1 // 2007-02-04  Edward Smith-Rowland <3dw4rd@verizon.net>
2 //
3 // Copyright (C) 2007-2016 Free Software Foundation, Inc.
4 //
5 // This file is part of the GNU ISO C++ Library.  This library is free
6 // software; you can redistribute it and/or modify it under the
7 // terms of the GNU General Public License as published by the
8 // Free Software Foundation; either version 3, or (at your option)
9 // any later version.
10 //
11 // This library is distributed in the hope that it will be useful,
12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14 // GNU General Public License for more details.
15 //
16 // You should have received a copy of the GNU General Public License along
17 // with this library; see the file COPYING3.  If not see
18 // <http://www.gnu.org/licenses/>.
19 
20 //  sph_neumann
21 
22 
23 //  Compare against values generated by the GNU Scientific Library.
24 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
25 
26 #include <tr1/cmath>
27 #if defined(__TEST_DEBUG)
28 #include <iostream>
29 #define VERIFY(A) \
30 if (!(A)) \
31   { \
32     std::cout << "line " << __LINE__ \
33       << "  max_abs_frac = " << max_abs_frac \
34       << std::endl; \
35   }
36 #else
37 #include <testsuite_hooks.h>
38 #endif
39 #include "../testcase.h"
40 
41 
42 // Test data for n=0.
43 testcase_sph_neumann<double> data001[] = {
44   { -3.8756496868425789, 0, 0.25000000000000000 },
45   { -1.7551651237807455, 0, 0.50000000000000000 },
46   { -0.97558515849842786, 0, 0.75000000000000000 },
47   { -0.54030230586813977, 0, 1.0000000000000000 },
48   { -0.25225788991621495, 0, 1.2500000000000000 },
49   { -0.047158134445135273, 0, 1.5000000000000000 },
50   { 0.10185488894256690, 0, 1.7500000000000000 },
51   { 0.20807341827357120, 0, 2.0000000000000000 },
52   { 0.27918827676566177, 0, 2.2500000000000000 },
53   { 0.32045744621877348, 0, 2.5000000000000000 },
54   { 0.33610995586635040, 0, 2.7500000000000000 },
55   { 0.32999749886681512, 0, 3.0000000000000000 },
56   { 0.30588605417862963, 0, 3.2500000000000000 },
57   { 0.26755905351165610, 0, 3.5000000000000000 },
58   { 0.21881582862388288, 0, 3.7500000000000000 },
59   { 0.16341090521590299, 0, 4.0000000000000000 },
60   { 0.10496176233265714, 0, 4.2500000000000000 },
61   { 0.046843510984617719, 0, 4.5000000000000000 },
62   { -0.0079162427132582220, 0, 4.7500000000000000 },
63   { -0.056732437092645263, 0, 5.0000000000000000 },
64 };
65 
66 // Test function for n=0.
67 template<typename Tp>
68   void
test001()69   test001()
70   {
71     bool test [[gnu::unused]] = true;
72     const Tp eps = std::numeric_limits<Tp>::epsilon();
73     Tp max_abs_diff = -Tp(1);
74     Tp max_abs_frac = -Tp(1);
75     unsigned int num_datum = sizeof(data001)
76 			   / sizeof(testcase_sph_neumann<double>);
77     for (unsigned int i = 0; i < num_datum; ++i)
78       {
79 	const Tp f = std::tr1::sph_neumann(Tp(data001[i].n), Tp(data001[i].x));
80 	const Tp f0 = data001[i].f0;
81 	const Tp diff = f - f0;
82 	if (std::abs(diff) > max_abs_diff)
83 	  max_abs_diff = std::abs(diff);
84 	if (std::abs(f0) > Tp(10) * eps
85 	 && std::abs(f) > Tp(10) * eps)
86 	  {
87 	    const Tp frac = diff / f0;
88 	    if (std::abs(frac) > max_abs_frac)
89 	      max_abs_frac = std::abs(frac);
90 	  }
91       }
92     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
93   }
94 
95 // Test data for n=1.
96 testcase_sph_neumann<double> data002[] = {
97   { -16.492214584388407, 1, 0.25000000000000000 },
98   { -4.4691813247698970, 1, 0.50000000000000000 },
99   { -2.2096318913623492, 1, 0.75000000000000000 },
100   { -1.3817732906760363, 1, 1.0000000000000000 },
101   { -0.96099400741744090, 1, 1.2500000000000000 },
102   { -0.69643541403279308, 1, 1.5000000000000000 },
103   { -0.50407489024649721, 1, 1.7500000000000000 },
104   { -0.35061200427605527, 1, 2.0000000000000000 },
105   { -0.22172663116544869, 1, 2.2500000000000000 },
106   { -0.11120587915407318, 1, 2.5000000000000000 },
107   { -0.016564013158538646, 1, 2.7500000000000000 },
108   { 0.062959163602315973, 1, 3.0000000000000000 },
109   { 0.12740959652576553, 1, 3.2500000000000000 },
110   { 0.17666922320036457, 1, 3.5000000000000000 },
111   { 0.21076723929766045, 1, 3.7500000000000000 },
112   { 0.23005335013095779, 1, 4.0000000000000000 },
113   { 0.23528261660264485, 1, 4.2500000000000000 },
114   { 0.22763858414438104, 1, 4.5000000000000000 },
115   { 0.20871085184465679, 1, 4.7500000000000000 },
116   { 0.18043836751409864, 1, 5.0000000000000000 },
117 };
118 
119 // Test function for n=1.
120 template<typename Tp>
121   void
test002()122   test002()
123   {
124     bool test [[gnu::unused]] = true;
125     const Tp eps = std::numeric_limits<Tp>::epsilon();
126     Tp max_abs_diff = -Tp(1);
127     Tp max_abs_frac = -Tp(1);
128     unsigned int num_datum = sizeof(data002)
129 			   / sizeof(testcase_sph_neumann<double>);
130     for (unsigned int i = 0; i < num_datum; ++i)
131       {
132 	const Tp f = std::tr1::sph_neumann(Tp(data002[i].n), Tp(data002[i].x));
133 	const Tp f0 = data002[i].f0;
134 	const Tp diff = f - f0;
135 	if (std::abs(diff) > max_abs_diff)
136 	  max_abs_diff = std::abs(diff);
137 	if (std::abs(f0) > Tp(10) * eps
138 	 && std::abs(f) > Tp(10) * eps)
139 	  {
140 	    const Tp frac = diff / f0;
141 	    if (std::abs(frac) > max_abs_frac)
142 	      max_abs_frac = std::abs(frac);
143 	  }
144       }
145     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
146   }
147 
148 // Test data for n=2.
149 testcase_sph_neumann<double> data003[] = {
150   { -194.03092532581832, 2, 0.25000000000000000 },
151   { -25.059922824838637, 2, 0.50000000000000000 },
152   { -7.8629424069509692, 2, 0.75000000000000000 },
153   { -3.6050175661599688, 2, 1.0000000000000000 },
154   { -2.0541277278856431, 2, 1.2500000000000000 },
155   { -1.3457126936204509, 2, 1.5000000000000000 },
156   { -0.96598327222227631, 2, 1.7500000000000000 },
157   { -0.73399142468765399, 2, 2.0000000000000000 },
158   { -0.57482378498626008, 2, 2.2500000000000000 },
159   { -0.45390450120366133, 2, 2.5000000000000000 },
160   { -0.35417978840293796, 2, 2.7500000000000000 },
161   { -0.26703833526449916, 2, 3.0000000000000000 },
162   { -0.18827719584715374, 2, 3.2500000000000000 },
163   { -0.11612829076848646, 2, 3.5000000000000000 },
164   { -0.050202037185754500, 2, 3.7500000000000000 },
165   { 0.0091291073823153435, 2, 4.0000000000000000 },
166   { 0.061120084680974532, 2, 4.2500000000000000 },
167   { 0.10491554511163632, 2, 4.5000000000000000 },
168   { 0.13973362282567303, 2, 4.7500000000000000 },
169   { 0.16499545760110443, 2, 5.0000000000000000 },
170 };
171 
172 // Test function for n=2.
173 template<typename Tp>
174   void
test003()175   test003()
176   {
177     bool test [[gnu::unused]] = true;
178     const Tp eps = std::numeric_limits<Tp>::epsilon();
179     Tp max_abs_diff = -Tp(1);
180     Tp max_abs_frac = -Tp(1);
181     unsigned int num_datum = sizeof(data003)
182 			   / sizeof(testcase_sph_neumann<double>);
183     for (unsigned int i = 0; i < num_datum; ++i)
184       {
185 	const Tp f = std::tr1::sph_neumann(Tp(data003[i].n), Tp(data003[i].x));
186 	const Tp f0 = data003[i].f0;
187 	const Tp diff = f - f0;
188 	if (std::abs(diff) > max_abs_diff)
189 	  max_abs_diff = std::abs(diff);
190 	if (std::abs(f0) > Tp(10) * eps
191 	 && std::abs(f) > Tp(10) * eps)
192 	  {
193 	    const Tp frac = diff / f0;
194 	    if (std::abs(frac) > max_abs_frac)
195 	      max_abs_frac = std::abs(frac);
196 	  }
197       }
198     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
199   }
200 
201 // Test data for n=5.
202 testcase_sph_neumann<double> data004[] = {
203   { -3884190.0626637731, 5, 0.25000000000000000 },
204   { -61327.563166980639, 5, 0.50000000000000000 },
205   { -5478.9529323190836, 5, 0.75000000000000000 },
206   { -999.44034339223640, 5, 1.0000000000000000 },
207   { -270.49720502942358, 5, 1.2500000000000000 },
208   { -94.236110085232468, 5, 1.5000000000000000 },
209   { -39.182827786584333, 5, 1.7500000000000000 },
210   { -18.591445311190984, 5, 2.0000000000000000 },
211   { -9.7821420203182274, 5, 2.2500000000000000 },
212   { -5.5991001548063233, 5, 2.5000000000000000 },
213   { -3.4400655233636823, 5, 2.7500000000000000 },
214   { -2.2470233284653904, 5, 3.0000000000000000 },
215   { -1.5491439945779160, 5, 3.2500000000000000 },
216   { -1.1205896325654248, 5, 3.5000000000000000 },
217   { -0.84592255605194844, 5, 3.7500000000000000 },
218   { -0.66280126645045878, 5, 4.0000000000000000 },
219   { -0.53589374436038528, 5, 4.2500000000000000 },
220   { -0.44430324229090551, 5, 4.5000000000000000 },
221   { -0.37520157232899892, 5, 4.7500000000000000 },
222   { -0.32046504674973919, 5, 5.0000000000000000 },
223 };
224 
225 // Test function for n=5.
226 template<typename Tp>
227   void
test004()228   test004()
229   {
230     bool test [[gnu::unused]] = true;
231     const Tp eps = std::numeric_limits<Tp>::epsilon();
232     Tp max_abs_diff = -Tp(1);
233     Tp max_abs_frac = -Tp(1);
234     unsigned int num_datum = sizeof(data004)
235 			   / sizeof(testcase_sph_neumann<double>);
236     for (unsigned int i = 0; i < num_datum; ++i)
237       {
238 	const Tp f = std::tr1::sph_neumann(Tp(data004[i].n), Tp(data004[i].x));
239 	const Tp f0 = data004[i].f0;
240 	const Tp diff = f - f0;
241 	if (std::abs(diff) > max_abs_diff)
242 	  max_abs_diff = std::abs(diff);
243 	if (std::abs(f0) > Tp(10) * eps
244 	 && std::abs(f) > Tp(10) * eps)
245 	  {
246 	    const Tp frac = diff / f0;
247 	    if (std::abs(frac) > max_abs_frac)
248 	      max_abs_frac = std::abs(frac);
249 	  }
250       }
251     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
252   }
253 
254 // Test data for n=10.
255 testcase_sph_neumann<double> data005[] = {
256   { -2750653598174213.5, 10, 0.25000000000000000 },
257   { -1349739281107.0554, 10, 0.50000000000000000 },
258   { -15733380424.953760, 10, 0.75000000000000000 },
259   { -672215008.25620842, 10, 1.0000000000000000 },
260   { -58607405.988679446, 10, 1.2500000000000000 },
261   { -8032728.8148234813, 10, 1.5000000000000000 },
262   { -1505955.5720640516, 10, 1.7500000000000000 },
263   { -355414.72008543846, 10, 2.0000000000000000 },
264   { -100086.80374425423, 10, 2.2500000000000000 },
265   { -32423.794085334419, 10, 2.5000000000000000 },
266   { -11772.863161809979, 10, 2.7500000000000000 },
267   { -4699.8591888113924, 10, 3.0000000000000000 },
268   { -2033.0183273853759, 10, 3.2500000000000000 },
269   { -942.19075028425493, 10, 3.5000000000000000 },
270   { -463.65206971202474, 10, 3.7500000000000000 },
271   { -240.53552987988931, 10, 4.0000000000000000 },
272   { -130.78478404631085, 10, 4.2500000000000000 },
273   { -74.170665501737531, 10, 4.5000000000000000 },
274   { -43.698249898184983, 10, 4.7500000000000000 },
275   { -26.656114405718711, 10, 5.0000000000000000 },
276 };
277 
278 // Test function for n=10.
279 template<typename Tp>
280   void
test005()281   test005()
282   {
283     bool test [[gnu::unused]] = true;
284     const Tp eps = std::numeric_limits<Tp>::epsilon();
285     Tp max_abs_diff = -Tp(1);
286     Tp max_abs_frac = -Tp(1);
287     unsigned int num_datum = sizeof(data005)
288 			   / sizeof(testcase_sph_neumann<double>);
289     for (unsigned int i = 0; i < num_datum; ++i)
290       {
291 	const Tp f = std::tr1::sph_neumann(Tp(data005[i].n), Tp(data005[i].x));
292 	const Tp f0 = data005[i].f0;
293 	const Tp diff = f - f0;
294 	if (std::abs(diff) > max_abs_diff)
295 	  max_abs_diff = std::abs(diff);
296 	if (std::abs(f0) > Tp(10) * eps
297 	 && std::abs(f) > Tp(10) * eps)
298 	  {
299 	    const Tp frac = diff / f0;
300 	    if (std::abs(frac) > max_abs_frac)
301 	      max_abs_frac = std::abs(frac);
302 	  }
303       }
304     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
305   }
306 
307 // Test data for n=20.
308 testcase_sph_neumann<double> data006[] = {
309   { -1.4077591402542251e+36, 20, 0.25000000000000000 },
310   { -6.7288761838234712e+29, 20, 0.50000000000000000 },
311   { -1.3544611382105945e+26, 20, 0.75000000000000000 },
312   { -3.2395922185789833e+23, 20, 1.0000000000000000 },
313   { -3.0096416715953060e+21, 20, 1.2500000000000000 },
314   { -6.5999646851668173e+19, 20, 1.5000000000000000 },
315   { -2.6193364753070735e+18, 20, 1.7500000000000000 },
316   { -1.6054364928152224e+17, 20, 2.0000000000000000 },
317   { -13719071872797762., 20, 2.2500000000000000 },
318   { -1524247248298953.8, 20, 2.5000000000000000 },
319   { -209484650509384.06, 20, 2.7500000000000000 },
320   { -34327545666696.488, 20, 3.0000000000000000 },
321   { -6522260876203.3174, 20, 3.2500000000000000 },
322   { -1406018871897.2307, 20, 3.5000000000000000 },
323   { -338025193731.78882, 20, 3.7500000000000000 },
324   { -89381690326.018677, 20, 4.0000000000000000 },
325   { -25701805899.474934, 20, 4.2500000000000000 },
326   { -7961859734.2407761, 20, 4.5000000000000000 },
327   { -2636237230.0850010, 20, 4.7500000000000000 },
328   { -926795140.30575466, 20, 5.0000000000000000 },
329 };
330 
331 // Test function for n=20.
332 template<typename Tp>
333   void
test006()334   test006()
335   {
336     bool test [[gnu::unused]] = true;
337     const Tp eps = std::numeric_limits<Tp>::epsilon();
338     Tp max_abs_diff = -Tp(1);
339     Tp max_abs_frac = -Tp(1);
340     unsigned int num_datum = sizeof(data006)
341 			   / sizeof(testcase_sph_neumann<double>);
342     for (unsigned int i = 0; i < num_datum; ++i)
343       {
344 	const Tp f = std::tr1::sph_neumann(Tp(data006[i].n), Tp(data006[i].x));
345 	const Tp f0 = data006[i].f0;
346 	const Tp diff = f - f0;
347 	if (std::abs(diff) > max_abs_diff)
348 	  max_abs_diff = std::abs(diff);
349 	if (std::abs(f0) > Tp(10) * eps
350 	 && std::abs(f) > Tp(10) * eps)
351 	  {
352 	    const Tp frac = diff / f0;
353 	    if (std::abs(frac) > max_abs_frac)
354 	      max_abs_frac = std::abs(frac);
355 	  }
356       }
357     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
358   }
359 
360 // Test data for n=50.
361 testcase_sph_neumann<double> data007[] = {
362   { -1.3823742808004061e+109, 50, 0.25000000000000000 },
363   { -6.1447912922121694e+93, 50, 0.50000000000000000 },
364   { -6.4348494908900529e+84, 50, 0.75000000000000000 },
365   { -2.7391922846297569e+78, 50, 1.0000000000000000 },
366   { -3.1365037573299931e+73, 50, 1.2500000000000000 },
367   { -2.8821098528635756e+69, 50, 1.5000000000000000 },
368   { -1.1148255024189452e+66, 50, 1.7500000000000000 },
369   { -1.2350219443670970e+63, 50, 2.0000000000000000 },
370   { -3.0565226939717125e+60, 50, 2.2500000000000000 },
371   { -1.4262702131152733e+58, 50, 2.5000000000000000 },
372   { -1.1118745474840939e+56, 50, 2.7500000000000000 },
373   { -1.3243260716629126e+54, 50, 3.0000000000000000 },
374   { -2.2519472094129334e+52, 50, 3.2500000000000000 },
375   { -5.1861507201100364e+50, 50, 3.5000000000000000 },
376   { -1.5513212909461383e+49, 50, 3.7500000000000000 },
377   { -5.8276471407899822e+47, 50, 4.0000000000000000 },
378   { -2.6745414086542661e+46, 50, 4.2500000000000000 },
379   { -1.4657308996352322e+45, 50, 4.5000000000000000 },
380   { -9.4102674366685358e+43, 50, 4.7500000000000000 },
381   { -6.9641091882698388e+42, 50, 5.0000000000000000 },
382 };
383 
384 // Test function for n=50.
385 template<typename Tp>
386   void
test007()387   test007()
388   {
389     bool test [[gnu::unused]] = true;
390     const Tp eps = std::numeric_limits<Tp>::epsilon();
391     Tp max_abs_diff = -Tp(1);
392     Tp max_abs_frac = -Tp(1);
393     unsigned int num_datum = sizeof(data007)
394 			   / sizeof(testcase_sph_neumann<double>);
395     for (unsigned int i = 0; i < num_datum; ++i)
396       {
397 	const Tp f = std::tr1::sph_neumann(Tp(data007[i].n), Tp(data007[i].x));
398 	const Tp f0 = data007[i].f0;
399 	const Tp diff = f - f0;
400 	if (std::abs(diff) > max_abs_diff)
401 	  max_abs_diff = std::abs(diff);
402 	if (std::abs(f0) > Tp(10) * eps
403 	 && std::abs(f) > Tp(10) * eps)
404 	  {
405 	    const Tp frac = diff / f0;
406 	    if (std::abs(frac) > max_abs_frac)
407 	      max_abs_frac = std::abs(frac);
408 	  }
409       }
410     VERIFY(max_abs_frac < Tp(5.0000000000000029e-12));
411   }
412 
413 // Test data for n=100.
414 testcase_sph_neumann<double> data008[] = {
415   { -4.2856109460516407e+247, 100, 0.25000000000000000 },
416   { -1.6911720011753781e+217, 100, 0.50000000000000000 },
417   { -2.7753107402139484e+199, 100, 0.75000000000000000 },
418   { -6.6830794632586774e+186, 100, 1.0000000000000000 },
419   { -1.0906342369729277e+177, 100, 1.2500000000000000 },
420   { -1.0993184254131119e+169, 100, 1.5000000000000000 },
421   { -1.9071480498141315e+162, 100, 1.7500000000000000 },
422   { -2.6559558301924957e+156, 100, 2.0000000000000000 },
423   { -1.8154136926485787e+151, 100, 2.2500000000000000 },
424   { -4.3527631662111383e+146, 100, 2.5000000000000000 },
425   { -2.8809537014100589e+142, 100, 2.7500000000000000 },
426   { -4.4102229953033134e+138, 100, 3.0000000000000000 },
427   { -1.3651904154045514e+135, 100, 3.2500000000000000 },
428   { -7.6980749101080730e+131, 100, 3.5000000000000000 },
429   { -7.2790553499254927e+128, 100, 3.7500000000000000 },
430   { -1.0796647795893970e+126, 100, 4.0000000000000000 },
431   { -2.3785795774445298e+123, 100, 4.2500000000000000 },
432   { -7.4391596631955861e+120, 100, 4.5000000000000000 },
433   { -3.1802258278279400e+118, 100, 4.7500000000000000 },
434   { -1.7997139826259740e+116, 100, 5.0000000000000000 },
435 };
436 
437 // Test function for n=100.
438 template<typename Tp>
439   void
test008()440   test008()
441   {
442     bool test [[gnu::unused]] = true;
443     const Tp eps = std::numeric_limits<Tp>::epsilon();
444     Tp max_abs_diff = -Tp(1);
445     Tp max_abs_frac = -Tp(1);
446     unsigned int num_datum = sizeof(data008)
447 			   / sizeof(testcase_sph_neumann<double>);
448     for (unsigned int i = 0; i < num_datum; ++i)
449       {
450 	const Tp f = std::tr1::sph_neumann(Tp(data008[i].n), Tp(data008[i].x));
451 	const Tp f0 = data008[i].f0;
452 	const Tp diff = f - f0;
453 	if (std::abs(diff) > max_abs_diff)
454 	  max_abs_diff = std::abs(diff);
455 	if (std::abs(f0) > Tp(10) * eps
456 	 && std::abs(f) > Tp(10) * eps)
457 	  {
458 	    const Tp frac = diff / f0;
459 	    if (std::abs(frac) > max_abs_frac)
460 	      max_abs_frac = std::abs(frac);
461 	  }
462       }
463     VERIFY(max_abs_frac < Tp(5.0000000000000029e-12));
464   }
465 //  sph_neumann
466 
467 // Test data for n=0.
468 testcase_sph_neumann<double> data009[] = {
469   { -0.056732437092645263, 0, 5.0000000000000000 },
470   { 0.083907152907645249, 0, 10.000000000000000 },
471   { 0.050645860857254747, 0, 15.000000000000000 },
472   { -0.020404103090669597, 0, 20.000000000000000 },
473   { -0.039648112474538942, 0, 25.000000000000000 },
474   { -0.0051417149962528020, 0, 30.000000000000000 },
475   { 0.025819777288328762, 0, 35.000000000000000 },
476   { 0.016673451541306544, 0, 40.000000000000000 },
477   { -0.011673821973727327, 0, 45.000000000000000 },
478   { -0.019299320569842265, 0, 50.000000000000000 },
479   { -0.00040230465930828606, 0, 55.000000000000000 },
480   { 0.015873549673585938, 0, 60.000000000000000 },
481   { 0.0086531361728949541, 0, 65.000000000000000 },
482   { -0.0090474171869471404, 0, 70.000000000000000 },
483   { -0.012290016929663325, 0, 75.000000000000000 },
484   { 0.0013798405479880944, 0, 80.000000000000000 },
485   { 0.011580901686988727, 0, 85.000000000000000 },
486   { 0.0049785957347685574, 0, 90.000000000000000 },
487   { -0.0076860374841559963, 0, 95.000000000000000 },
488   { -0.0086231887228768404, 0, 100.00000000000000 },
489 };
490 
491 // Test function for n=0.
492 template<typename Tp>
493   void
test009()494   test009()
495   {
496     bool test [[gnu::unused]] = true;
497     const Tp eps = std::numeric_limits<Tp>::epsilon();
498     Tp max_abs_diff = -Tp(1);
499     Tp max_abs_frac = -Tp(1);
500     unsigned int num_datum = sizeof(data009)
501 			   / sizeof(testcase_sph_neumann<double>);
502     for (unsigned int i = 0; i < num_datum; ++i)
503       {
504 	const Tp f = std::tr1::sph_neumann(Tp(data009[i].n), Tp(data009[i].x));
505 	const Tp f0 = data009[i].f0;
506 	const Tp diff = f - f0;
507 	if (std::abs(diff) > max_abs_diff)
508 	  max_abs_diff = std::abs(diff);
509 	if (std::abs(f0) > Tp(10) * eps
510 	 && std::abs(f) > Tp(10) * eps)
511 	  {
512 	    const Tp frac = diff / f0;
513 	    if (std::abs(frac) > max_abs_frac)
514 	      max_abs_frac = std::abs(frac);
515 	  }
516       }
517     VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
518   }
519 
520 // Test data for n=1.
521 testcase_sph_neumann<double> data010[] = {
522   { 0.18043836751409864, 1, 5.0000000000000000 },
523   { 0.062792826379701502, 1, 10.000000000000000 },
524   { -0.039976131953324147, 1, 15.000000000000000 },
525   { -0.046667467690914864, 1, 20.000000000000000 },
526   { 0.0037081455049293634, 1, 25.000000000000000 },
527   { 0.032762996969886965, 1, 30.000000000000000 },
528   { 0.012971498479556563, 1, 35.000000000000000 },
529   { -0.018210992723451058, 1, 40.000000000000000 },
530   { -0.019168385477952129, 1, 45.000000000000000 },
531   { 0.0048615106626817301, 1, 50.000000000000000 },
532   { 0.018170052158169303, 1, 55.000000000000000 },
533   { 0.0053447361795967109, 1, 60.000000000000000 },
534   { -0.012587316051033977, 1, 65.000000000000000 },
535   { -0.011184829982069090, 1, 70.000000000000000 },
536   { 0.0050065549130635621, 1, 75.000000000000000 },
537   { 0.012440856180892041, 1, 80.000000000000000 },
538   { 0.0022077237839479508, 1, 85.000000000000000 },
539   { -0.0098779785318421041, 1, 90.000000000000000 },
540   { -0.0072731342338976518, 1, 95.000000000000000 },
541   { 0.0049774245238688201, 1, 100.00000000000000 },
542 };
543 
544 // Test function for n=1.
545 template<typename Tp>
546   void
test010()547   test010()
548   {
549     bool test [[gnu::unused]] = true;
550     const Tp eps = std::numeric_limits<Tp>::epsilon();
551     Tp max_abs_diff = -Tp(1);
552     Tp max_abs_frac = -Tp(1);
553     unsigned int num_datum = sizeof(data010)
554 			   / sizeof(testcase_sph_neumann<double>);
555     for (unsigned int i = 0; i < num_datum; ++i)
556       {
557 	const Tp f = std::tr1::sph_neumann(Tp(data010[i].n), Tp(data010[i].x));
558 	const Tp f0 = data010[i].f0;
559 	const Tp diff = f - f0;
560 	if (std::abs(diff) > max_abs_diff)
561 	  max_abs_diff = std::abs(diff);
562 	if (std::abs(f0) > Tp(10) * eps
563 	 && std::abs(f) > Tp(10) * eps)
564 	  {
565 	    const Tp frac = diff / f0;
566 	    if (std::abs(frac) > max_abs_frac)
567 	      max_abs_frac = std::abs(frac);
568 	  }
569       }
570     VERIFY(max_abs_frac < Tp(2.5000000000000014e-11));
571   }
572 
573 // Test data for n=2.
574 testcase_sph_neumann<double> data011[] = {
575   { 0.16499545760110443, 2, 5.0000000000000000 },
576   { -0.065069304993734783, 2, 10.000000000000000 },
577   { -0.058641087247919575, 2, 15.000000000000000 },
578   { 0.013403982937032370, 2, 20.000000000000000 },
579   { 0.040093089935130458, 2, 25.000000000000000 },
580   { 0.0084180146932414986, 2, 30.000000000000000 },
581   { -0.024707934561509628, 2, 35.000000000000000 },
582   { -0.018039275995565374, 2, 40.000000000000000 },
583   { 0.010395929608530518, 2, 45.000000000000000 },
584   { 0.019591011209603170, 2, 50.000000000000000 },
585   { 0.0013933984133902479, 2, 55.000000000000000 },
586   { -0.015606312864606101, 2, 60.000000000000000 },
587   { -0.0092340892214042153, 2, 65.000000000000000 },
588   { 0.0085680673305727519, 2, 70.000000000000000 },
589   { 0.012490279126185866, 2, 75.000000000000000 },
590   { -0.00091330844120464274, 2, 80.000000000000000 },
591   { -0.011502982024025860, 2, 85.000000000000000 },
592   { -0.0053078616858299611, 2, 90.000000000000000 },
593   { 0.0074563595609802797, 2, 95.000000000000000 },
594   { 0.0087725114585929052, 2, 100.00000000000000 },
595 };
596 
597 // Test function for n=2.
598 template<typename Tp>
599   void
test011()600   test011()
601   {
602     bool test [[gnu::unused]] = true;
603     const Tp eps = std::numeric_limits<Tp>::epsilon();
604     Tp max_abs_diff = -Tp(1);
605     Tp max_abs_frac = -Tp(1);
606     unsigned int num_datum = sizeof(data011)
607 			   / sizeof(testcase_sph_neumann<double>);
608     for (unsigned int i = 0; i < num_datum; ++i)
609       {
610 	const Tp f = std::tr1::sph_neumann(Tp(data011[i].n), Tp(data011[i].x));
611 	const Tp f0 = data011[i].f0;
612 	const Tp diff = f - f0;
613 	if (std::abs(diff) > max_abs_diff)
614 	  max_abs_diff = std::abs(diff);
615 	if (std::abs(f0) > Tp(10) * eps
616 	 && std::abs(f) > Tp(10) * eps)
617 	  {
618 	    const Tp frac = diff / f0;
619 	    if (std::abs(frac) > max_abs_frac)
620 	      max_abs_frac = std::abs(frac);
621 	  }
622       }
623     VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
624   }
625 
626 // Test data for n=5.
627 testcase_sph_neumann<double> data012[] = {
628   { -0.32046504674973919, 5, 5.0000000000000000 },
629   { 0.093833541678691818, 5, 10.000000000000000 },
630   { 0.020475698281859061, 5, 15.000000000000000 },
631   { -0.048172347757372780, 5, 20.000000000000000 },
632   { -0.018309489232548347, 5, 25.000000000000000 },
633   { 0.026639390496569996, 5, 30.000000000000000 },
634   { 0.022006038985576210, 5, 35.000000000000000 },
635   { -0.011268975348057965, 5, 40.000000000000000 },
636   { -0.021770388372274858, 5, 45.000000000000000 },
637   { -0.00069711319645853701, 5, 50.000000000000000 },
638   { 0.017439589450220901, 5, 55.000000000000000 },
639   { 0.0088699170919343089, 5, 60.000000000000000 },
640   { -0.010421334444951861, 5, 65.000000000000000 },
641   { -0.012746769858008553, 5, 70.000000000000000 },
642   { 0.0026282888028967737, 5, 75.000000000000000 },
643   { 0.012477658581324189, 5, 80.000000000000000 },
644   { 0.0040771816818182642, 5, 85.000000000000000 },
645   { -0.0089777759570579818, 5, 90.000000000000000 },
646   { -0.0083184557896676149, 5, 95.000000000000000 },
647   { 0.0037206784862748965, 5, 100.00000000000000 },
648 };
649 
650 // Test function for n=5.
651 template<typename Tp>
652   void
test012()653   test012()
654   {
655     bool test [[gnu::unused]] = true;
656     const Tp eps = std::numeric_limits<Tp>::epsilon();
657     Tp max_abs_diff = -Tp(1);
658     Tp max_abs_frac = -Tp(1);
659     unsigned int num_datum = sizeof(data012)
660 			   / sizeof(testcase_sph_neumann<double>);
661     for (unsigned int i = 0; i < num_datum; ++i)
662       {
663 	const Tp f = std::tr1::sph_neumann(Tp(data012[i].n), Tp(data012[i].x));
664 	const Tp f0 = data012[i].f0;
665 	const Tp diff = f - f0;
666 	if (std::abs(diff) > max_abs_diff)
667 	  max_abs_diff = std::abs(diff);
668 	if (std::abs(f0) > Tp(10) * eps
669 	 && std::abs(f) > Tp(10) * eps)
670 	  {
671 	    const Tp frac = diff / f0;
672 	    if (std::abs(frac) > max_abs_frac)
673 	      max_abs_frac = std::abs(frac);
674 	  }
675       }
676     VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
677   }
678 
679 // Test data for n=10.
680 testcase_sph_neumann<double> data013[] = {
681   { -26.656114405718711, 10, 5.0000000000000000 },
682   { -0.17245367208805784, 10, 10.000000000000000 },
683   { 0.078461689849642580, 10, 15.000000000000000 },
684   { -0.036843410496289961, 10, 20.000000000000000 },
685   { -0.021158339301097475, 10, 25.000000000000000 },
686   { 0.031219591064754939, 10, 30.000000000000000 },
687   { 0.012840593422414807, 10, 35.000000000000000 },
688   { -0.021803068636888072, 10, 40.000000000000000 },
689   { -0.014071636804469044, 10, 45.000000000000000 },
690   { 0.013524687511158758, 10, 50.000000000000000 },
691   { 0.015684932653180595, 10, 55.000000000000000 },
692   { -0.0056356895567262122, 10, 60.000000000000000 },
693   { -0.015364490270315362, 10, 65.000000000000000 },
694   { -0.0014525575672261295, 10, 70.000000000000000 },
695   { 0.012648951699549433, 10, 75.000000000000000 },
696   { 0.0068571608061120367, 10, 80.000000000000000 },
697   { -0.0080151152941401460, 10, 85.000000000000000 },
698   { -0.0098139742219019149, 10, 90.000000000000000 },
699   { 0.0025002854072314951, 10, 95.000000000000000 },
700   { 0.010025777373636155, 10, 100.00000000000000 },
701 };
702 
703 // Test function for n=10.
704 template<typename Tp>
705   void
test013()706   test013()
707   {
708     bool test [[gnu::unused]] = true;
709     const Tp eps = std::numeric_limits<Tp>::epsilon();
710     Tp max_abs_diff = -Tp(1);
711     Tp max_abs_frac = -Tp(1);
712     unsigned int num_datum = sizeof(data013)
713 			   / sizeof(testcase_sph_neumann<double>);
714     for (unsigned int i = 0; i < num_datum; ++i)
715       {
716 	const Tp f = std::tr1::sph_neumann(Tp(data013[i].n), Tp(data013[i].x));
717 	const Tp f0 = data013[i].f0;
718 	const Tp diff = f - f0;
719 	if (std::abs(diff) > max_abs_diff)
720 	  max_abs_diff = std::abs(diff);
721 	if (std::abs(f0) > Tp(10) * eps
722 	 && std::abs(f) > Tp(10) * eps)
723 	  {
724 	    const Tp frac = diff / f0;
725 	    if (std::abs(frac) > max_abs_frac)
726 	      max_abs_frac = std::abs(frac);
727 	  }
728       }
729     VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
730   }
731 
732 // Test data for n=20.
733 testcase_sph_neumann<double> data014[] = {
734   { -926795140.30575466, 20, 5.0000000000000000 },
735   { -1211.2106053526036, 20, 10.000000000000000 },
736   { -1.5559965765652175, 20, 15.000000000000000 },
737   { -0.093401132250914398, 20, 20.000000000000000 },
738   { 0.044031985675276462, 20, 25.000000000000000 },
739   { -0.036078033606613907, 20, 30.000000000000000 },
740   { 0.029828405631319645, 20, 35.000000000000000 },
741   { -0.0048414810986760759, 20, 40.000000000000000 },
742   { -0.020504694681516944, 20, 45.000000000000000 },
743   { 0.013759531302541216, 20, 50.000000000000000 },
744   { 0.012783038861734196, 20, 55.000000000000000 },
745   { -0.013117009421906418, 20, 60.000000000000000 },
746   { -0.010338106075674407, 20, 65.000000000000000 },
747   { 0.010538610814111244, 20, 70.000000000000000 },
748   { 0.010200029094273744, 20, 75.000000000000000 },
749   { -0.0073123450945617122, 20, 80.000000000000000 },
750   { -0.010581510354950906, 20, 85.000000000000000 },
751   { 0.0036866374015298723, 20, 90.000000000000000 },
752   { 0.010498384318338270, 20, 95.000000000000000 },
753   { 5.6317293788334978e-05, 20, 100.00000000000000 },
754 };
755 
756 // Test function for n=20.
757 template<typename Tp>
758   void
test014()759   test014()
760   {
761     bool test [[gnu::unused]] = true;
762     const Tp eps = std::numeric_limits<Tp>::epsilon();
763     Tp max_abs_diff = -Tp(1);
764     Tp max_abs_frac = -Tp(1);
765     unsigned int num_datum = sizeof(data014)
766 			   / sizeof(testcase_sph_neumann<double>);
767     for (unsigned int i = 0; i < num_datum; ++i)
768       {
769 	const Tp f = std::tr1::sph_neumann(Tp(data014[i].n), Tp(data014[i].x));
770 	const Tp f0 = data014[i].f0;
771 	const Tp diff = f - f0;
772 	if (std::abs(diff) > max_abs_diff)
773 	  max_abs_diff = std::abs(diff);
774 	if (std::abs(f0) > Tp(10) * eps
775 	 && std::abs(f) > Tp(10) * eps)
776 	  {
777 	    const Tp frac = diff / f0;
778 	    if (std::abs(frac) > max_abs_frac)
779 	      max_abs_frac = std::abs(frac);
780 	  }
781       }
782     VERIFY(max_abs_frac < Tp(1.0000000000000007e-09));
783   }
784 
785 // Test data for n=50.
786 testcase_sph_neumann<double> data015[] = {
787   { -6.9641091882698388e+42, 50, 5.0000000000000000 },
788   { -4.5282272723512023e+27, 50, 10.000000000000000 },
789   { -9.0004902645887037e+18, 50, 15.000000000000000 },
790   { -9542541667002.5117, 50, 20.000000000000000 },
791   { -363518140.71026671, 50, 25.000000000000000 },
792   { -152551.57233157745, 50, 30.000000000000000 },
793   { -386.26599186208625, 50, 35.000000000000000 },
794   { -4.3290507947291035, 50, 40.000000000000000 },
795   { -0.19968460851503758, 50, 45.000000000000000 },
796   { -0.041900001504607758, 50, 50.000000000000000 },
797   { 0.010696040672421902, 50, 55.000000000000000 },
798   { 0.0078198768555267188, 50, 60.000000000000000 },
799   { -0.010088474938191242, 50, 65.000000000000000 },
800   { 0.0062423671279824801, 50, 70.000000000000000 },
801   { 0.0011284242794941733, 50, 75.000000000000000 },
802   { -0.0093934266037485562, 50, 80.000000000000000 },
803   { 0.013108079602843424, 50, 85.000000000000000 },
804   { -0.0075396607225722626, 50, 90.000000000000000 },
805   { -0.0042605703552836558, 50, 95.000000000000000 },
806   { 0.010747822973682470, 50, 100.00000000000000 },
807 };
808 
809 // Test function for n=50.
810 template<typename Tp>
811   void
test015()812   test015()
813   {
814     bool test [[gnu::unused]] = true;
815     const Tp eps = std::numeric_limits<Tp>::epsilon();
816     Tp max_abs_diff = -Tp(1);
817     Tp max_abs_frac = -Tp(1);
818     unsigned int num_datum = sizeof(data015)
819 			   / sizeof(testcase_sph_neumann<double>);
820     for (unsigned int i = 0; i < num_datum; ++i)
821       {
822 	const Tp f = std::tr1::sph_neumann(Tp(data015[i].n), Tp(data015[i].x));
823 	const Tp f0 = data015[i].f0;
824 	const Tp diff = f - f0;
825 	if (std::abs(diff) > max_abs_diff)
826 	  max_abs_diff = std::abs(diff);
827 	if (std::abs(f0) > Tp(10) * eps
828 	 && std::abs(f) > Tp(10) * eps)
829 	  {
830 	    const Tp frac = diff / f0;
831 	    if (std::abs(frac) > max_abs_frac)
832 	      max_abs_frac = std::abs(frac);
833 	  }
834       }
835     VERIFY(max_abs_frac < Tp(2.5000000000000014e-11));
836   }
837 
838 // Test data for n=100.
839 testcase_sph_neumann<double> data016[] = {
840   { -1.7997139826259740e+116, 100, 5.0000000000000000 },
841   { -8.5732263093296268e+85, 100, 10.000000000000000 },
842   { -1.9270658593711677e+68, 100, 15.000000000000000 },
843   { -7.2208893582952385e+55, 100, 20.000000000000000 },
844   { -2.0868752613007946e+46, 100, 25.000000000000000 },
845   { -4.2496124023612646e+38, 100, 30.000000000000000 },
846   { -1.7042898348910271e+32, 100, 35.000000000000000 },
847   { -6.3021565260724554e+26, 100, 40.000000000000000 },
848   { -1.3199917400494367e+22, 100, 45.000000000000000 },
849   { -1.1256928913265988e+18, 100, 50.000000000000000 },
850   { -309801083340343.25, 100, 55.000000000000000 },
851   { -232585620046.64737, 100, 60.000000000000000 },
852   { -421135935.93756074, 100, 65.000000000000000 },
853   { -1680637.4531202621, 100, 70.000000000000000 },
854   { -13868.302591128844, 100, 75.000000000000000 },
855   { -227.24385709173322, 100, 80.000000000000000 },
856   { -7.2807038787138731, 100, 85.000000000000000 },
857   { -0.46648154448250878, 100, 90.000000000000000 },
858   { -0.067270772720654556, 100, 95.000000000000000 },
859   { -0.022983850491562267, 100, 100.00000000000000 },
860 };
861 
862 // Test function for n=100.
863 template<typename Tp>
864   void
test016()865   test016()
866   {
867     bool test [[gnu::unused]] = true;
868     const Tp eps = std::numeric_limits<Tp>::epsilon();
869     Tp max_abs_diff = -Tp(1);
870     Tp max_abs_frac = -Tp(1);
871     unsigned int num_datum = sizeof(data016)
872 			   / sizeof(testcase_sph_neumann<double>);
873     for (unsigned int i = 0; i < num_datum; ++i)
874       {
875 	const Tp f = std::tr1::sph_neumann(Tp(data016[i].n), Tp(data016[i].x));
876 	const Tp f0 = data016[i].f0;
877 	const Tp diff = f - f0;
878 	if (std::abs(diff) > max_abs_diff)
879 	  max_abs_diff = std::abs(diff);
880 	if (std::abs(f0) > Tp(10) * eps
881 	 && std::abs(f) > Tp(10) * eps)
882 	  {
883 	    const Tp frac = diff / f0;
884 	    if (std::abs(frac) > max_abs_frac)
885 	      max_abs_frac = std::abs(frac);
886 	  }
887       }
888     VERIFY(max_abs_frac < Tp(2.5000000000000015e-12));
889   }
890 
891 int
main()892 main()
893 {
894   test001<double>();
895   test002<double>();
896   test003<double>();
897   test004<double>();
898   test005<double>();
899   test006<double>();
900   test007<double>();
901   test008<double>();
902   test009<double>();
903   test010<double>();
904   test011<double>();
905   test012<double>();
906   test013<double>();
907   test014<double>();
908   test015<double>();
909   test016<double>();
910   return 0;
911 }
912