1 // { dg-do run { target c++11 } }
2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
3 //
4 // Copyright (C) 2016-2020 Free Software Foundation, Inc.
5 //
6 // This file is part of the GNU ISO C++ Library. This library is free
7 // software; you can redistribute it and/or modify it under the
8 // terms of the GNU General Public License as published by the
9 // Free Software Foundation; either version 3, or (at your option)
10 // any later version.
11 //
12 // This library is distributed in the hope that it will be useful,
13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 // GNU General Public License for more details.
16 //
17 // You should have received a copy of the GNU General Public License along
18 // with this library; see the file COPYING3. If not see
19 // <http://www.gnu.org/licenses/>.
20
21 // cyl_bessel_i
22 // Compare against values generated by the GNU Scientific Library.
23 // The GSL can be found on the web: http://www.gnu.org/software/gsl/
24 #include <limits>
25 #include <cmath>
26 #if defined(__TEST_DEBUG)
27 # include <iostream>
28 # define VERIFY(A) \
29 if (!(A)) \
30 { \
31 std::cout << "line " << __LINE__ \
32 << " max_abs_frac = " << max_abs_frac \
33 << std::endl; \
34 }
35 #else
36 # include <testsuite_hooks.h>
37 #endif
38 #include <specfun_testcase.h>
39
40 // Test data for nu=0.0000000000000000.
41 // max(|f - f_GSL|): 5.2402526762307389e-14 at index 12
42 // max(|f - f_GSL| / |f_GSL|): 1.0747725055352992e-14
43 // mean(f - f_GSL): -1.9624513654326576e-14
44 // variance(f - f_GSL): 4.0630093099383162e-30
45 // stddev(f - f_GSL): 2.0156907773610308e-15
46 const testcase_cyl_bessel_i<double>
47 data007[21] =
48 {
49 { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
50 { 1.0156861412236078, 0.0000000000000000, 0.25000000000000000, 0.0 },
51 { 1.0634833707413236, 0.0000000000000000, 0.50000000000000000, 0.0 },
52 { 1.1456467780440014, 0.0000000000000000, 0.75000000000000000, 0.0 },
53 { 1.2660658777520082, 0.0000000000000000, 1.0000000000000000, 0.0 },
54 { 1.4304687177218294, 0.0000000000000000, 1.2500000000000000, 0.0 },
55 { 1.6467231897728904, 0.0000000000000000, 1.5000000000000000, 0.0 },
56 { 1.9252521538585021, 0.0000000000000000, 1.7500000000000000, 0.0 },
57 { 2.2795853023360668, 0.0000000000000000, 2.0000000000000000, 0.0 },
58 { 2.7270783071907951, 0.0000000000000000, 2.2500000000000000, 0.0 },
59 { 3.2898391440501231, 0.0000000000000000, 2.5000000000000000, 0.0 },
60 { 3.9959131072376550, 0.0000000000000000, 2.7500000000000000, 0.0 },
61 { 4.8807925858650245, 0.0000000000000000, 3.0000000000000000, 0.0 },
62 { 5.9893359979395138, 0.0000000000000000, 3.2500000000000000, 0.0 },
63 { 7.3782034322254750, 0.0000000000000000, 3.5000000000000000, 0.0 },
64 { 9.1189458608445655, 0.0000000000000000, 3.7500000000000000, 0.0 },
65 { 11.301921952136325, 0.0000000000000000, 4.0000000000000000, 0.0 },
66 { 14.041263683000595, 0.0000000000000000, 4.2500000000000000, 0.0 },
67 { 17.481171855609272, 0.0000000000000000, 4.5000000000000000, 0.0 },
68 { 21.803898740902120, 0.0000000000000000, 4.7500000000000000, 0.0 },
69 { 27.239871823604439, 0.0000000000000000, 5.0000000000000000, 0.0 },
70 };
71 const double toler007 = 1.0000000000000008e-12;
72
73 // Test data for nu=0.33333333333333331.
74 // max(|f - f_GSL|): 6.2172489379008766e-15 at index 14
75 // max(|f - f_GSL| / |f_GSL|): 9.1624880778907085e-16
76 // mean(f - f_GSL): 1.1525172350870673e-15
77 // variance(f - f_GSL): 6.9735538801568761e-32
78 // stddev(f - f_GSL): 2.6407487347638500e-16
79 const testcase_cyl_bessel_i<double>
80 data008[21] =
81 {
82 { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000, 0.0 },
83 { 0.56650686557808660, 0.33333333333333331, 0.25000000000000000, 0.0 },
84 { 0.73897315642511863, 0.33333333333333331, 0.50000000000000000, 0.0 },
85 { 0.89532320365836815, 0.33333333333333331, 0.75000000000000000, 0.0 },
86 { 1.0646313978895283, 0.33333333333333331, 1.0000000000000000, 0.0 },
87 { 1.2623776732605250, 0.33333333333333331, 1.2500000000000000, 0.0 },
88 { 1.5014290000224382, 0.33333333333333331, 1.5000000000000000, 0.0 },
89 { 1.7951195525946040, 0.33333333333333331, 1.7500000000000000, 0.0 },
90 { 2.1587825813728614, 0.33333333333333331, 2.0000000000000000, 0.0 },
91 { 2.6109134564811405, 0.33333333333333331, 2.2500000000000000, 0.0 },
92 { 3.1743242297241938, 0.33333333333333331, 2.5000000000000000, 0.0 },
93 { 3.8774551722182093, 0.33333333333333331, 2.7500000000000000, 0.0 },
94 { 4.7559569371646946, 0.33333333333333331, 3.0000000000000000, 0.0 },
95 { 5.8546499652731825, 0.33333333333333331, 3.2500000000000000, 0.0 },
96 { 7.2299798619171129, 0.33333333333333331, 3.5000000000000000, 0.0 },
97 { 8.9531114355506318, 0.33333333333333331, 3.7500000000000000, 0.0 },
98 { 11.113838389991479, 0.33333333333333331, 4.0000000000000000, 0.0 },
99 { 13.825531136529117, 0.33333333333333331, 4.2500000000000000, 0.0 },
100 { 17.231403968478318, 0.33333333333333331, 4.5000000000000000, 0.0 },
101 { 21.512458099556554, 0.33333333333333331, 4.7500000000000000, 0.0 },
102 { 26.897553069268362, 0.33333333333333331, 5.0000000000000000, 0.0 },
103 };
104 const double toler008 = 2.5000000000000020e-13;
105
106 // Test data for nu=0.50000000000000000.
107 // max(|f - f_GSL|): 1.4210854715202004e-14 at index 19
108 // max(|f - f_GSL| / |f_GSL|): 9.6042704318763827e-16
109 // mean(f - f_GSL): 1.9296733523246769e-16
110 // variance(f - f_GSL): 1.9549106045027772e-33
111 // stddev(f - f_GSL): 4.4214371017835108e-17
112 const testcase_cyl_bessel_i<double>
113 data009[21] =
114 {
115 { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
116 { 0.40311093489975897, 0.50000000000000000, 0.25000000000000000, 0.0 },
117 { 0.58799308679041573, 0.50000000000000000, 0.50000000000000000, 0.0 },
118 { 0.75761498638991298, 0.50000000000000000, 0.75000000000000000, 0.0 },
119 { 0.93767488824548695, 0.50000000000000000, 1.0000000000000000, 0.0 },
120 { 1.1432089853159872, 0.50000000000000000, 1.2500000000000000, 0.0 },
121 { 1.3871617204034761, 0.50000000000000000, 1.5000000000000000, 0.0 },
122 { 1.6830217804556813, 0.50000000000000000, 1.7500000000000000, 0.0 },
123 { 2.0462368630890526, 0.50000000000000000, 2.0000000000000000, 0.0 },
124 { 2.4953405089360046, 0.50000000000000000, 2.2500000000000000, 0.0 },
125 { 3.0530935381967175, 0.50000000000000000, 2.5000000000000000, 0.0 },
126 { 3.7477882494879449, 0.50000000000000000, 2.7500000000000000, 0.0 },
127 { 4.6148229034075969, 0.50000000000000000, 3.0000000000000000, 0.0 },
128 { 5.6986505325335486, 0.50000000000000000, 3.2500000000000000, 0.0 },
129 { 7.0552194086911859, 0.50000000000000000, 3.5000000000000000, 0.0 },
130 { 8.7550467841188979, 0.50000000000000000, 3.7500000000000000, 0.0 },
131 { 10.887101798588422, 0.50000000000000000, 4.0000000000000000, 0.0 },
132 { 13.563718712579764, 0.50000000000000000, 4.2500000000000000, 0.0 },
133 { 16.926820080158183, 0.50000000000000000, 4.5000000000000000, 0.0 },
134 { 21.155804306570005, 0.50000000000000000, 4.7500000000000000, 0.0 },
135 { 26.477547497559065, 0.50000000000000000, 5.0000000000000000, 0.0 },
136 };
137 const double toler009 = 2.5000000000000020e-13;
138
139 // Test data for nu=0.66666666666666663.
140 // max(|f - f_GSL|): 1.9539925233402755e-14 at index 16
141 // max(|f - f_GSL| / |f_GSL|): 2.2100364323953014e-15
142 // mean(f - f_GSL): -5.2312651565075830e-15
143 // variance(f - f_GSL): 1.4792059082391298e-31
144 // stddev(f - f_GSL): 3.8460446022363414e-16
145 const testcase_cyl_bessel_i<double>
146 data010[21] =
147 {
148 { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000, 0.0 },
149 { 0.27953690613200444, 0.66666666666666663, 0.25000000000000000, 0.0 },
150 { 0.45628323113556890, 0.66666666666666663, 0.50000000000000000, 0.0 },
151 { 0.62594569838182623, 0.66666666666666663, 0.75000000000000000, 0.0 },
152 { 0.80752128860612971, 0.66666666666666663, 1.0000000000000000, 0.0 },
153 { 1.0139484513577173, 0.66666666666666663, 1.2500000000000000, 0.0 },
154 { 1.2572918396962993, 0.66666666666666663, 1.5000000000000000, 0.0 },
155 { 1.5505806938325581, 0.66666666666666663, 1.7500000000000000, 0.0 },
156 { 1.9089492968236210, 0.66666666666666663, 2.0000000000000000, 0.0 },
157 { 2.3506463490300340, 0.66666666666666663, 2.2500000000000000, 0.0 },
158 { 2.8981161894224896, 0.66666666666666663, 2.5000000000000000, 0.0 },
159 { 3.5792654911068724, 0.66666666666666663, 2.7500000000000000, 0.0 },
160 { 4.4290087213549514, 0.66666666666666663, 3.0000000000000000, 0.0 },
161 { 5.4911895720097705, 0.66666666666666663, 3.2500000000000000, 0.0 },
162 { 6.8209918044137305, 0.66666666666666663, 3.5000000000000000, 0.0 },
163 { 8.4879784249619785, 0.66666666666666663, 3.7500000000000000, 0.0 },
164 { 10.579932774013004, 0.66666666666666663, 4.0000000000000000, 0.0 },
165 { 13.207720355482458, 0.66666666666666663, 4.2500000000000000, 0.0 },
166 { 16.511448404200543, 0.66666666666666663, 4.5000000000000000, 0.0 },
167 { 20.668274532832392, 0.66666666666666663, 4.7500000000000000, 0.0 },
168 { 25.902310583215122, 0.66666666666666663, 5.0000000000000000, 0.0 },
169 };
170 const double toler010 = 2.5000000000000020e-13;
171
172 // Test data for nu=1.0000000000000000.
173 // max(|f - f_GSL|): 1.2967404927621828e-13 at index 17
174 // max(|f - f_GSL| / |f_GSL|): 1.0977631741433893e-14
175 // mean(f - f_GSL): -3.0188814411265717e-14
176 // variance(f - f_GSL): 3.7247797767076778e-29
177 // stddev(f - f_GSL): 6.1030973912495271e-15
178 const testcase_cyl_bessel_i<double>
179 data011[21] =
180 {
181 { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000, 0.0 },
182 { 0.12597910894546793, 1.0000000000000000, 0.25000000000000000, 0.0 },
183 { 0.25789430539089631, 1.0000000000000000, 0.50000000000000000, 0.0 },
184 { 0.40199246158092228, 1.0000000000000000, 0.75000000000000000, 0.0 },
185 { 0.56515910399248503, 1.0000000000000000, 1.0000000000000000, 0.0 },
186 { 0.75528141834074725, 1.0000000000000000, 1.2500000000000000, 0.0 },
187 { 0.98166642857790720, 1.0000000000000000, 1.5000000000000000, 0.0 },
188 { 1.2555375122401728, 1.0000000000000000, 1.7500000000000000, 0.0 },
189 { 1.5906368546373291, 1.0000000000000000, 2.0000000000000000, 0.0 },
190 { 2.0039674569295931, 1.0000000000000000, 2.2500000000000000, 0.0 },
191 { 2.5167162452886984, 1.0000000000000000, 2.5000000000000000, 0.0 },
192 { 3.1554101386190028, 1.0000000000000000, 2.7500000000000000, 0.0 },
193 { 3.9533702174026097, 1.0000000000000000, 3.0000000000000000, 0.0 },
194 { 4.9525461659085490, 1.0000000000000000, 3.2500000000000000, 0.0 },
195 { 6.2058349222583642, 1.0000000000000000, 3.5000000000000000, 0.0 },
196 { 7.7800152298244170, 1.0000000000000000, 3.7500000000000000, 0.0 },
197 { 9.7594651537044523, 1.0000000000000000, 4.0000000000000000, 0.0 },
198 { 12.250874667409304, 1.0000000000000000, 4.2500000000000000, 0.0 },
199 { 15.389222753735924, 1.0000000000000000, 4.5000000000000000, 0.0 },
200 { 19.345361447520226, 1.0000000000000000, 4.7500000000000000, 0.0 },
201 { 24.335642142450524, 1.0000000000000000, 5.0000000000000000, 0.0 },
202 };
203 const double toler011 = 1.0000000000000008e-12;
204
205 // Test data for nu=2.0000000000000000.
206 // max(|f - f_GSL|): 1.8474111129762605e-13 at index 20
207 // max(|f - f_GSL| / |f_GSL|): 1.0796880796865132e-14
208 // mean(f - f_GSL): -3.8692841919903068e-14
209 // variance(f - f_GSL): 1.1198300918819667e-27
210 // stddev(f - f_GSL): 3.3463862477035829e-14
211 const testcase_cyl_bessel_i<double>
212 data012[21] =
213 {
214 { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000, 0.0 },
215 { 0.0078532696598645167, 2.0000000000000000, 0.25000000000000000, 0.0 },
216 { 0.031906149177738249, 2.0000000000000000, 0.50000000000000000, 0.0 },
217 { 0.073666880494875436, 2.0000000000000000, 0.75000000000000000, 0.0 },
218 { 0.13574766976703831, 2.0000000000000000, 1.0000000000000000, 0.0 },
219 { 0.22201844837663415, 2.0000000000000000, 1.2500000000000000, 0.0 },
220 { 0.33783461833568068, 2.0000000000000000, 1.5000000000000000, 0.0 },
221 { 0.49035213986973314, 2.0000000000000000, 1.7500000000000000, 0.0 },
222 { 0.68894844769873831, 2.0000000000000000, 2.0000000000000000, 0.0 },
223 { 0.94577390103115722, 2.0000000000000000, 2.2500000000000000, 0.0 },
224 { 1.2764661478191643, 2.0000000000000000, 2.5000000000000000, 0.0 },
225 { 1.7010693700601991, 2.0000000000000000, 2.7500000000000000, 0.0 },
226 { 2.2452124409299512, 2.0000000000000000, 3.0000000000000000, 0.0 },
227 { 2.9416152804573357, 2.0000000000000000, 3.2500000000000000, 0.0 },
228 { 3.8320120480778415, 2.0000000000000000, 3.5000000000000000, 0.0 },
229 { 4.9696044049382113, 2.0000000000000000, 3.7500000000000000, 0.0 },
230 { 6.4221893752841055, 2.0000000000000000, 4.0000000000000000, 0.0 },
231 { 8.2761461924550552, 2.0000000000000000, 4.2500000000000000, 0.0 },
232 { 10.641517298393307, 2.0000000000000000, 4.5000000000000000, 0.0 },
233 { 13.658483394577813, 2.0000000000000000, 4.7500000000000000, 0.0 },
234 { 17.505614966624233, 2.0000000000000000, 5.0000000000000000, 0.0 },
235 };
236 const double toler012 = 1.0000000000000008e-12;
237
238 // Test data for nu=5.0000000000000000.
239 // max(|f - f_GSL|): 2.2204460492503131e-14 at index 20
240 // max(|f - f_GSL| / |f_GSL|): 1.1379865680381910e-14
241 // mean(f - f_GSL): -3.4502652328999478e-15
242 // variance(f - f_GSL): 1.8465291591354433e-29
243 // stddev(f - f_GSL): 4.2971259687556788e-15
244 const testcase_cyl_bessel_i<double>
245 data013[21] =
246 {
247 { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000, 0.0 },
248 { 2.5497616449882785e-07, 5.0000000000000000, 0.25000000000000000, 0.0 },
249 { 8.2231713131092646e-06, 5.0000000000000000, 0.50000000000000000, 0.0 },
250 { 6.3261122739811725e-05, 5.0000000000000000, 0.75000000000000000, 0.0 },
251 { 0.00027146315595697195, 5.0000000000000000, 1.0000000000000000, 0.0 },
252 { 0.00084793613616686856, 5.0000000000000000, 1.2500000000000000, 0.0 },
253 { 0.0021705595690975554, 5.0000000000000000, 1.5000000000000000, 0.0 },
254 { 0.0048504513371845385, 5.0000000000000000, 1.7500000000000000, 0.0 },
255 { 0.0098256793231317023, 5.0000000000000000, 2.0000000000000000, 0.0 },
256 { 0.018486577941045829, 5.0000000000000000, 2.2500000000000000, 0.0 },
257 { 0.032843475172023219, 5.0000000000000000, 2.5000000000000000, 0.0 },
258 { 0.055750882754221943, 5.0000000000000000, 2.7500000000000000, 0.0 },
259 { 0.091206477661513338, 5.0000000000000000, 3.0000000000000000, 0.0 },
260 { 0.14474880546308083, 5.0000000000000000, 3.2500000000000000, 0.0 },
261 { 0.22398495470190780, 5.0000000000000000, 3.5000000000000000, 0.0 },
262 { 0.33928899170999877, 5.0000000000000000, 3.7500000000000000, 0.0 },
263 { 0.50472436311316637, 5.0000000000000000, 4.0000000000000000, 0.0 },
264 { 0.73925961816682961, 5.0000000000000000, 4.2500000000000000, 0.0 },
265 { 1.0683677743764701, 5.0000000000000000, 4.5000000000000000, 0.0 },
266 { 1.5261268693599621, 5.0000000000000000, 4.7500000000000000, 0.0 },
267 { 2.1579745473225476, 5.0000000000000000, 5.0000000000000000, 0.0 },
268 };
269 const double toler013 = 1.0000000000000008e-12;
270
271 // Test data for nu=10.000000000000000.
272 // max(|f - f_GSL|): 5.0306980803327406e-17 at index 20
273 // max(|f - f_GSL| / |f_GSL|): 1.2741587624782699e-14
274 // mean(f - f_GSL): -5.4602116438803446e-18
275 // variance(f - f_GSL): 1.0558971696213844e-34
276 // stddev(f - f_GSL): 1.0275685717368863e-17
277 const testcase_cyl_bessel_i<double>
278 data014[21] =
279 {
280 { 0.0000000000000000, 10.000000000000000, 0.0000000000000000, 0.0 },
281 { 2.5701232848571186e-16, 10.000000000000000, 0.25000000000000000, 0.0 },
282 { 2.6430419258812784e-13, 10.000000000000000, 0.50000000000000000, 0.0 },
283 { 1.5349659676120412e-11, 10.000000000000000, 0.75000000000000000, 0.0 },
284 { 2.7529480398368732e-10, 10.000000000000000, 1.0000000000000000, 0.0 },
285 { 2.5967897782035928e-09, 10.000000000000000, 1.2500000000000000, 0.0 },
286 { 1.6330924437799743e-08, 10.000000000000000, 1.5000000000000000, 0.0 },
287 { 7.7706676834614079e-08, 10.000000000000000, 1.7500000000000000, 0.0 },
288 { 3.0169638793506839e-07, 10.000000000000000, 2.0000000000000000, 0.0 },
289 { 1.0034459057774481e-06, 10.000000000000000, 2.2500000000000000, 0.0 },
290 { 2.9557436109680578e-06, 10.000000000000000, 2.5000000000000000, 0.0 },
291 { 7.8955603774082724e-06, 10.000000000000000, 2.7500000000000000, 0.0 },
292 { 1.9464393470612970e-05, 10.000000000000000, 3.0000000000000000, 0.0 },
293 { 4.4875369479742435e-05, 10.000000000000000, 3.2500000000000000, 0.0 },
294 { 9.7760848514528916e-05, 10.000000000000000, 3.5000000000000000, 0.0 },
295 { 0.00020289011210063496, 10.000000000000000, 3.7500000000000000, 0.0 },
296 { 0.00040378896132693058, 10.000000000000000, 4.0000000000000000, 0.0 },
297 { 0.00077478519551669892, 10.000000000000000, 4.2500000000000000, 0.0 },
298 { 0.0014397060684919682, 10.000000000000000, 4.5000000000000000, 0.0 },
299 { 0.0026004486016189452, 10.000000000000000, 4.7500000000000000, 0.0 },
300 { 0.0045800444191760525, 10.000000000000000, 5.0000000000000000, 0.0 },
301 };
302 const double toler014 = 1.0000000000000008e-12;
303
304 // Test data for nu=20.000000000000000.
305 // max(|f - f_GSL|): 6.9147129330604657e-25 at index 20
306 // max(|f - f_GSL| / |f_GSL|): 1.6061319023473306e-14
307 // mean(f - f_GSL): -5.1436249496041580e-26
308 // variance(f - f_GSL): 2.1506355008505938e-50
309 // stddev(f - f_GSL): 1.4665045178418625e-25
310 const testcase_cyl_bessel_i<double>
311 data015[21] =
312 {
313 { 0.0000000000000000, 20.000000000000000, 0.0000000000000000, 0.0 },
314 { 3.5677858077910353e-37, 20.000000000000000, 0.25000000000000000, 0.0 },
315 { 3.7494538480790194e-31, 20.000000000000000, 0.50000000000000000, 0.0 },
316 { 1.2514356342425337e-27, 20.000000000000000, 0.75000000000000000, 0.0 },
317 { 3.9668359858190197e-25, 20.000000000000000, 1.0000000000000000, 0.0 },
318 { 3.4637832909868234e-23, 20.000000000000000, 1.2500000000000000, 0.0 },
319 { 1.3388331839683472e-21, 20.000000000000000, 1.5000000000000000, 0.0 },
320 { 2.9502376732679751e-20, 20.000000000000000, 1.7500000000000000, 0.0 },
321 { 4.3105605761095479e-19, 20.000000000000000, 2.0000000000000000, 0.0 },
322 { 4.6032451406433059e-18, 20.000000000000000, 2.2500000000000000, 0.0 },
323 { 3.8400317244170310e-17, 20.000000000000000, 2.5000000000000000, 0.0 },
324 { 2.6239115263043263e-16, 20.000000000000000, 2.7500000000000000, 0.0 },
325 { 1.5209660019426689e-15, 20.000000000000000, 3.0000000000000000, 0.0 },
326 { 7.6806450728249953e-15, 20.000000000000000, 3.2500000000000000, 0.0 },
327 { 3.4495528847222945e-14, 20.000000000000000, 3.5000000000000000, 0.0 },
328 { 1.4006589294850677e-13, 20.000000000000000, 3.7500000000000000, 0.0 },
329 { 5.2100734221993054e-13, 20.000000000000000, 4.0000000000000000, 0.0 },
330 { 1.7946903269488168e-12, 20.000000000000000, 4.2500000000000000, 0.0 },
331 { 5.7763830562279699e-12, 20.000000000000000, 4.5000000000000000, 0.0 },
332 { 1.7502433074548735e-11, 20.000000000000000, 4.7500000000000000, 0.0 },
333 { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000, 0.0 },
334 };
335 const double toler015 = 1.0000000000000008e-12;
336 // cyl_bessel_i
337
338 // Test data for nu=0.0000000000000000.
339 // max(|f - f_GSL|): 2.5841998320082313e+28 at index 20
340 // max(|f - f_GSL| / |f_GSL|): 2.4067014886642843e-14
341 // mean(f - f_GSL): -1.2242902567974868e+27
342 // variance(f - f_GSL): inf
343 // stddev(f - f_GSL): inf
344 const testcase_cyl_bessel_i<double>
345 data016[21] =
346 {
347 { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
348 { 27.239871823604439, 0.0000000000000000, 5.0000000000000000, 0.0 },
349 { 2815.7166284662558, 0.0000000000000000, 10.000000000000000, 0.0 },
350 { 339649.37329791381, 0.0000000000000000, 15.000000000000000, 0.0 },
351 { 43558282.559553474, 0.0000000000000000, 20.000000000000000, 0.0 },
352 { 5774560606.4663124, 0.0000000000000000, 25.000000000000000, 0.0 },
353 { 781672297823.97925, 0.0000000000000000, 30.000000000000000, 0.0 },
354 { 107338818494514.42, 0.0000000000000000, 35.000000000000000, 0.0 },
355 { 14894774793419916., 0.0000000000000000, 40.000000000000000, 0.0 },
356 { 2.0834140751773164e+18, 0.0000000000000000, 45.000000000000000, 0.0 },
357 { 2.9325537838493457e+20, 0.0000000000000000, 50.000000000000000, 0.0 },
358 { 4.1487895607332160e+22, 0.0000000000000000, 55.000000000000000, 0.0 },
359 { 5.8940770556098216e+24, 0.0000000000000000, 60.000000000000000, 0.0 },
360 { 8.4030398456255582e+26, 0.0000000000000000, 65.000000000000000, 0.0 },
361 { 1.2015889579125424e+29, 0.0000000000000000, 70.000000000000000, 0.0 },
362 { 1.7226390780357976e+31, 0.0000000000000000, 75.000000000000000, 0.0 },
363 { 2.4751784043341661e+33, 0.0000000000000000, 80.000000000000000, 0.0 },
364 { 3.5634776304081403e+35, 0.0000000000000000, 85.000000000000000, 0.0 },
365 { 5.1392383455086475e+37, 0.0000000000000000, 90.000000000000000, 0.0 },
366 { 7.4233258618752072e+39, 0.0000000000000000, 95.000000000000000, 0.0 },
367 { 1.0737517071310986e+42, 0.0000000000000000, 100.00000000000000, 0.0 },
368 };
369 const double toler016 = 2.5000000000000015e-12;
370
371 // Test data for nu=0.33333333333333331.
372 // max(|f - f_GSL|): 1.0986717848657750e+28 at index 20
373 // max(|f - f_GSL| / |f_GSL|): 1.2017640663876795e-14
374 // mean(f - f_GSL): -5.2068252642007974e+26
375 // variance(f - f_GSL): inf
376 // stddev(f - f_GSL): inf
377 const testcase_cyl_bessel_i<double>
378 data017[21] =
379 {
380 { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000, 0.0 },
381 { 26.897553069268362, 0.33333333333333331, 5.0000000000000000, 0.0 },
382 { 2799.2396097056790, 0.33333333333333331, 10.000000000000000, 0.0 },
383 { 338348.63146593666, 0.33333333333333331, 15.000000000000000, 0.0 },
384 { 43434263.927938424, 0.33333333333333331, 20.000000000000000, 0.0 },
385 { 5761474759.6213636, 0.33333333333333331, 25.000000000000000, 0.0 },
386 { 780201111830.30237, 0.33333333333333331, 30.000000000000000, 0.0 },
387 { 107166066959051.91, 0.33333333333333331, 35.000000000000000, 0.0 },
388 { 14873836574083762., 0.33333333333333331, 40.000000000000000, 0.0 },
389 { 2.0808143020217085e+18, 0.33333333333333331, 45.000000000000000, 0.0 },
390 { 2.9292639365644226e+20, 0.33333333333333331, 50.000000000000000, 0.0 },
391 { 4.1445621624120489e+22, 0.33333333333333331, 55.000000000000000, 0.0 },
392 { 5.8885758374365916e+24, 0.33333333333333331, 60.000000000000000, 0.0 },
393 { 8.3958047021083941e+26, 0.33333333333333331, 65.000000000000000, 0.0 },
394 { 1.2006287819446431e+29, 0.33333333333333331, 70.000000000000000, 0.0 },
395 { 1.7213548977150022e+31, 0.33333333333333331, 75.000000000000000, 0.0 },
396 { 2.4734492458444449e+33, 0.33333333333333331, 80.000000000000000, 0.0 },
397 { 3.5611354547857122e+35, 0.33333333333333331, 85.000000000000000, 0.0 },
398 { 5.1360491295551848e+37, 0.33333333333333331, 90.000000000000000, 0.0 },
399 { 7.4189629097600431e+39, 0.33333333333333331, 95.000000000000000, 0.0 },
400 { 1.0731523308358370e+42, 0.33333333333333331, 100.00000000000000, 0.0 },
401 };
402 const double toler017 = 1.0000000000000008e-12;
403
404 // Test data for nu=0.50000000000000000.
405 // max(|f - f_GSL|): 7.1181552258909366e+27 at index 20
406 // max(|f - f_GSL| / |f_GSL|): 1.2230293310085236e-14
407 // mean(f - f_GSL): -3.3462733503919608e+26
408 // variance(f - f_GSL): inf
409 // stddev(f - f_GSL): inf
410 const testcase_cyl_bessel_i<double>
411 data018[21] =
412 {
413 { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
414 { 26.477547497559065, 0.50000000000000000, 5.0000000000000000, 0.0 },
415 { 2778.7846038745711, 0.50000000000000000, 10.000000000000000, 0.0 },
416 { 336729.88718706399, 0.50000000000000000, 15.000000000000000, 0.0 },
417 { 43279746.272428922, 0.50000000000000000, 20.000000000000000, 0.0 },
418 { 5745159748.3464680, 0.50000000000000000, 25.000000000000000, 0.0 },
419 { 778366068840.44580, 0.50000000000000000, 30.000000000000000, 0.0 },
420 { 106950522408567.66, 0.50000000000000000, 35.000000000000000, 0.0 },
421 { 14847705549021960., 0.50000000000000000, 40.000000000000000, 0.0 },
422 { 2.0775691824625661e+18, 0.50000000000000000, 45.000000000000000, 0.0 },
423 { 2.9251568529912984e+20, 0.50000000000000000, 50.000000000000000, 0.0 },
424 { 4.1392840094781220e+22, 0.50000000000000000, 55.000000000000000, 0.0 },
425 { 5.8817065760751945e+24, 0.50000000000000000, 60.000000000000000, 0.0 },
426 { 8.3867695787277245e+26, 0.50000000000000000, 65.000000000000000, 0.0 },
427 { 1.1994296461653203e+29, 0.50000000000000000, 70.000000000000000, 0.0 },
428 { 1.7197510246063334e+31, 0.50000000000000000, 75.000000000000000, 0.0 },
429 { 2.4712895036230794e+33, 0.50000000000000000, 80.000000000000000, 0.0 },
430 { 3.5582099086757769e+35, 0.50000000000000000, 85.000000000000000, 0.0 },
431 { 5.1320654031231128e+37, 0.50000000000000000, 90.000000000000000, 0.0 },
432 { 7.4135128383495239e+39, 0.50000000000000000, 95.000000000000000, 0.0 },
433 { 1.0724035825423179e+42, 0.50000000000000000, 100.00000000000000, 0.0 },
434 };
435 const double toler018 = 1.0000000000000008e-12;
436
437 // Test data for nu=0.66666666666666663.
438 // max(|f - f_GSL|): 4.6422751473201760e+27 at index 20
439 // max(|f - f_GSL| / |f_GSL|): 8.8432218147527708e-15
440 // mean(f - f_GSL): -2.2367290021744526e+26
441 // variance(f - f_GSL): inf
442 // stddev(f - f_GSL): inf
443 const testcase_cyl_bessel_i<double>
444 data019[21] =
445 {
446 { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000, 0.0 },
447 { 25.902310583215122, 0.66666666666666663, 5.0000000000000000, 0.0 },
448 { 2750.4090423459315, 0.66666666666666663, 10.000000000000000, 0.0 },
449 { 334476.98138574377, 0.66666666666666663, 15.000000000000000, 0.0 },
450 { 43064361.686912313, 0.66666666666666663, 20.000000000000000, 0.0 },
451 { 5722397441.9603882, 0.66666666666666663, 25.000000000000000, 0.0 },
452 { 775804343498.02661, 0.66666666666666663, 30.000000000000000, 0.0 },
453 { 106649495512800.88, 0.66666666666666663, 35.000000000000000, 0.0 },
454 { 14811199896983754., 0.66666666666666663, 40.000000000000000, 0.0 },
455 { 2.0730345814356961e+18, 0.66666666666666663, 45.000000000000000, 0.0 },
456 { 2.9194166755257467e+20, 0.66666666666666663, 50.000000000000000, 0.0 },
457 { 4.1319059569935374e+22, 0.66666666666666663, 55.000000000000000, 0.0 },
458 { 5.8721031476386222e+24, 0.66666666666666663, 60.000000000000000, 0.0 },
459 { 8.3741368248217830e+26, 0.66666666666666663, 65.000000000000000, 0.0 },
460 { 1.1977528777008688e+29, 0.66666666666666663, 70.000000000000000, 0.0 },
461 { 1.7175081240014333e+31, 0.66666666666666663, 75.000000000000000, 0.0 },
462 { 2.4682690458513916e+33, 0.66666666666666663, 80.000000000000000, 0.0 },
463 { 3.5541181975850724e+35, 0.66666666666666663, 85.000000000000000, 0.0 },
464 { 5.1264933963228892e+37, 0.66666666666666663, 90.000000000000000, 0.0 },
465 { 7.4058894880134064e+39, 0.66666666666666663, 95.000000000000000, 0.0 },
466 { 1.0713562154788124e+42, 0.66666666666666663, 100.00000000000000, 0.0 },
467 };
468 const double toler019 = 5.0000000000000039e-13;
469
470 // Test data for nu=1.0000000000000000.
471 // max(|f - f_GSL|): 5.4159876718735387e+27 at index 20
472 // max(|f - f_GSL| / |f_GSL|): 7.0819761463168391e-15
473 // mean(f - f_GSL): 2.5933470782682662e+26
474 // variance(f - f_GSL): inf
475 // stddev(f - f_GSL): inf
476 const testcase_cyl_bessel_i<double>
477 data020[21] =
478 {
479 { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000, 0.0 },
480 { 24.335642142450524, 1.0000000000000000, 5.0000000000000000, 0.0 },
481 { 2670.9883037012560, 1.0000000000000000, 10.000000000000000, 0.0 },
482 { 328124.92197020649, 1.0000000000000000, 15.000000000000000, 0.0 },
483 { 42454973.385127783, 1.0000000000000000, 20.000000000000000, 0.0 },
484 { 5657865129.8787022, 1.0000000000000000, 25.000000000000000, 0.0 },
485 { 768532038938.95667, 1.0000000000000000, 30.000000000000000, 0.0 },
486 { 105794126051896.17, 1.0000000000000000, 35.000000000000000, 0.0 },
487 { 14707396163259352., 1.0000000000000000, 40.000000000000000, 0.0 },
488 { 2.0601334620815780e+18, 1.0000000000000000, 45.000000000000000, 0.0 },
489 { 2.9030785901035638e+20, 1.0000000000000000, 50.000000000000000, 0.0 },
490 { 4.1108986452992812e+22, 1.0000000000000000, 55.000000000000000, 0.0 },
491 { 5.8447515883904527e+24, 1.0000000000000000, 60.000000000000000, 0.0 },
492 { 8.3381485471501288e+26, 1.0000000000000000, 65.000000000000000, 0.0 },
493 { 1.1929750788892366e+29, 1.0000000000000000, 70.000000000000000, 0.0 },
494 { 1.7111160152965382e+31, 1.0000000000000000, 75.000000000000000, 0.0 },
495 { 2.4596595795675343e+33, 1.0000000000000000, 80.000000000000000, 0.0 },
496 { 3.5424536064404024e+35, 1.0000000000000000, 85.000000000000000, 0.0 },
497 { 5.1106068152566129e+37, 1.0000000000000000, 90.000000000000000, 0.0 },
498 { 7.3841518091360182e+39, 1.0000000000000000, 95.000000000000000, 0.0 },
499 { 1.0683693903381569e+42, 1.0000000000000000, 100.00000000000000, 0.0 },
500 };
501 const double toler020 = 5.0000000000000039e-13;
502
503 // Test data for nu=2.0000000000000000.
504 // max(|f - f_GSL|): 6.1897001964269014e+27 at index 20
505 // max(|f - f_GSL| / |f_GSL|): 1.0553248866140883e-14
506 // mean(f - f_GSL): 2.9514880793266611e+26
507 // variance(f - f_GSL): inf
508 // stddev(f - f_GSL): inf
509 const testcase_cyl_bessel_i<double>
510 data021[21] =
511 {
512 { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000, 0.0 },
513 { 17.505614966624233, 2.0000000000000000, 5.0000000000000000, 0.0 },
514 { 2281.5189677260046, 2.0000000000000000, 10.000000000000000, 0.0 },
515 { 295899.38370188628, 2.0000000000000000, 15.000000000000000, 0.0 },
516 { 39312785.221040756, 2.0000000000000000, 20.000000000000000, 0.0 },
517 { 5321931396.0760155, 2.0000000000000000, 25.000000000000000, 0.0 },
518 { 730436828561.38013, 2.0000000000000000, 30.000000000000000, 0.0 },
519 { 101293439862977.19, 2.0000000000000000, 35.000000000000000, 0.0 },
520 { 14159404985256920., 2.0000000000000000, 40.000000000000000, 0.0 },
521 { 1.9918525879736883e+18, 2.0000000000000000, 45.000000000000000, 0.0 },
522 { 2.8164306402451938e+20, 2.0000000000000000, 50.000000000000000, 0.0 },
523 { 3.9993023372677540e+22, 2.0000000000000000, 55.000000000000000, 0.0 },
524 { 5.6992520026634433e+24, 2.0000000000000000, 60.000000000000000, 0.0 },
525 { 8.1464814287900364e+26, 2.0000000000000000, 65.000000000000000, 0.0 },
526 { 1.1675039556585663e+29, 2.0000000000000000, 70.000000000000000, 0.0 },
527 { 1.6770093176278926e+31, 2.0000000000000000, 75.000000000000000, 0.0 },
528 { 2.4136869148449879e+33, 2.0000000000000000, 80.000000000000000, 0.0 },
529 { 3.4801257808448186e+35, 2.0000000000000000, 85.000000000000000, 0.0 },
530 { 5.0256693051696307e+37, 2.0000000000000000, 90.000000000000000, 0.0 },
531 { 7.2678700343145818e+39, 2.0000000000000000, 95.000000000000000, 0.0 },
532 { 1.0523843193243042e+42, 2.0000000000000000, 100.00000000000000, 0.0 },
533 };
534 const double toler021 = 1.0000000000000008e-12;
535
536 // Test data for nu=5.0000000000000000.
537 // max(|f - f_GSL|): 1.0831975343747077e+27 at index 20
538 // max(|f - f_GSL| / |f_GSL|): 1.0289491375166011e-14
539 // mean(f - f_GSL): -5.2041812077613416e+25
540 // variance(f - f_GSL): inf
541 // stddev(f - f_GSL): inf
542 const testcase_cyl_bessel_i<double>
543 data022[21] =
544 {
545 { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000, 0.0 },
546 { 2.1579745473225476, 5.0000000000000000, 5.0000000000000000, 0.0 },
547 { 777.18828640326012, 5.0000000000000000, 10.000000000000000, 0.0 },
548 { 144572.01120063409, 5.0000000000000000, 15.000000000000000, 0.0 },
549 { 23018392.213413671, 5.0000000000000000, 20.000000000000000, 0.0 },
550 { 3472466208.7419176, 5.0000000000000000, 25.000000000000000, 0.0 },
551 { 512151465476.93494, 5.0000000000000000, 30.000000000000000, 0.0 },
552 { 74756743552251.547, 5.0000000000000000, 35.000000000000000, 0.0 },
553 { 10858318337624278., 5.0000000000000000, 40.000000000000000, 0.0 },
554 { 1.5736087399245911e+18, 5.0000000000000000, 45.000000000000000, 0.0 },
555 { 2.2785483079112825e+20, 5.0000000000000000, 50.000000000000000, 0.0 },
556 { 3.2989391052963687e+22, 5.0000000000000000, 55.000000000000000, 0.0 },
557 { 4.7777652072561732e+24, 5.0000000000000000, 60.000000000000000, 0.0 },
558 { 6.9232165147172657e+26, 5.0000000000000000, 65.000000000000000, 0.0 },
559 { 1.0038643002095155e+29, 5.0000000000000000, 70.000000000000000, 0.0 },
560 { 1.4566328222327073e+31, 5.0000000000000000, 75.000000000000000, 0.0 },
561 { 2.1151488565944835e+33, 5.0000000000000000, 80.000000000000000, 0.0 },
562 { 3.0735883450768239e+35, 5.0000000000000000, 85.000000000000000, 0.0 },
563 { 4.4694790189230327e+37, 5.0000000000000000, 90.000000000000000, 0.0 },
564 { 6.5037505570430995e+39, 5.0000000000000000, 95.000000000000000, 0.0 },
565 { 9.4700938730355882e+41, 5.0000000000000000, 100.00000000000000, 0.0 },
566 };
567 const double toler022 = 1.0000000000000008e-12;
568
569 // Test data for nu=10.000000000000000.
570 // max(|f - f_GSL|): 1.5474250491067253e+26 at index 20
571 // max(|f - f_GSL| / |f_GSL|): 1.2009151331790140e-14
572 // mean(f - f_GSL): 7.4845081675400805e+24
573 // variance(f - f_GSL): inf
574 // stddev(f - f_GSL): inf
575 const testcase_cyl_bessel_i<double>
576 data023[21] =
577 {
578 { 0.0000000000000000, 10.000000000000000, 0.0000000000000000, 0.0 },
579 { 0.0045800444191760525, 10.000000000000000, 5.0000000000000000, 0.0 },
580 { 21.891706163723381, 10.000000000000000, 10.000000000000000, 0.0 },
581 { 12267.475049806462, 10.000000000000000, 15.000000000000000, 0.0 },
582 { 3540200.2090195213, 10.000000000000000, 20.000000000000000, 0.0 },
583 { 771298871.17072666, 10.000000000000000, 25.000000000000000, 0.0 },
584 { 145831809975.96710, 10.000000000000000, 30.000000000000000, 0.0 },
585 { 25449470018534.777, 10.000000000000000, 35.000000000000000, 0.0 },
586 { 4228469210516757.0, 10.000000000000000, 40.000000000000000, 0.0 },
587 { 6.8049404557505165e+17, 10.000000000000000, 45.000000000000000, 0.0 },
588 { 1.0715971594776370e+20, 10.000000000000000, 50.000000000000000, 0.0 },
589 { 1.6618215752886714e+22, 10.000000000000000, 55.000000000000000, 0.0 },
590 { 2.5486246072566784e+24, 10.000000000000000, 60.000000000000000, 0.0 },
591 { 3.8764628702155475e+26, 10.000000000000000, 65.000000000000000, 0.0 },
592 { 5.8592538145409686e+28, 10.000000000000000, 70.000000000000000, 0.0 },
593 { 8.8135370711317444e+30, 10.000000000000000, 75.000000000000000, 0.0 },
594 { 1.3207418268325279e+33, 10.000000000000000, 80.000000000000000, 0.0 },
595 { 1.9732791360862190e+35, 10.000000000000000, 85.000000000000000, 0.0 },
596 { 2.9411893748384672e+37, 10.000000000000000, 90.000000000000000, 0.0 },
597 { 4.3754494922439984e+39, 10.000000000000000, 95.000000000000000, 0.0 },
598 { 6.4989755247201446e+41, 10.000000000000000, 100.00000000000000, 0.0 },
599 };
600 const double toler023 = 1.0000000000000008e-12;
601
602 // Test data for nu=20.000000000000000.
603 // max(|f - f_GSL|): 1.9342813113834067e+25 at index 20
604 // max(|f - f_GSL| / |f_GSL|): 1.5819230756119302e-14
605 // mean(f - f_GSL): 1.0213821732843951e+24
606 // variance(f - f_GSL): inf
607 // stddev(f - f_GSL): inf
608 const testcase_cyl_bessel_i<double>
609 data024[21] =
610 {
611 { 0.0000000000000000, 20.000000000000000, 0.0000000000000000, 0.0 },
612 { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000, 0.0 },
613 { 0.00012507997356449481, 20.000000000000000, 10.000000000000000, 0.0 },
614 { 1.6470152535015836, 20.000000000000000, 15.000000000000000, 0.0 },
615 { 3188.7503288536154, 20.000000000000000, 20.000000000000000, 0.0 },
616 { 2449840.5422952301, 20.000000000000000, 25.000000000000000, 0.0 },
617 { 1126985104.4483771, 20.000000000000000, 30.000000000000000, 0.0 },
618 { 379617876611.88580, 20.000000000000000, 35.000000000000000, 0.0 },
619 { 104459633129479.88, 20.000000000000000, 40.000000000000000, 0.0 },
620 { 25039579987216524., 20.000000000000000, 45.000000000000000, 0.0 },
621 { 5.4420084027529984e+18, 20.000000000000000, 50.000000000000000, 0.0 },
622 { 1.1007498584335495e+21, 20.000000000000000, 55.000000000000000, 0.0 },
623 { 2.1091734863057236e+23, 20.000000000000000, 60.000000000000000, 0.0 },
624 { 3.8763618091286891e+25, 20.000000000000000, 65.000000000000000, 0.0 },
625 { 6.8946130527930870e+27, 20.000000000000000, 70.000000000000000, 0.0 },
626 { 1.1946319948836447e+30, 20.000000000000000, 75.000000000000000, 0.0 },
627 { 2.0265314377577587e+32, 20.000000000000000, 80.000000000000000, 0.0 },
628 { 3.3784665214179985e+34, 20.000000000000000, 85.000000000000000, 0.0 },
629 { 5.5516089411796646e+36, 20.000000000000000, 90.000000000000000, 0.0 },
630 { 9.0129310795305151e+38, 20.000000000000000, 95.000000000000000, 0.0 },
631 { 1.4483461256427176e+41, 20.000000000000000, 100.00000000000000, 0.0 },
632 };
633 const double toler024 = 1.0000000000000008e-12;
634
635 // Test data for nu=50.000000000000000.
636 // max(|f - f_GSL|): 4.4862481587261630e+22 at index 20
637 // max(|f - f_GSL| / |f_GSL|): 6.0191728870880627e-14
638 // mean(f - f_GSL): 2.1246678955085789e+21
639 // variance(f - f_GSL): inf
640 // stddev(f - f_GSL): inf
641 const testcase_cyl_bessel_i<double>
642 data025[21] =
643 {
644 { 0.0000000000000000, 50.000000000000000, 0.0000000000000000, 0.0 },
645 { 2.9314696468108517e-45, 50.000000000000000, 5.0000000000000000, 0.0 },
646 { 4.7568945607268435e-30, 50.000000000000000, 10.000000000000000, 0.0 },
647 { 5.5468372730667069e-21, 50.000000000000000, 15.000000000000000, 0.0 },
648 { 2.2551205757604056e-14, 50.000000000000000, 20.000000000000000, 0.0 },
649 { 4.5344251866130257e-09, 50.000000000000000, 25.000000000000000, 0.0 },
650 { 0.00014590106916468940, 50.000000000000000, 30.000000000000000, 0.0 },
651 { 1.3965549457254882, 50.000000000000000, 35.000000000000000, 0.0 },
652 { 5726.8656631289887, 50.000000000000000, 40.000000000000000, 0.0 },
653 { 12672593.113027781, 50.000000000000000, 45.000000000000000, 0.0 },
654 { 17650802430.016712, 50.000000000000000, 50.000000000000000, 0.0 },
655 { 17220231607789.926, 50.000000000000000, 55.000000000000000, 0.0 },
656 { 12704607933652176., 50.000000000000000, 60.000000000000000, 0.0 },
657 { 7.4989491942193715e+18, 50.000000000000000, 65.000000000000000, 0.0 },
658 { 3.6944034898904922e+21, 50.000000000000000, 70.000000000000000, 0.0 },
659 { 1.5691634774370186e+24, 50.000000000000000, 75.000000000000000, 0.0 },
660 { 5.8927749458163587e+26, 50.000000000000000, 80.000000000000000, 0.0 },
661 { 1.9958849054749339e+29, 50.000000000000000, 85.000000000000000, 0.0 },
662 { 6.1946050361781500e+31, 50.000000000000000, 90.000000000000000, 0.0 },
663 { 1.7845429728697119e+34, 50.000000000000000, 95.000000000000000, 0.0 },
664 { 4.8219580855940819e+36, 50.000000000000000, 100.00000000000000, 0.0 },
665 };
666 const double toler025 = 5.0000000000000029e-12;
667
668 // Test data for nu=100.00000000000000.
669 // max(|f - f_GSL|): 185597952.00000000 at index 20
670 // max(|f - f_GSL| / |f_GSL|): 2.8278213985558577e-13
671 // mean(f - f_GSL): 8855366.2060860656
672 // variance(f - f_GSL): 4.2527168883984777e+19
673 // stddev(f - f_GSL): 6521285830.5693655
674 const testcase_cyl_bessel_i<double>
675 data026[21] =
676 {
677 { 0.0000000000000000, 100.00000000000000, 0.0000000000000000, 0.0 },
678 { 7.0935514885313123e-119, 100.00000000000000, 5.0000000000000000, 0.0 },
679 { 1.0823442017492015e-88, 100.00000000000000, 10.000000000000000, 0.0 },
680 { 5.9887888536468904e-71, 100.00000000000000, 15.000000000000000, 0.0 },
681 { 2.8703193216428771e-58, 100.00000000000000, 20.000000000000000, 0.0 },
682 { 2.4426896913122370e-48, 100.00000000000000, 25.000000000000000, 0.0 },
683 { 3.9476420053334271e-40, 100.00000000000000, 30.000000000000000, 0.0 },
684 { 4.2836596180818780e-33, 100.00000000000000, 35.000000000000000, 0.0 },
685 { 6.6249380222596129e-27, 100.00000000000000, 40.000000000000000, 0.0 },
686 { 2.3702587262788900e-21, 100.00000000000000, 45.000000000000000, 0.0 },
687 { 2.7278879470966917e-16, 100.00000000000000, 50.000000000000000, 0.0 },
688 { 1.2763258878228082e-11, 100.00000000000000, 55.000000000000000, 0.0 },
689 { 2.8832770906491972e-07, 100.00000000000000, 60.000000000000000, 0.0 },
690 { 0.0035805902717061223, 100.00000000000000, 65.000000000000000, 0.0 },
691 { 27.017219102595387, 100.00000000000000, 70.000000000000000, 0.0 },
692 { 134001.44891209516, 100.00000000000000, 75.000000000000000, 0.0 },
693 { 465194832.85060996, 100.00000000000000, 80.000000000000000, 0.0 },
694 { 1189280653119.4814, 100.00000000000000, 85.000000000000000, 0.0 },
695 { 2334119331258728.0, 100.00000000000000, 90.000000000000000, 0.0 },
696 { 3.6399223078502436e+18, 100.00000000000000, 95.000000000000000, 0.0 },
697 { 4.6415349416162005e+21, 100.00000000000000, 100.00000000000000, 0.0 },
698 };
699 const double toler026 = 2.5000000000000014e-11;
700
701 template<typename Ret, unsigned int Num>
702 void
test(const testcase_cyl_bessel_i<Ret> (& data)[Num],Ret toler)703 test(const testcase_cyl_bessel_i<Ret> (&data)[Num], Ret toler)
704 {
705 bool test __attribute__((unused)) = true;
706 const Ret eps = std::numeric_limits<Ret>::epsilon();
707 Ret max_abs_diff = -Ret(1);
708 Ret max_abs_frac = -Ret(1);
709 unsigned int num_datum = Num;
710 for (unsigned int i = 0; i < num_datum; ++i)
711 {
712 const Ret f = std::cyl_bessel_i(data[i].nu, data[i].x);
713 const Ret f0 = data[i].f0;
714 const Ret diff = f - f0;
715 if (std::abs(diff) > max_abs_diff)
716 max_abs_diff = std::abs(diff);
717 if (std::abs(f0) > Ret(10) * eps
718 && std::abs(f) > Ret(10) * eps)
719 {
720 const Ret frac = diff / f0;
721 if (std::abs(frac) > max_abs_frac)
722 max_abs_frac = std::abs(frac);
723 }
724 }
725 VERIFY(max_abs_frac < toler);
726 }
727
728 int
main()729 main()
730 {
731 test(data007, toler007);
732 test(data008, toler008);
733 test(data009, toler009);
734 test(data010, toler010);
735 test(data011, toler011);
736 test(data012, toler012);
737 test(data013, toler013);
738 test(data014, toler014);
739 test(data015, toler015);
740 test(data016, toler016);
741 test(data017, toler017);
742 test(data018, toler018);
743 test(data019, toler019);
744 test(data020, toler020);
745 test(data021, toler021);
746 test(data022, toler022);
747 test(data023, toler023);
748 test(data024, toler024);
749 test(data025, toler025);
750 test(data026, toler026);
751 return 0;
752 }
753