angle = " << angle
539 << " , h1 = " << h1 << " , h2 = " << h2
540 << " , h3 = " << h3 << " , h4 = " << h4
541 << " , h5 = " << h5 << " , h6 = " << h6
542 << " is " << ::boost::math::cylindrical(r, angle,
543 h1, h2, h3, h4, h5, h6));
544
545 double real_1(1);
546 ::std::complex<double> complex_1(1);
547 ::std::complex<double> complex_i(0,1);
548 ::boost::math::quaternion<double> quaternion_1(1);
549 ::boost::math::quaternion<double> quaternion_i(0,1);
550 ::boost::math::quaternion<double> quaternion_j(0,0,1);
551 ::boost::math::quaternion<double> quaternion_k(0,0,0,1);
552 ::boost::math::octonion<double> octonion_1(1);
553 ::boost::math::octonion<double> octonion_i(0,1);
554 ::boost::math::octonion<double> octonion_j(0,0,1);
555 ::boost::math::octonion<double> octonion_k(0,0,0,1);
556 ::boost::math::octonion<double> octonion_e_prime(0,0,0,0,1);
557 ::boost::math::octonion<double> octonion_i_prime(0,0,0,0,0,1);
558 ::boost::math::octonion<double> octonion_j_prime(0,0,0,0,0,0,1);
559 ::boost::math::octonion<double> octonion_k_prime(0,0,0,0,0,0,0,1);
560
561
562 BOOST_TEST_MESSAGE(" ");
563
564 BOOST_TEST_MESSAGE( "Real 1: " << real_1
565 << " ; Complex 1: " << complex_1
566 << " ; Quaternion 1: " << quaternion_1
567 << " ; Octonion 1: " << octonion_1 << " .");
568
569 BOOST_TEST_MESSAGE( "Complex i: " << complex_i
570 << " ; Quaternion i: " << quaternion_i
571 << " ; Octonion i : " << octonion_i << " .");
572
573 BOOST_TEST_MESSAGE( "Quaternion j: " << quaternion_j
574 << " ; Octonion j: " << octonion_j << " .");
575
576 BOOST_TEST_MESSAGE( "Quaternion k: " << quaternion_k
577 << " ; Octonion k: " << octonion_k << " .");
578
579 BOOST_TEST_MESSAGE( "Quaternion e\': " << octonion_e_prime << " .");
580
581 BOOST_TEST_MESSAGE( "Quaternion i\': " << octonion_i_prime << " .");
582
583 BOOST_TEST_MESSAGE( "Quaternion j\': " << octonion_j_prime << " .");
584
585 BOOST_TEST_MESSAGE( "Quaternion k\': " << octonion_k_prime << " .");
586
587 BOOST_TEST_MESSAGE(" ");
588
589 BOOST_TEST_MESSAGE( octonion_1*octonion_1 << " ; "
590 << octonion_1*octonion_i << " ; "
591 << octonion_1*octonion_j << " ; "
592 << octonion_1*octonion_k << " ; "
593 << octonion_1*octonion_e_prime << " ; "
594 << octonion_1*octonion_i_prime << " ; "
595 << octonion_1*octonion_j_prime << " ; "
596 << octonion_1*octonion_k_prime << " ; ");
597
598 BOOST_TEST_MESSAGE( octonion_i*octonion_1 << " ; "
599 << octonion_i*octonion_i << " ; "
600 << octonion_i*octonion_j << " ; "
601 << octonion_i*octonion_k << " ; "
602 << octonion_i*octonion_e_prime << " ; "
603 << octonion_i*octonion_i_prime << " ; "
604 << octonion_i*octonion_j_prime << " ; "
605 << octonion_i*octonion_k_prime << " ; ");
606
607 BOOST_TEST_MESSAGE( octonion_j*octonion_1 << " ; "
608 << octonion_j*octonion_i << " ; "
609 << octonion_j*octonion_j << " ; "
610 << octonion_j*octonion_k << " ; "
611 << octonion_j*octonion_e_prime << " ; "
612 << octonion_j*octonion_i_prime << " ; "
613 << octonion_j*octonion_j_prime << " ; "
614 << octonion_j*octonion_k_prime << " ; ");
615
616 BOOST_TEST_MESSAGE( octonion_k*octonion_1 << " ; "
617 << octonion_k*octonion_i << " ; "
618 << octonion_k*octonion_j << " ; "
619 << octonion_k*octonion_k << " ; "
620 << octonion_k*octonion_e_prime << " ; "
621 << octonion_k*octonion_i_prime << " ; "
622 << octonion_k*octonion_j_prime << " ; "
623 << octonion_k*octonion_k_prime << " ; ");
624
625 BOOST_TEST_MESSAGE( octonion_e_prime*octonion_1 << " ; "
626 << octonion_e_prime*octonion_i << " ; "
627 << octonion_e_prime*octonion_j << " ; "
628 << octonion_e_prime*octonion_k << " ; "
629 << octonion_e_prime*octonion_e_prime << " ; "
630 << octonion_e_prime*octonion_i_prime << " ; "
631 << octonion_e_prime*octonion_j_prime << " ; "
632 << octonion_e_prime*octonion_k_prime << " ; ");
633
634 BOOST_TEST_MESSAGE( octonion_i_prime*octonion_1 << " ; "
635 << octonion_i_prime*octonion_i << " ; "
636 << octonion_i_prime*octonion_j << " ; "
637 << octonion_i_prime*octonion_k << " ; "
638 << octonion_i_prime*octonion_e_prime << " ; "
639 << octonion_i_prime*octonion_i_prime << " ; "
640 << octonion_i_prime*octonion_j_prime << " ; "
641 << octonion_i_prime*octonion_k_prime << " ; ");
642
643 BOOST_TEST_MESSAGE( octonion_j_prime*octonion_1 << " ; "
644 << octonion_j_prime*octonion_i << " ; "
645 << octonion_j_prime*octonion_j << " ; "
646 << octonion_j_prime*octonion_k << " ; "
647 << octonion_j_prime*octonion_e_prime << " ; "
648 << octonion_j_prime*octonion_i_prime << " ; "
649 << octonion_j_prime*octonion_j_prime << " ; "
650 << octonion_j_prime*octonion_k_prime << " ; ");
651
652 BOOST_TEST_MESSAGE( octonion_k_prime*octonion_1 << " ; "
653 << octonion_k_prime*octonion_i << " ; "
654 << octonion_k_prime*octonion_j << " ; "
655 << octonion_k_prime*octonion_k << " ; "
656 << octonion_k_prime*octonion_e_prime << " ; "
657 << octonion_k_prime*octonion_i_prime << " ; "
658 << octonion_k_prime*octonion_j_prime << " ; "
659 << octonion_k_prime*octonion_k_prime << " ; ");
660
661 BOOST_TEST_MESSAGE(" ");
662
663 BOOST_TEST_MESSAGE("i\'*(e\'*j) : "
664 << octonion_i_prime*(octonion_e_prime*octonion_j) << " ;");
665
666 BOOST_TEST_MESSAGE("(i\'*e\')*j : "
667 << (octonion_i_prime*octonion_e_prime)*octonion_j << " ;");
668
669 BOOST_TEST_MESSAGE(" ");
670 }
671
672
BOOST_TEST_CASE_TEMPLATE_FUNCTION(multiplication_test,T)673 BOOST_TEST_CASE_TEMPLATE_FUNCTION(multiplication_test, T)
674 {
675 #if BOOST_WORKAROUND(__GNUC__, < 3)
676 #else /* BOOST_WORKAROUND(__GNUC__, < 3) */
677 using ::std::numeric_limits;
678
679 using ::boost::math::abs;
680 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
681
682
683 BOOST_TEST_MESSAGE("Testing multiplication for "
684 << string_type_name<T>::_() << ".");
685
686 BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
687 (abs(::boost::math::octonion<T>(1,0,0,0,0,0,0,0)*
688 ::boost::math::octonion<T>(1,0,0,0,0,0,0,0)-
689 static_cast<T>(1)))
690 (numeric_limits<T>::epsilon()));
691
692 for (int idx = 1; idx < 8; ++idx)
693 {
694 ::boost::math::octonion<T> toto = index_i_element<T>(idx);
695
696 BOOST_REQUIRE_PREDICATE(::std::less_equal<T>(),
697 (abs(toto*toto+static_cast<T>(1)))
698 (numeric_limits<T>::epsilon()));
699 }
700 }
701
702
BOOST_TEST_CASE_TEMPLATE_FUNCTION(exp_test,T)703 BOOST_TEST_CASE_TEMPLATE_FUNCTION(exp_test, T)
704 {
705 #if BOOST_WORKAROUND(__GNUC__, < 3)
706 #else /* BOOST_WORKAROUND(__GNUC__, < 3) */
707 using ::std::numeric_limits;
708
709 using ::std::atan;
710
711 using ::boost::math::abs;
712 #endif /* BOOST_WORKAROUND(__GNUC__, < 3) */
713
714
715 BOOST_TEST_MESSAGE("Testing exp for "
716 << string_type_name<T>::_() << ".");
717
718 for (int idx = 1; idx < 8; ++idx)
719 {
720 ::boost::math::octonion<T> toto =
721 static_cast<T>(4)*atan(static_cast<T>(1))*index_i_element<T>(idx);
722
723 BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
724 (abs(exp(toto)+static_cast<T>(1)))
725 (2*numeric_limits<T>::epsilon()));
726 }
727 }
728
729
init_unit_test_suite(int,char * [])730 boost::unit_test::test_suite * init_unit_test_suite(int, char *[])
731 {
732 ::boost::unit_test::unit_test_log.
733 set_threshold_level(::boost::unit_test::log_messages);
734
735 boost::unit_test::test_suite * test =
736 BOOST_TEST_SUITE("octonion_test");
737
738 BOOST_TEST_MESSAGE("Results of octonion test.");
739 BOOST_TEST_MESSAGE(" ");
740 BOOST_TEST_MESSAGE("(C) Copyright Hubert Holin 2003-2005.");
741 BOOST_TEST_MESSAGE("Distributed under the Boost Software License, Version 1.0.");
742 BOOST_TEST_MESSAGE("(See accompanying file LICENSE_1_0.txt or copy at");
743 BOOST_TEST_MESSAGE("http://www.boost.org/LICENSE_1_0.txt)");
744 BOOST_TEST_MESSAGE(" ");
745
746 #define BOOST_OCTONION_COMMON_GENERATOR(fct) \
747 test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, test_types));
748
749 #define BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(fct) \
750 test->add(BOOST_TEST_CASE_TEMPLATE(fct##_test, near_eps_test_types));
751
752
753 #define BOOST_OCTONION_TEST \
754 BOOST_OCTONION_COMMON_GENERATOR(multiplication) \
755 BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS(exp)
756
757
758 BOOST_OCTONION_TEST
759
760
761 #undef BOOST_OCTONION_TEST
762
763 #undef BOOST_OCTONION_COMMON_GENERATOR
764 #undef BOOST_OCTONION_COMMON_GENERATOR_NEAR_EPS
765
766 #ifdef BOOST_OCTONION_TEST_VERBOSE
767
768 test->add(BOOST_TEST_CASE(octonion_manual_test));
769
770 #endif /* BOOST_OCTONION_TEST_VERBOSE */
771
772 return test;
773 }
774
775 #undef DEFINE_TYPE_NAME
776