| blob | ee9fa057f66f191a008467575170919ac8a36509 |
1 use Test::More 'no_plan';
2 use Math::GSL qw/:all/;
3 use Math::GSL::Const qw/:all/;
4 use Math::GSL::Errno qw/:all/;
5 use Math::GSL::SF qw/:all/;
6 use Math::GSL::Machine qw/:all/;
7 use Math::GSL::Math qw/:all/;
8 use Math::GSL::Poly qw/:all/;
9 use Data::Dumper;
10 use strict;
11 use warnings;
13 BEGIN{ gsl_set_error_handler_off(); }
15 my $factor = 100;
16 my $TOL0 = $factor*2.0*$GSL_DBL_EPSILON;
17 my $TOL1 = $factor*16.0*$GSL_DBL_EPSILON;
18 my $TOL2 = $factor*256.0*$GSL_DBL_EPSILON;
19 my $TOL3 = $factor*2048.0*$GSL_DBL_EPSILON;
20 my $TOL4 = $factor*16384.0*$GSL_DBL_EPSILON;
21 my $TOL5 = $factor*131072.0*$GSL_DBL_EPSILON;
22 my $TOL6 = $factor*1048576.0*$GSL_DBL_EPSILON;
23 my $SQRT_TOL0 = 2.0*$GSL_SQRT_DBL_EPSILON;
24 my $TEST_SNGL = 1.0e-06;
26 my $w = 0.8*$GSL_LOG_DBL_MAX;
27 my $DBL_MAX = 1.7976931348623157e+308;
28 my $y = 0.2*$GSL_DBL_MAX;
29 my $DELTA = 1.2246467991473531772e-16;
32 my $results = {
33 # GSL does not seem to have one argument versions of Ai(x)
34 #'gsl_sf_airy_Ai_e(-5, $Math::GSL::GSL_MODE_DEFAULT, $r)' => 0.3507610090241142,
35 #'gsl_sf_airy_Ai_e(-500,$Math::GSL::GSL_MODE_DEFAULT, $r)' => 0.0725901201040411396,
36 "gsl_sf_bessel_J0(0.1)" => 0.99750156206604003230,
37 "gsl_sf_bessel_J0(2.0)" => 0.22389077914123566805,
38 "gsl_sf_bessel_J0(5)" => -0.17759677131433830434739701,
39 "gsl_sf_bessel_J0(100)" => 0.019985850304223122424,
40 "gsl_sf_bessel_J0(1e10)" => 2.1755917502468917269e-06,
41 "gsl_sf_erf(5)" => 0.999999999998463,
42 "gsl_sf_dilog(-3.0)" => -1.9393754207667089531,
43 "gsl_sf_dilog(-0.5)" => -0.4484142069236462024,
44 "gsl_sf_gamma(6.3)" => [ 201.813275184748, 1e-12 ],
45 "gsl_sf_dilog(-0.001)" => -0.0009997501110486510834,
46 "gsl_sf_dilog(0.1)" => 0.1026177910993911,
47 "gsl_sf_dilog(0.7)" => 0.8893776242860387386,
48 "gsl_sf_dilog(1.0)" => 1.6449340668482260,
49 "gsl_sf_gamma(-1)" => "nan",
50 "gsl_sf_clausen ($M_PI/20.0)" => [0.4478882448133546, $TOL0 ],
51 "gsl_sf_clausen ($M_PI/6.0)" => [0.8643791310538927, $TOL0 ],
52 "gsl_sf_clausen ($M_PI/3.0)" => [1.0149416064096535, $TOL0 ],
53 "gsl_sf_clausen ( 2.0*$M_PI + $M_PI/3.0)" => [1.0149416064096535, $TOL0 ],
54 "gsl_sf_clausen (100.0*$M_PI + $M_PI/3.0)" => [1.0149416064096535, $TOL0 ],
55 "gsl_sf_coupling_3j (0, 1, 1, 0, 1, -1)" => [sqrt(1.0/2.0), $TOL0 ],
56 "gsl_sf_coupling_3j (1, 1, 2, 1, -1, 0)" => [sqrt(1.0/6.0), $TOL0 ],
57 "gsl_sf_coupling_3j (2, 4, 6, 0, 2, -2)" => [sqrt(8.0/105.0), $TOL0 ],
58 "gsl_sf_coupling_3j (4, 4, 8, 0, 0, 0)" => [sqrt(2.0/35.0), $TOL0 ],
59 "gsl_sf_coupling_3j (4, 4, 8, 2, -2, 0)" => [2.0/3.0*sqrt(2.0/35.0), $TOL2 ],
60 "gsl_sf_coupling_3j (4, 4, 8, 4, -4, 0)" => [1.0/(3.0*sqrt(70.0)), $TOL2 ],
61 "gsl_sf_coupling_3j (-1, 1, 2, 1, -1, 0)" => [$GSL_NAN, $GSL_NAN ],
62 "gsl_sf_coupling_3j (1, -1, 2, 1, -1, 0)" => [$GSL_NAN, $GSL_NAN ],
63 "gsl_sf_coupling_3j (1, 1, -2, 1, -1, 0)" => [$GSL_NAN, $GSL_NAN ],
64 "gsl_sf_coupling_3j (1, 1, 2, 2, -1, 0)" => [0, 0 ],
65 "gsl_sf_coupling_3j (1, 1, 2, 1, -2, 0)" => [0, 0 ],
66 "gsl_sf_coupling_3j (1, 1, 2, 1, -1, 3)" => [0, 0 ],
67 "gsl_sf_coupling_3j (1, 1, 3, 1, -1, 0)" => [0, 0 ],
68 "gsl_sf_coupling_3j (1, 4, 2, 1, -1, 0)" => [0, 0 ],
69 "gsl_sf_coupling_3j (4, 1, 2, 1, -1, 0)" => [0, 0 ],
70 "gsl_sf_coupling_6j (2, 2, 4, 2, 2, 2)" => [ 1.0/6.0, $TOL0 ],
71 "gsl_sf_coupling_6j (4, 4, 2, 4, 4, 4)" => [-1.0/10.0, $TOL0 ],
72 "gsl_sf_coupling_6j (4, 4, 2, 4, 4, 2)" => [ 1.0/6.0, $TOL0 ],
73 "gsl_sf_coupling_6j (4, 4, 2, 2, 2, 2)" => [-0.5/sqrt(5.0), $TOL0 ],
74 "gsl_sf_coupling_6j (4, 4, 4, 2, 2, 2)" => [ sqrt(7.0/3.0)/10.0, $TOL0 ],
75 "gsl_sf_coupling_6j (6, 6, 6, 4, 4, 4)" => [-sqrt(3.0/5.0)/14.0, $TOL0 ],
76 "gsl_sf_coupling_6j (6, 6, 6, 4, 4, 2)" => [-sqrt(3.0/5.0)/7.0, $TOL0 ],
77 "gsl_sf_coupling_6j (-2, 2, 4, 2, 2, 2)" => [$GSL_NAN, $GSL_NAN ],
78 "gsl_sf_coupling_6j (2, -2, 4, 2, 2, 2)" => [$GSL_NAN, $GSL_NAN ],
79 "gsl_sf_coupling_6j (2, 2, -4, 2, 2, 2)" => [$GSL_NAN, $GSL_NAN ],
80 "gsl_sf_coupling_6j (2, 2, 4, -2, 2, 2)" => [$GSL_NAN, $GSL_NAN ],
81 "gsl_sf_coupling_6j (2, 2, 4, 2, -2, 2)" => [$GSL_NAN, $GSL_NAN ],
82 "gsl_sf_coupling_6j (2, 2, 4, 2, 2, -2)" => [$GSL_NAN, $GSL_NAN ],
83 "gsl_sf_coupling_6j (2, 2, 4, 2, 2, 7)" => [0, 0 ],
84 "gsl_sf_coupling_6j (2, 2, 4, 2, 7, 2)" => [0, 0 ],
85 "gsl_sf_coupling_6j (2, 2, 4, 7, 2, 2)" => [0, 0 ],
86 "gsl_sf_coupling_6j (2, 2, 7, 2, 2, 2)" => [0, 0 ],
87 "gsl_sf_coupling_6j (2, 7, 4, 2, 2, 2)" => [0, 0 ],
88 "gsl_sf_coupling_6j (7, 2, 4, 2, 2, 2)" => [0, 0 ],
89 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 2, 1, 1, 2)" => [-sqrt(1.0/6.0)/10.0, $TOL2 ],
90 "gsl_sf_coupling_9j (8, 4, 10, 7, 3, 8, 1, 1, 2)" => [ sqrt(7.0/3.0)/60.0, $TOL2 ],
91 "gsl_sf_coupling_9j (-4, 2, 4, 3, 3, 2, 1, 1, 2)" => [$GSL_NAN, $GSL_NAN ],
92 "gsl_sf_coupling_9j (4, -2, 4, 3, 3, 2, 1, 1, 2)" => [$GSL_NAN, $GSL_NAN ],
93 "gsl_sf_coupling_9j (4, 2, -4, 3, 3, 2, 1, 1, 2)" => [$GSL_NAN, $GSL_NAN ],
94 "gsl_sf_coupling_9j (4, 2, 4, -3, 3, 2, 1, 1, 2)" => [$GSL_NAN, $GSL_NAN ],
95 "gsl_sf_coupling_9j (4, 2, 4, 3, -3, 2, 1, 1, 2)" => [$GSL_NAN, $GSL_NAN ],
96 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, -2, 1, 1, 2)" => [$GSL_NAN, $GSL_NAN ],
97 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 2, -1, 1, 2)" => [$GSL_NAN, $GSL_NAN ],
98 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 2, 1, -1, 2)" => [$GSL_NAN, $GSL_NAN ],
99 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 2, 1, 1, -2)" => [$GSL_NAN, $GSL_NAN ],
100 "gsl_sf_coupling_9j (10, 2, 4, 3, 3, 2, 1, 1, 2)" => [0, 0 ],
101 "gsl_sf_coupling_9j (4, 10, 4, 3, 3, 2, 1, 1, 2)" => [0, 0 ],
102 "gsl_sf_coupling_9j (4, 2, 10, 3, 3, 2, 1, 1, 2)" => [0, 0 ],
103 "gsl_sf_coupling_9j (4, 2, 4, 10, 3, 2, 1, 1, 2)" => [0, 0 ],
104 "gsl_sf_coupling_9j (4, 2, 4, 3, 10, 2, 1, 1, 2)" => [0, 0 ],
105 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 10, 1, 1, 2)" => [0, 0 ],
106 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 2, 10, 1, 2)" => [0, 0 ],
107 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 2, 1, 10, 2)" => [0, 0 ],
108 "gsl_sf_coupling_9j (4, 2, 4, 3, 3, 2, 1, 1, 10)" => [0, 0 ],
109 "gsl_sf_dawson (1.0e-15)" => [1.0e-15, $TOL0 ],
110 "gsl_sf_dawson (0.5)" => [0.4244363835020222959, $TOL0 ],
111 "gsl_sf_dawson (2.0)" => [0.30134038892379196603, $TOL0 ],
112 "gsl_sf_dawson (1000.0)" => [0.0005000002500003750009, $TOL0 ],
113 "gsl_sf_debye_1 (0.1)" => [ 0.975277750004723276, $TOL0 ],
114 "gsl_sf_debye_1 (1.0)" => [ 0.777504634112248239, $TOL0 ],
115 "gsl_sf_debye_1 (10.0)" => [0.164443465679946027, $TOL0 ],
116 "gsl_sf_debye_2 (0.1)" => [ 0.967083287045302664, $TOL0 ],
117 "gsl_sf_debye_2 (1.0)" => [ 0.70787847562782924, $TOL0 ],
118 "gsl_sf_debye_2 (10.0)" => [0.0479714980201218708, $TOL0 ],
119 "gsl_sf_debye_3 (0.1)" => [ 0.962999940487211048, $TOL0 ],
120 "gsl_sf_debye_3 (1.0)" => [ 0.674415564077814667, $TOL0 ],
121 "gsl_sf_debye_3 (10.0)" => [0.0192957656903454886, $TOL0 ],
122 "gsl_sf_debye_4 (0.1)" => [ 0.960555486124335944, $TOL0 ],
123 "gsl_sf_debye_4 (1.0)" => [ 0.654874068886737049, $TOL0 ],
124 "gsl_sf_debye_4 (10.0)" => [0.00967367556027115896, $TOL0 ],
125 "gsl_sf_debye_5 (0.1)" => [ 0.95892849428310568745, $TOL0 ],
126 "gsl_sf_debye_5 (1.0)" => [ 0.6421002580217790246, $TOL0 ],
127 "gsl_sf_debye_5 (10.0)" => [0.005701535852992908538, $TOL0 ],
128 "gsl_sf_debye_6 (0.1)" => [ 0.95776777382605465878, $TOL0 ],
129 "gsl_sf_debye_6 (1.0)" => [ 0.63311142583495107588, $TOL0 ],
130 "gsl_sf_debye_6 (10.0)" => [3.7938493294615955279e-3, $TOL0 ],
131 "gsl_sf_multiply (-3.0,2.0)" => [-6.0, $TOL0 ],
132 "gsl_sf_multiply ($y, 1.0/$y)" => [ 1.0, $TOL0 ],
133 #"gsl_sf_multiply ($y, 0.2)" => [ 0.04*$GSL_DBL_MAX, $TOL1 ],
134 #"gsl_sf_multiply ($y, 4.0)" => [ 0.8*$GSL_DBL_MAX, $TOL1 ],
135 "gsl_sf_ellint_Kcomp ( 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [3.3566005233611923760, $TOL0 ],
136 "gsl_sf_ellint_Kcomp ( 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [1.6857503548125960429, $TOL0 ],
137 "gsl_sf_ellint_Kcomp (0.010, $Math::GSL::GSL_MODE_DEFAULT)" => [1.5708355989121522360, $TOL0 ],
138 "gsl_sf_ellint_Ecomp (0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [1.0284758090288040010, $TOL0 ],
139 "gsl_sf_ellint_Ecomp (0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [1.4674622093394271555, $TOL0 ],
140 "gsl_sf_ellint_Ecomp (0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [1.5707570561503852873, $TOL0 ],
141 "gsl_sf_ellint_Pcomp (0.99, 0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [3.13792612351836506315593, $TOL0 ],
142 "gsl_sf_ellint_Pcomp (0.50, 0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [1.60455249360848890075108, $TOL0 ],
143 "gsl_sf_ellint_Pcomp (0.01, 0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [1.49773208536003801277453, $TOL0 ],
144 "gsl_sf_ellint_Dcomp (0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [2.375395076351788975665323192, $TOL0 ],
145 "gsl_sf_ellint_Dcomp (0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [0.8731525818926755496456335628, $TOL0 ],
146 "gsl_sf_ellint_Dcomp (0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [0.7854276176694868932799393751, $TOL0 ],
147 "gsl_sf_ellint_F ($M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [1.3065333392738766762, $TOL0 ],
148 "gsl_sf_ellint_F ($M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [1.0895506700518854093, $TOL0 ],
149 "gsl_sf_ellint_F ($M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [1.0472129063770918952, $TOL0 ],
150 "gsl_sf_ellint_E ($M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [0.8704819220377943536, $TOL0 ],
151 "gsl_sf_ellint_E ($M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [1.0075555551444720293, $TOL0 ],
152 "gsl_sf_ellint_E ($M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [1.0471821963889481104, $TOL0 ],
153 "gsl_sf_ellint_P ($M_PI/3.0, 0.99, 0.5, $Math::GSL::GSL_MODE_DEFAULT)" => [1.1288726598764099882, $TOL0 ],
154 "gsl_sf_ellint_P ($M_PI/3.0, 0.50, 0.5, $Math::GSL::GSL_MODE_DEFAULT)" => [0.9570574331323584890, $TOL0 ],
155 "gsl_sf_ellint_P ($M_PI/3.0, 0.01, 0.5, $Math::GSL::GSL_MODE_DEFAULT)" => [0.9228868127118118465, $TOL0 ],
156 "gsl_sf_ellint_RF (5.0e-11, 1.0e-10, 1.0, $Math::GSL::GSL_MODE_DEFAULT)" => [12.36441982979439, $TOL0 ],
157 "gsl_sf_ellint_RF (1.0, 2.0, 3.0, $Math::GSL::GSL_MODE_DEFAULT)" => [0.7269459354689082, $TOL0 ],
158 "gsl_sf_ellint_RD (5.0e-11, 1.0e-10, 1.0, $Math::GSL::GSL_MODE_DEFAULT)" => [34.0932594919337362, $TOL0 ],
159 "gsl_sf_ellint_RD (1.0, 2.0, 3.0, $Math::GSL::GSL_MODE_DEFAULT)" => [0.2904602810289906, $TOL0 ],
160 "gsl_sf_ellint_RC (1.0, 2.0, $Math::GSL::GSL_MODE_DEFAULT)" => [0.7853981633974482, $TOL0 ],
161 "gsl_sf_ellint_RJ (2.0, 3.0, 4.0, 5.0, $Math::GSL::GSL_MODE_DEFAULT)" => [0.1429757966715675, $TOL0 ],
162 "gsl_sf_ellint_E ($M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [1.02847580902880400098389, $TOL0 ],
163 "gsl_sf_ellint_E ($M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [1.46746220933942715545980, $TOL0 ],
164 "gsl_sf_ellint_E ($M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [1.57075705615038528733708, $TOL0 ],
165 "gsl_sf_ellint_E (2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [1.18646969601981364833972, $TOL1 ],
166 "gsl_sf_ellint_E (2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [1.92736886353438228163734, $TOL0 ],
167 "gsl_sf_ellint_E (2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [2.09433191591182246425715, $TOL0 ],
168 "gsl_sf_ellint_E ($M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [2.05695161805760800196777, $TOL0 ],
169 "gsl_sf_ellint_E ($M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [2.93492441867885431091959, $TOL0 ],
170 "gsl_sf_ellint_E ($M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [3.14151411230077057467416, $TOL0 ],
171 "gsl_sf_ellint_E (4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [2.92743354009540235559582, $TOL0 ],
172 "gsl_sf_ellint_E (4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [3.94247997382332634020184, $TOL0 ],
173 "gsl_sf_ellint_E (4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [4.18869630868971868509117, $TOL0 ],
174 "gsl_sf_ellint_E (3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [3.08542742708641200295166, $TOL0 ],
175 "gsl_sf_ellint_E (3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [4.40238662801828146637939, $TOL0 ],
176 "gsl_sf_ellint_E (3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [4.71227116845115586201123, $TOL0 ],
177 "gsl_sf_ellint_E (5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [3.24342131407742165030750, $TOL1 ],
178 "gsl_sf_ellint_E (5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [4.86229328221323659255693, $TOL0 ],
179 "gsl_sf_ellint_E (5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [5.23584602821259303893130, $TOL0 ],
180 "gsl_sf_ellint_E (2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [4.11390323611521600393555, $TOL0 ],
181 "gsl_sf_ellint_E (2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [5.86984883735770862183918, $TOL0 ],
182 "gsl_sf_ellint_E (2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [6.28302822460154114934831, $TOL0 ],
183 "gsl_sf_ellint_E (7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [4.98438515815301035756360, $TOL0 ],
184 "gsl_sf_ellint_E (7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [6.87740439250218065112143, $TOL0 ],
185 "gsl_sf_ellint_E (7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [7.33021042099048925976532, $TOL0 ],
186 "gsl_sf_ellint_E (-$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.02847580902880400098389, $TOL0 ],
187 "gsl_sf_ellint_E (-$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.46746220933942715545980, $TOL0 ],
188 "gsl_sf_ellint_E (-$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.57075705615038528733708, $TOL0 ],
189 "gsl_sf_ellint_E (-2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.18646969601981364833972, $TOL1 ],
190 "gsl_sf_ellint_E (-2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.92736886353438228163734, $TOL0 ],
191 "gsl_sf_ellint_E (-2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.09433191591182246425715, $TOL0 ],
192 "gsl_sf_ellint_E (-$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.05695161805760800196777, $TOL0 ],
193 "gsl_sf_ellint_E (-$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.93492441867885431091959, $TOL0 ],
194 "gsl_sf_ellint_E (-$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.14151411230077057467416, $TOL0 ],
195 "gsl_sf_ellint_E (-4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.92743354009540235559582, $TOL0 ],
196 "gsl_sf_ellint_E (-4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.94247997382332634020184, $TOL0 ],
197 "gsl_sf_ellint_E (-4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.18869630868971868509117, $TOL0 ],
198 "gsl_sf_ellint_E (-3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.08542742708641200295166, $TOL0 ],
199 "gsl_sf_ellint_E (-3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.40238662801828146637939, $TOL0 ],
200 "gsl_sf_ellint_E (-3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.71227116845115586201123, $TOL0 ],
201 "gsl_sf_ellint_E (-5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.24342131407742165030750, $TOL1 ],
202 "gsl_sf_ellint_E (-5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.86229328221323659255693, $TOL0 ],
203 "gsl_sf_ellint_E (-5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.23584602821259303893130, $TOL0 ],
204 "gsl_sf_ellint_E (-2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.11390323611521600393555, $TOL0 ],
205 "gsl_sf_ellint_E (-2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.86984883735770862183918, $TOL0 ],
206 "gsl_sf_ellint_E (-2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-6.28302822460154114934831, $TOL0 ],
207 "gsl_sf_ellint_E (-7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.98438515815301035756360, $TOL0 ],
208 "gsl_sf_ellint_E (-7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-6.87740439250218065112143, $TOL0 ],
209 "gsl_sf_ellint_E (-7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-7.33021042099048925976532, $TOL0 ],
210 "gsl_sf_ellint_F ($M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [3.35660052336119237603347, $TOL0 ],
211 "gsl_sf_ellint_F ($M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [1.68575035481259604287120, $TOL0 ],
212 "gsl_sf_ellint_F ($M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [1.57083559891215223602641, $TOL0 ],
213 "gsl_sf_ellint_F (2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [5.40666770744850807588478, $TOL0 ],
214 "gsl_sf_ellint_F (2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [2.28195003957330667648585, $TOL0 ],
215 "gsl_sf_ellint_F (2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [2.09445829144721257687207, $TOL0 ],
216 "gsl_sf_ellint_F ($M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [6.71320104672238475206694, $TOL0 ],
217 "gsl_sf_ellint_F ($M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [3.37150070962519208574241, $TOL0 ],
218 "gsl_sf_ellint_F ($M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [3.14167119782430447205281, $TOL0 ],
219 "gsl_sf_ellint_F (4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [8.01973438599626142824910, $TOL0 ],
220 "gsl_sf_ellint_F (4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [4.46105137967707749499897, $TOL0 ],
221 "gsl_sf_ellint_F (4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [4.18888410420139636723356, $TOL0 ],
222 "gsl_sf_ellint_F (3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [10.0698015700835771281004, $TOL0 ],
223 "gsl_sf_ellint_F (3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [5.05725106443778812861361, $TOL0 ],
224 "gsl_sf_ellint_F (3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [4.71250679673645670807922, $TOL0 ],
225 "gsl_sf_ellint_F (5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [12.1198687541708928279517, $TOL0 ],
226 "gsl_sf_ellint_F (5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [5.65345074919849876222825, $TOL0 ],
227 "gsl_sf_ellint_F (5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [5.23612948927151704892488, $TOL0 ],
228 "gsl_sf_ellint_F (2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [13.4264020934447695041339, $TOL0 ],
229 "gsl_sf_ellint_F (2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [6.74300141925038417148481, $TOL0 ],
230 "gsl_sf_ellint_F (2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [6.28334239564860894410562, $TOL0 ],
231 "gsl_sf_ellint_F (7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [14.7329354327186461803160, $TOL0 ],
232 "gsl_sf_ellint_F (7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [7.83255208930226958074138, $TOL0 ],
233 "gsl_sf_ellint_F (7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [7.33055530202570083928637, $TOL0 ],
234 "gsl_sf_ellint_F (-$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.35660052336119237603347, $TOL0 ],
235 "gsl_sf_ellint_F (-$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.68575035481259604287120, $TOL0 ],
236 "gsl_sf_ellint_F (-$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.57083559891215223602641, $TOL0 ],
237 "gsl_sf_ellint_F (-2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.40666770744850807588478, $TOL0 ],
238 "gsl_sf_ellint_F (-2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.28195003957330667648585, $TOL0 ],
239 "gsl_sf_ellint_F (-2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.09445829144721257687207, $TOL0 ],
240 "gsl_sf_ellint_F (-$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-6.71320104672238475206694, $TOL0 ],
241 "gsl_sf_ellint_F (-$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.37150070962519208574241, $TOL0 ],
242 "gsl_sf_ellint_F (-$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.14167119782430447205281, $TOL0 ],
243 "gsl_sf_ellint_F (-4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-8.01973438599626142824910, $TOL0 ],
244 "gsl_sf_ellint_F (-4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.46105137967707749499897, $TOL0 ],
245 "gsl_sf_ellint_F (-4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.18888410420139636723356, $TOL0 ],
246 "gsl_sf_ellint_F (-3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-10.0698015700835771281004, $TOL0 ],
247 "gsl_sf_ellint_F (-3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.05725106443778812861361, $TOL0 ],
248 "gsl_sf_ellint_F (-3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.71250679673645670807922, $TOL0 ],
249 "gsl_sf_ellint_F (-5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-12.1198687541708928279517, $TOL0 ],
250 "gsl_sf_ellint_F (-5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.65345074919849876222825, $TOL0 ],
251 "gsl_sf_ellint_F (-5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.23612948927151704892488, $TOL0 ],
252 "gsl_sf_ellint_F (-2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-13.4264020934447695041339, $TOL0 ],
253 "gsl_sf_ellint_F (-2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-6.74300141925038417148481, $TOL0 ],
254 "gsl_sf_ellint_F (-2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-6.28334239564860894410562, $TOL0 ],
255 "gsl_sf_ellint_F (-7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT)" => [-14.7329354327186461803160, $TOL0 ],
256 "gsl_sf_ellint_F (-7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT)" => [-7.83255208930226958074138, $TOL0 ],
257 "gsl_sf_ellint_F (-7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT)" => [-7.33055530202570083928637, $TOL0 ],
258 "gsl_sf_ellint_P ($M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [3.61678162163246646783050, $TOL0 ],
259 "gsl_sf_ellint_P ($M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [1.78030349465454812629168, $TOL0 ],
260 "gsl_sf_ellint_P ($M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [1.65580719756898353270922, $TOL0 ],
261 "gsl_sf_ellint_P (2*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [5.88008918207571119911983, $TOL0 ],
262 "gsl_sf_ellint_P (2*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [2.43655207300356008717867, $TOL0 ],
263 "gsl_sf_ellint_P (2*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [2.23211110528200554950903, $TOL0 ],
264 "gsl_sf_ellint_P ($M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [7.23356324326493293566099, $TOL0 ],
265 "gsl_sf_ellint_P ($M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [3.56060698930909625258336, $TOL0 ],
266 "gsl_sf_ellint_P ($M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [3.31161439513796706541844, $TOL0 ],
267 "gsl_sf_ellint_P (4*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [8.58703730445415467220216, $TOL0 ],
268 "gsl_sf_ellint_P (4*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [4.68466190561463241798805, $TOL0 ],
269 "gsl_sf_ellint_P (4*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [4.39111768499392858132786, $TOL0 ],
270 "gsl_sf_ellint_P (3*$M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [10.8503448648973994034915, $TOL0 ],
271 "gsl_sf_ellint_P (3*$M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [5.34091048396364437887504, $TOL0 ],
272 "gsl_sf_ellint_P (3*$M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [4.96742159270695059812767, $TOL0 ],
273 "gsl_sf_ellint_P (5*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [13.1136524253406441347808, $TOL0 ],
274 "gsl_sf_ellint_P (5*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [5.99715906231265633976204, $TOL0 ],
275 "gsl_sf_ellint_P (5*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [5.54372550041997261492747, $TOL0 ],
276 "gsl_sf_ellint_P (2*$M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [14.4671264865298658713220, $TOL0 ],
277 "gsl_sf_ellint_P (2*$M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [7.12121397861819250516672, $TOL0 ],
278 "gsl_sf_ellint_P (2*$M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [6.62322879027593413083689, $TOL0 ],
279 "gsl_sf_ellint_P (7*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [15.8206005477190876078631, $TOL0 ],
280 "gsl_sf_ellint_P (7*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [8.24526889492372867057141, $TOL0 ],
281 "gsl_sf_ellint_P (7*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [7.70273208013189564674630, $TOL0 ],
282 "gsl_sf_ellint_P (-$M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.61678162163246646783050, $TOL0 ],
283 "gsl_sf_ellint_P (-$M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.78030349465454812629168, $TOL0 ],
284 "gsl_sf_ellint_P (-$M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.65580719756898353270922, $TOL0 ],
285 "gsl_sf_ellint_P (-2*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.88008918207571119911983, $TOL0 ],
286 "gsl_sf_ellint_P (-2*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.43655207300356008717867, $TOL0 ],
287 "gsl_sf_ellint_P (-2*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.23211110528200554950903, $TOL0 ],
288 "gsl_sf_ellint_P (-$M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-7.23356324326493293566099, $TOL0 ],
289 "gsl_sf_ellint_P (-$M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.56060698930909625258336, $TOL0 ],
290 "gsl_sf_ellint_P (-$M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.31161439513796706541844, $TOL0 ],
291 "gsl_sf_ellint_P (-4*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-8.58703730445415467220216, $TOL0 ],
292 "gsl_sf_ellint_P (-4*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.68466190561463241798805, $TOL0 ],
293 "gsl_sf_ellint_P (-4*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.39111768499392858132786, $TOL0 ],
294 "gsl_sf_ellint_P (-3*$M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-10.8503448648973994034915, $TOL0 ],
295 "gsl_sf_ellint_P (-3*$M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.34091048396364437887504, $TOL0 ],
296 "gsl_sf_ellint_P (-3*$M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.96742159270695059812767, $TOL0 ],
297 "gsl_sf_ellint_P (-5*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-13.1136524253406441347808, $TOL0 ],
298 "gsl_sf_ellint_P (-5*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.99715906231265633976204, $TOL0 ],
299 "gsl_sf_ellint_P (-5*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.54372550041997261492747, $TOL0 ],
300 "gsl_sf_ellint_P (-2*$M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-14.4671264865298658713220, $TOL0 ],
301 "gsl_sf_ellint_P (-2*$M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-7.12121397861819250516672, $TOL0 ],
302 "gsl_sf_ellint_P (-2*$M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-6.62322879027593413083689, $TOL0 ],
303 "gsl_sf_ellint_P (-7*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-15.8206005477190876078631, $TOL0 ],
304 "gsl_sf_ellint_P (-7*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-8.24526889492372867057141, $TOL0 ],
305 "gsl_sf_ellint_P (-7*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT)" => [-7.70273208013189564674630, $TOL0 ],
306 "gsl_sf_ellint_D ($M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [2.375395076351788975665323192, $TOL0 ],
307 "gsl_sf_ellint_D ($M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [0.8731525818926755496456335628, $TOL0 ],
308 "gsl_sf_ellint_D ($M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [0.7854276176694868932799393751, $TOL0 ],
309 "gsl_sf_ellint_D (2*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [4.305885125424644860264320635, $TOL0 ],
310 "gsl_sf_ellint_D (2*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [1.418324704155697579394036402, $TOL0 ],
311 "gsl_sf_ellint_D (2*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [1.263755353901126149206022061, $TOL0 ],
312 "gsl_sf_ellint_D ($M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [4.750790152703577951330646444, $TOL0 ],
313 "gsl_sf_ellint_D ($M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [1.746305163785351099291267125, $TOL0 ],
314 "gsl_sf_ellint_D ($M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [1.570855235338973786559878750, $TOL0 ],
315 "gsl_sf_ellint_D (4*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [5.195695179982511042396972113, $TOL0 ],
316 "gsl_sf_ellint_D (4*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [2.074285623415004619188497818, $TOL0 ],
317 "gsl_sf_ellint_D (4*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [1.877955116776821423913735408, $TOL0 ],
318 "gsl_sf_ellint_D (3*$M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [7.126185229055366926995969476, $TOL0 ],
319 "gsl_sf_ellint_D (3*$M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [2.619457745678026648936900687, $TOL0 ],
320 "gsl_sf_ellint_D (3*$M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [2.356282853008460679839818125, $TOL0 ],
321 "gsl_sf_ellint_D (5*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [9.056675278128222811594967044, $TOL0 ],
322 "gsl_sf_ellint_D (5*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [3.164629867941048678685303509, $TOL0 ],
323 "gsl_sf_ellint_D (5*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [2.834610589240099935765900794, $TOL0 ],
324 "gsl_sf_ellint_D (2*$M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [9.501580305407155902661292832, $TOL0 ],
325 "gsl_sf_ellint_D (2*$M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [3.492610327570702198582534249, $TOL0 ],
326 "gsl_sf_ellint_D (2*$M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [3.141710470677947573119757500, $TOL0 ],
327 "gsl_sf_ellint_D (7*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [9.946485332686088993727618315, $TOL0 ],
328 "gsl_sf_ellint_D (7*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [3.820590787200355718479764901, $TOL0 ],
329 "gsl_sf_ellint_D (7*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [3.448810352115795210473614120, $TOL0 ],
330 "gsl_sf_ellint_D (-$M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.375395076351788975665323192, $TOL0 ],
331 "gsl_sf_ellint_D (-$M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-0.8731525818926755496456335628, $TOL0 ],
332 "gsl_sf_ellint_D (-$M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-0.7854276176694868932799393751, $TOL0 ],
333 "gsl_sf_ellint_D (-2*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.305885125424644860264320635, $TOL0 ],
334 "gsl_sf_ellint_D (-2*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.418324704155697579394036402, $TOL0 ],
335 "gsl_sf_ellint_D (-2*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.263755353901126149206022061, $TOL0 ],
336 "gsl_sf_ellint_D (-$M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-4.750790152703577951330646444, $TOL0 ],
337 "gsl_sf_ellint_D (-$M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.746305163785351099291267125, $TOL0 ],
338 "gsl_sf_ellint_D (-$M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.570855235338973786559878750, $TOL0 ],
339 "gsl_sf_ellint_D (-4*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-5.195695179982511042396972113, $TOL0 ],
340 "gsl_sf_ellint_D (-4*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.074285623415004619188497818, $TOL0 ],
341 "gsl_sf_ellint_D (-4*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-1.877955116776821423913735408, $TOL0 ],
342 "gsl_sf_ellint_D (-3*$M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-7.126185229055366926995969476, $TOL0 ],
343 "gsl_sf_ellint_D (-3*$M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.619457745678026648936900687, $TOL0 ],
344 "gsl_sf_ellint_D (-3*$M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.356282853008460679839818125, $TOL0 ],
345 "gsl_sf_ellint_D (-5*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-9.056675278128222811594967044, $TOL0 ],
346 "gsl_sf_ellint_D (-5*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.164629867941048678685303509, $TOL0 ],
347 "gsl_sf_ellint_D (-5*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-2.834610589240099935765900794, $TOL0 ],
348 "gsl_sf_ellint_D (-2*$M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-9.501580305407155902661292832, $TOL0 ],
349 "gsl_sf_ellint_D (-2*$M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.492610327570702198582534249, $TOL0 ],
350 "gsl_sf_ellint_D (-2*$M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.141710470677947573119757500, $TOL0 ],
351 "gsl_sf_ellint_D (-7*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-9.946485332686088993727618315, $TOL0 ],
352 "gsl_sf_ellint_D (-7*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.820590787200355718479764901, $TOL0 ],
353 "gsl_sf_ellint_D (-7*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT)" => [-3.448810352115795210473614120, $TOL0 ],
354 "gsl_sf_erfc (-10.0)" => [2.0, $TOL0 ],
355 "gsl_sf_erfc (-5.0000002)" => [1.9999999999984625433, $TOL0 ],
356 "gsl_sf_erfc (-5.0)" => [1.9999999999984625402, $TOL0 ],
357 "gsl_sf_erfc (-1.0)" => [1.8427007929497148693, $TOL0 ],
358 "gsl_sf_erfc (-0.5)" => [1.5204998778130465377, $TOL0 ],
359 "gsl_sf_erfc (1.0)" => [0.15729920705028513066, $TOL0 ],
360 "gsl_sf_erfc (3.0)" => [0.000022090496998585441373, $TOL1 ],
361 "gsl_sf_erfc (7.0)" => [4.183825607779414399e-23, $TOL2 ],
362 "gsl_sf_erfc (10.0)" => [2.0884875837625447570e-45, $TOL2 ],
363 "gsl_sf_log_erfc (-1.0)" => [log(1.842700792949714869), $TOL0 ],
364 "gsl_sf_log_erfc (-0.1)" => [0.106576400586522485015, $TOL0 ],
365 "gsl_sf_log_erfc (-1e-10)" => [ 1.1283791670318505967e-10, $TOL0 ],
366 "gsl_sf_log_erfc (0.0)" => [log(1.0), $TOL0 ],
367 "gsl_sf_log_erfc (1e-10)" => [-1.128379167159174551e-10, $TOL0 ],
368 "gsl_sf_log_erfc (0.001)" => [-0.0011290158896213548027, $TOL0 ],
369 "gsl_sf_log_erfc (0.1)" => [-0.119304973737395598329, $TOL0 ],
370 "gsl_sf_log_erfc (1.0)" => [log(0.15729920705028513066), $TOL0 ],
371 "gsl_sf_log_erfc (10.0)" => [log(2.0884875837625447570e-45), $TOL0 ],
372 "gsl_sf_erf (-10.0)" => [-1.0000000000000000000, $TOL0 ],
373 "gsl_sf_erf (0.5)" => [0.5204998778130465377, $TOL0 ],
374 "gsl_sf_erf (1.0)" => [0.8427007929497148693, $TOL0 ],
375 "gsl_sf_erf (10.0)" => [1.0000000000000000000, $TOL0 ],
376 "gsl_sf_erf_Z (1.0)" => [ 0.24197072451914334980, $TOL0 ],
377 "gsl_sf_erf_Q (10.0)" => [7.619853024160526066e-24, $TOL2 ],
378 "gsl_sf_hazard (-20.0)" => [5.5209483621597631896e-88, $TOL2 ],
379 "gsl_sf_hazard (-10.0)" => [7.6945986267064193463e-23, $TOL2 ],
380 "gsl_sf_hazard (-1.0)" => [0.28759997093917836123, $TOL0 ],
381 "gsl_sf_hazard ( 0.0)" => [0.79788456080286535588, $TOL0 ],
382 "gsl_sf_hazard ( 1.0)" => [1.5251352761609812091, $TOL0 ],
383 "gsl_sf_hazard (10.0)" => [10.098093233962511963, $TOL2 ],
384 "gsl_sf_hazard (20.0)" => [20.049753068527850542, $TOL2 ],
385 "gsl_sf_hazard (30.0)" => [30.033259667433677037, $TOL2 ],
386 "gsl_sf_hazard (50.0)" => [50.019984031905639809, $TOL0 ],
387 "gsl_sf_hazard (80.0)" => [80.012496096798234468, $TOL0 ],
388 "gsl_sf_hazard (150.0)" => [150.00666607420571802, $TOL0 ],
389 "gsl_sf_hazard (300.0)" => [300.00333325926337415, $TOL2 ],
390 "gsl_sf_hazard (900.0)" => [900.00111110836764382, $TOL0 ],
391 "gsl_sf_hazard (1001.0)" => [1001.0009989990049990, $TOL0 ],
392 "gsl_sf_hazard (2000.0)" => [2000.0004999997500003, $TOL0 ],
393 "gsl_sf_exp (-10.0)" => [exp(-10.0), $TOL0 ],
394 "gsl_sf_exp ( 10.0)" => [exp( 10.0), $TOL0 ],
395 #"gsl_sf_exp_err (-10.0, $TOL1)" => [exp(-10.0), $TOL1 ],
396 #"gsl_sf_exp_err ( 10.0, $TOL1)" => [exp( 10.0), $TOL1 ],
397 "gsl_sf_exp_mult (-10.0, 1.0e-06)" => [1.0e-06*exp(-10.0), $TOL0 ],
398 "gsl_sf_exp_mult (-10.0, 2.0)" => [ 2.0*exp(-10.0), $TOL0 ],
399 "gsl_sf_exp_mult (-10.0, -2.0)" => [ -2.0*exp(-10.0), $TOL0 ],
400 "gsl_sf_exp_mult ( 10.0, 1.0e-06)" => [1.0e-06*exp( 10.0), $TOL0 ],
401 "gsl_sf_exp_mult ( 10.0, -2.0)" => [ -2.0*exp( 10.0), $TOL0 ],
402 #"gsl_sf_exp_mult ($w, 1.000001)" => [ 1.000001*exp($w), $TOL3 ],
403 #"gsl_sf_exp_mult ($w, 1.000000001)" => [ 1.000000001*exp($w), $TOL3 ],
404 #"gsl_sf_exp_mult ($w, 100.0)" => [ 100.0*exp($w), $TOL3 ],
405 #"gsl_sf_exp_mult ($w, 1.0e+20)" => [ 1.0e+20*exp($w), $TOL3 ],
406 #"gsl_sf_exp_mult ($w, exp(-$w)*exp($M_LN2))" => [2.0, $TOL4 ],
407 #"gsl_sf_exp_mult_err (-10.0, $SQRT_TOL0, 2.0, $SQRT_TOL0)" => [2.0*exp(-10.0), $SQRT_TOL0 ],
408 #"gsl_sf_exp_mult_err ($w, $SQRT_TOL0*$w, exp(-$w)*exp($M_LN2), $SQRT_TOL0*exp(-$w)*exp($M_LN2))" => [2.0, $SQRT_TOL0 ],
409 "gsl_sf_expm1 (-10.0)" => [exp(-10.0)-1.0, $TOL0 ],
410 "gsl_sf_expm1 (-0.001)" => [-0.00099950016662500845, $TOL0 ],
411 "gsl_sf_expm1 (-1.0e-8)" => [-1.0e-08 + 0.5e-16, $TOL0 ],
412 "gsl_sf_expm1 ( 1.0e-8)" => [1.0e-08 + 0.5e-16, $TOL0 ],
413 "gsl_sf_expm1 ( 0.001)" => [0.0010005001667083417, $TOL0 ],
414 "gsl_sf_expm1 ( 10.0)" => [exp(10.0)-1.0, $TOL0 ],
415 "gsl_sf_exprel (-10.0)" => [0.0999954600070237515, $TOL0 ],
416 "gsl_sf_exprel (-0.001)" => [0.9995001666250084, $TOL0 ],
417 "gsl_sf_exprel (-1.0e-8)" => [1.0 - 0.5e-08, $TOL0 ],
418 "gsl_sf_exprel ( 1.0e-8)" => [1.0 + 0.5e-08, $TOL0 ],
419 "gsl_sf_exprel ( 0.001)" => [1.0005001667083417, $TOL0 ],
420 "gsl_sf_exprel ( 10.0)" => [2202.5465794806716517, $TOL2 ],
421 "gsl_sf_exprel_2 (-10.0)" => [0.18000090799859524970, $TOL0 ],
422 "gsl_sf_exprel_2 (-0.001)" => [0.9996667499833361107, $TOL0 ],
423 "gsl_sf_exprel_2 (-1.0e-8)" => [0.9999999966666666750, $TOL0 ],
424 "gsl_sf_exprel_2 ( 1.0e-8)" => [1.0000000033333333417, $TOL0 ],
425 "gsl_sf_exprel_2 ( 0.001)" => [1.0003334166833361115, $TOL0 ],
426 "gsl_sf_exprel_2 ( 10.0)" => [440.3093158961343303, 10*$TOL0 ],
427 "gsl_sf_exprel_n (3, -1000.0)" => [0.00299400600000000000, $TOL0 ],
428 "gsl_sf_exprel_n (3, -100.0)" => [0.02940600000000000000, $TOL0 ],
429 "gsl_sf_exprel_n (3, -10.0)" => [0.24599972760042142509, $TOL0 ],
430 "gsl_sf_exprel_n (3, -3.0)" => [0.5444917625849191238, $TOL0 ],
431 "gsl_sf_exprel_n (3, -0.001)" => [0.9997500499916678570, $TOL0 ],
432 "gsl_sf_exprel_n (3, -1.0e-8)" => [0.9999999975000000050, $TOL0 ],
433 "gsl_sf_exprel_n (3, 1.0e-8)" => [1.0000000025000000050, $TOL0 ],
434 "gsl_sf_exprel_n (3, 0.001)" => [1.0002500500083345240, $TOL0 ],
435 "gsl_sf_exprel_n (3, 3.0)" => [2.5745637607083706091, $TOL0 ],
436 "gsl_sf_exprel_n (3, 3.1)" => [2.6772417068460206247, $TOL0 ],
437 "gsl_sf_exprel_n (3, 10.0)" => [131.79279476884029910, $TOL1 ],
438 "gsl_sf_exprel_n (3, 100.0)" => [1.6128702850896812690e+38, $TOL2 ],
439 "gsl_sf_exprel_n (50, -1000.0)" => [0.04766231609253975959, $TOL0 ],
440 "gsl_sf_exprel_n (50, -100.0)" => [0.3348247572345889317, $TOL0 ],
441 "gsl_sf_exprel_n (50, -10.0)" => [0.8356287051853286482, $TOL0 ],
442 "gsl_sf_exprel_n (50, -3.0)" => [0.9443881609152163615, $TOL0 ],
443 "gsl_sf_exprel_n (50, -1.0)" => [0.980762245565660617, $TOL0 ],
444 "gsl_sf_exprel_n (50, -1.0e-8)" => [1.0 -1.0e-8/51.0, $TOL0 ],
445 "gsl_sf_exprel_n (50, 1.0e-8)" => [1.0 +1.0e-8/51.0, $TOL0 ],
446 "gsl_sf_exprel_n (50, 1.0)" => [1.01999216583666790, $TOL0 ],
447 "gsl_sf_exprel_n (50, 3.0)" => [1.0624205757460368307, $TOL0 ],
448 "gsl_sf_exprel_n (50, 48.0)" => [7.499573876877194416, $TOL0 ],
449 "gsl_sf_exprel_n (50, 50.1)" => [9.311803306230992272, $TOL4 ],
450 #"gsl_sf_exprel_n (50, 100.0)" => [8.175664432485807634e+07, $TOL4 ],
451 #"gsl_sf_exprel_n (50, 500.0)" => [4.806352370663185330e+146, $TOL3 ],
452 "gsl_sf_exprel_n (500, -1000.0)" => [0.3334815803127619256, $TOL0 ],
453 "gsl_sf_exprel_n (500, -100.0)" => [0.8335646217536183909, $TOL0 ],
454 "gsl_sf_exprel_n (500, -10.0)" => [0.9804297803131823066, $TOL0 ],
455 "gsl_sf_exprel_n (500, -3.0)" => [0.9940475488850672997, $TOL0 ],
456 "gsl_sf_exprel_n (500, -1.0)" => [0.9980079602383488808, $TOL0 ],
457 "gsl_sf_exprel_n (500, -1.0e-8)" => [1.0 -1.0e-8/501.0, $TOL0 ],
458 "gsl_sf_exprel_n (500, 1.0e-8)" => [1.0 +1.0e-8/501.0, $TOL0 ],
459 "gsl_sf_exprel_n (500, 1.0)" => [1.0019999920160634252, $TOL0 ],
460 "gsl_sf_exprel_n (500, 3.0)" => [1.0060240236632444934, $TOL0 ],
461 "gsl_sf_exprel_n (500, 48.0)" => [1.1059355517981272174, $TOL0 ],
462 "gsl_sf_exprel_n (500, 100.0)" => [1.2492221464878287204, $TOL1 ],
463 "gsl_sf_exprel_n (500, 500.0)" => [28.363019877927630858, $TOL2 ],
464 #"gsl_sf_exprel_n (500, 1000.0)" => [2.4037563160335300322e+68, $TOL4 ],
465 #"gsl_sf_exprel_n (500, 1600.0)" => [7.899293535320607403e+226, $TOL4 ],
466 "gsl_sf_expint_E1 (-1.0)" => [-1.8951178163559367555, $TOL0 ],
467 "gsl_sf_expint_E1 (1.0e-10)" => [22.448635265138923980, $TOL0 ],
468 "gsl_sf_expint_E1 (1.0e-05)" => [10.935719800043695615, $TOL0 ],
469 "gsl_sf_expint_E1 (0.1)" => [1.82292395841939066610, $TOL0 ],
470 "gsl_sf_expint_E1 (1.0)" => [0.21938393439552027368, $TOL0 ],
471 "gsl_sf_expint_E1 (10.0)" => [4.156968929685324277e-06, $TOL1 ],
472 "gsl_sf_expint_E1 (50.0)" => [3.783264029550459019e-24, $TOL2 ],
473 "gsl_sf_expint_E1 (300.0)" => [1.710384276804510115e-133, $TOL2 ],
474 "gsl_sf_expint_E2 (-1.0)" => [0.8231640121031084799, $TOL1 ],
475 "gsl_sf_expint_E2 (0.0)" => [1.0, $TOL0 ],
476 "gsl_sf_expint_E2 (1.0/4294967296.0)" => [0.9999999947372139168, $TOL0 ],
477 "gsl_sf_expint_E2 (1.0/65536.0)" => [0.9998243233207178845, $TOL0 ],
478 "gsl_sf_expint_E2 (0.1)" => [0.7225450221940205066, $TOL0 ],
479 "gsl_sf_expint_E2 (1.0)" => [0.14849550677592204792, $TOL0 ],
480 "gsl_sf_expint_E2 (10.0)" => [3.830240465631608762e-06, $TOL1 ],
481 "gsl_sf_expint_E2 (50.0)" => [3.711783318868827367e-24, $TOL2 ],
482 "gsl_sf_expint_E2 (300.0)" => [1.7047391998483433998e-133, $TOL2 ],
483 "gsl_sf_expint_En (1,-1.0)" => [-1.8951178163559367555, $TOL0 ],
484 "gsl_sf_expint_En (1,1.0e-10)" => [22.448635265138923980, $TOL0 ],
485 "gsl_sf_expint_En (1,1.0e-05)" => [10.935719800043695615, $TOL0 ],
486 "gsl_sf_expint_En (1,0.1)" => [1.82292395841939066610, $TOL0 ],
487 "gsl_sf_expint_En (1,1.0)" => [0.21938393439552027368, $TOL0 ],
488 "gsl_sf_expint_En (1,10.0)" => [4.156968929685324277e-06, $TOL1 ],
489 "gsl_sf_expint_En (1,50.0)" => [3.783264029550459019e-24, $TOL2 ],
490 "gsl_sf_expint_En (1,300.0)" => [1.710384276804510115e-133, $TOL2 ],
491 "gsl_sf_expint_En (2,-1.0)" => [0.8231640121031084799, $TOL1 ],
492 "gsl_sf_expint_En (2,0.0)" => [1.0, $TOL0 ],
493 "gsl_sf_expint_En (2,1.0/4294967296.0)" => [0.9999999947372139168, $TOL0 ],
494 "gsl_sf_expint_En (2,1.0/65536.0)" => [0.9998243233207178845, $TOL0 ],
495 "gsl_sf_expint_En (2,0.1)" => [0.7225450221940205066, $TOL0 ],
496 "gsl_sf_expint_En (2,1.0)" => [0.14849550677592204792, $TOL0 ],
497 "gsl_sf_expint_En (2,10.0)" => [3.830240465631608762e-06, $TOL1 ],
498 "gsl_sf_expint_En (2,50.0)" => [3.711783318868827367e-24, $TOL2 ],
499 "gsl_sf_expint_En (2,300.0)" => [1.7047391998483433998e-133, $TOL2 ],
500 "gsl_sf_expint_En (3,0.0)" => [0.5, $TOL0 ],
501 "gsl_sf_expint_En (3,1.0/4294967296.0)" => [0.499999999767169356972, $TOL1 ],
502 "gsl_sf_expint_En (3,1.0/65536.0)" => [0.4999847426094515610, $TOL0 ],
503 "gsl_sf_expint_En (3,0.1)" => [0.4162914579082787612543, $TOL0 ],
504 "gsl_sf_expint_En (3,1.0)" => [0.10969196719776013683858, $TOL1 ],
505 "gsl_sf_expint_En (3,10.0)" => [.000003548762553084381959981, $TOL1 ],
506 "gsl_sf_expint_En (3,50.0)" => [3.6429094264752049812e-24, $TOL2 ],
507 "gsl_sf_expint_En (3,300.0)" => [.699131143349179084e-133, $TOL2 ],
508 "gsl_sf_expint_En (10,0.0)" => [0.111111111111111111, $TOL0 ],
509 "gsl_sf_expint_En (10,1.0/4294967296.0)" => [0.111111111082007280658, $TOL2 ],
510 "gsl_sf_expint_En (10,1.0/65536.0)" => [0.11110920377910896018606, $TOL1 ],
511 "gsl_sf_expint_En (10,0.1)" => [0.099298432000896813567905, $TOL1 ],
512 "gsl_sf_expint_En (10,1.0)" => [0.036393994031416401634164534, $TOL1 ],
513 "gsl_sf_expint_En (10,10.0)" => [0.00000232530265702821081778968, $TOL1 ],
514 "gsl_sf_expint_En (10,50.0)" => [3.223296586749110919572e-24, $TOL2 ],
515 "gsl_sf_expint_En (10,300.0)" => [1.6608815083360041367294736e-133, $TOL2 ],
516 "gsl_sf_expint_Ei (-1.0)" => [-0.21938393439552027368, $TOL0 ],
517 "gsl_sf_expint_Ei (1.0/4294967296.0)" => [-21.603494112783886397, $TOL0 ],
518 "gsl_sf_expint_Ei (1.0)" => [1.8951178163559367555, $TOL0 ],
519 "gsl_sf_expint_E1_scaled (-10000.0)" => [-0.00010001000200060024012, $TOL0 ],
520 "gsl_sf_expint_E1_scaled (-1000.0)" => [-0.0010010020060241207251, $TOL0 ],
521 "gsl_sf_expint_E1_scaled (-10.0)" => [-0.11314702047341077803, $TOL0 ],
522 "gsl_sf_expint_E1_scaled (-1.0)" => [-0.69717488323506606877, $TOL0 ],
523 "gsl_sf_expint_E1_scaled (1.0e-10)" => [22.448635267383787506, $TOL0 ],
524 "gsl_sf_expint_E1_scaled (1.0e-05)" => [10.935829157788483865, $TOL0 ],
525 "gsl_sf_expint_E1_scaled (0.1)" => [2.0146425447084516791, $TOL0 ],
526 "gsl_sf_expint_E1_scaled (1.0)" => [0.59634736232319407434, $TOL0 ],
527 "gsl_sf_expint_E1_scaled (10.0)" => [0.091563333939788081876, $TOL0 ],
528 "gsl_sf_expint_E1_scaled (50.0)" => [0.019615109930114870365, $TOL0 ],
529 "gsl_sf_expint_E1_scaled (300.0)" => [0.0033222955652707070644, $TOL0 ],
530 "gsl_sf_expint_E1_scaled (1000.0)" => [0.00099900199402388071500, $TOL0 ],
531 "gsl_sf_expint_E1_scaled (10000.0)" => [0.000099990001999400239880, $TOL0 ],
532 "gsl_sf_expint_E2_scaled (-10000.0)" => [-0.00010002000600240120072, $TOL3 ],
533 "gsl_sf_expint_E2_scaled (-1000.0)" => [-0.0010020060241207250807, $TOL3 ],
534 "gsl_sf_expint_E2_scaled (-10.0)" => [-0.13147020473410778034, $TOL1 ],
535 "gsl_sf_expint_E2_scaled (-1.0)" => [0.30282511676493393123, $TOL1 ],
536 "gsl_sf_expint_E2_scaled (0.0)" => [1.0, $TOL1 ],
537 "gsl_sf_expint_E2_scaled (1.0/4294967296.0)" => [0.99999999497004455927, $TOL0 ],
538 "gsl_sf_expint_E2_scaled (1.0/65536.0)" => [0.99983957954556245453, $TOL0 ],
539 "gsl_sf_expint_E2_scaled (0.1)" => [0.79853574552915483209, $TOL0 ],
540 "gsl_sf_expint_E2_scaled (1.0)" => [0.40365263767680592566, $TOL0 ],
541 "gsl_sf_expint_E2_scaled (10.0)" => [0.084366660602119181239, $TOL1 ],
542 "gsl_sf_expint_E2_scaled (50.0)" => [0.019244503494256481735, $TOL2 ],
543 "gsl_sf_expint_E2_scaled (300.0)" => [0.0033113304187878806691, $TOL0 ],
544 "gsl_sf_expint_E2_scaled (1000.0)" => [0.00099800597611928500004, $TOL0 ],
545 "gsl_sf_expint_E2_scaled (10000.0)" => [0.000099980005997601199281, $TOL0 ],
546 "gsl_sf_expint_En_scaled (1,-10000.0)" => [-0.00010001000200060024012, $TOL0 ],
547 "gsl_sf_expint_En_scaled (1,-1000.0)" => [-0.0010010020060241207251, $TOL0 ],
548 "gsl_sf_expint_En_scaled (1,-10.0)" => [-0.11314702047341077803, $TOL0 ],
549 "gsl_sf_expint_En_scaled (1,-1.0)" => [-0.69717488323506606877, $TOL0 ],
550 "gsl_sf_expint_En_scaled (1,1.0e-10)" => [22.448635267383787506, $TOL0 ],
551 "gsl_sf_expint_En_scaled (1,1.0e-05)" => [10.935829157788483865, $TOL0 ],
552 "gsl_sf_expint_En_scaled (1,0.1)" => [2.0146425447084516791, $TOL0 ],
553 "gsl_sf_expint_En_scaled (1,1.0)" => [0.59634736232319407434, $TOL0 ],
554 "gsl_sf_expint_En_scaled (1,10.0)" => [0.091563333939788081876, $TOL0 ],
555 "gsl_sf_expint_En_scaled (1,50.0)" => [0.019615109930114870365, $TOL0 ],
556 "gsl_sf_expint_En_scaled (1,300.0)" => [0.0033222955652707070644, $TOL0 ],
557 "gsl_sf_expint_En_scaled (1,1000.0)" => [0.00099900199402388071500, $TOL0 ],
558 "gsl_sf_expint_En_scaled (1,10000.0)" => [0.000099990001999400239880, $TOL0 ],
559 "gsl_sf_expint_En_scaled (2,-10000.0)" => [-0.00010002000600240120072, $TOL3 ],
560 "gsl_sf_expint_En_scaled (2,-1000.0)" => [-0.0010020060241207250807, $TOL3 ],
561 "gsl_sf_expint_En_scaled (2,-10.0)" => [-0.13147020473410778034, $TOL1 ],
562 "gsl_sf_expint_En_scaled (2,-1.0)" => [0.30282511676493393123, $TOL1 ],
563 "gsl_sf_expint_En_scaled (2,0.0)" => [1.0, $TOL1 ],
564 "gsl_sf_expint_En_scaled (2,1.0/4294967296.0)" => [0.99999999497004455927, $TOL0 ],
565 "gsl_sf_expint_En_scaled (2,1.0/65536.0)" => [0.99983957954556245453, $TOL0 ],
566 "gsl_sf_expint_En_scaled (2,0.1)" => [0.79853574552915483209, $TOL0 ],
567 "gsl_sf_expint_En_scaled (2,1.0)" => [0.40365263767680592566, $TOL0 ],
568 "gsl_sf_expint_En_scaled (2,10.0)" => [0.084366660602119181239, $TOL1 ],
569 "gsl_sf_expint_En_scaled (2,50.0)" => [0.019244503494256481735, $TOL2 ],
570 "gsl_sf_expint_En_scaled (2,300.0)" => [0.0033113304187878806691, $TOL0 ],
571 "gsl_sf_expint_En_scaled (2,1000.0)" => [0.00099800597611928500004, $TOL0 ],
572 "gsl_sf_expint_En_scaled (2,10000.0)" => [0.000099980005997601199281, $TOL0 ],
573 "gsl_sf_expint_En_scaled (3,0.0)" => [0.5, $TOL0 ],
574 "gsl_sf_expint_En_scaled (3,1.0/4294967296.0)" => [0.4999999998835846787586, $TOL1 ],
575 "gsl_sf_expint_En_scaled (3,1.0/65536.0)" => [0.4999923718293796877864492, $TOL0 ],
576 "gsl_sf_expint_En_scaled (3,0.1)" => [0.4600732127235422583955, $TOL0 ],
577 "gsl_sf_expint_En_scaled (3,1.0)" => [0.298173681161597037170539, $TOL1 ],
578 "gsl_sf_expint_En_scaled (3,10.0)" => [0.07816669698940409380349, $TOL1 ],
579 "gsl_sf_expint_En_scaled (3,50.0)" => [0.0188874126435879566345, $TOL2 ],
580 "gsl_sf_expint_En_scaled (3,300.0)" => [0.00330043718181789963028657675, $TOL2 ],
581 "gsl_sf_expint_En_scaled (10,0.0)" => [0.111111111111111111, $TOL0 ],
582 "gsl_sf_expint_En_scaled (10,1.0/4294967296.0)" => [0.11111111110787735217158, $TOL2 ],
583 "gsl_sf_expint_En_scaled (10,1.0/65536.0)" => [0.1111108991839472074435, $TOL1 ],
584 "gsl_sf_expint_En_scaled (10,0.1)" => [0.1097417392579033988025, $TOL1 ],
585 "gsl_sf_expint_En_scaled (10,1.0)" => [0.09892913264064615521915, $TOL1 ],
586 "gsl_sf_expint_En_scaled (10,10.0)" => [0.0512181994376050593314159875, $TOL1 ],
587 "gsl_sf_expint_En_scaled (10,50.0)" => [0.0167118436335939556034579, $TOL2 ],
588 "gsl_sf_expint_En_scaled (10,300.0)" => [0.0032261400811599644878615, $TOL2 ],
589 "gsl_sf_expint_Ei_scaled (-1000.0)" => [-0.00099900199402388071500, $TOL0 ],
590 "gsl_sf_expint_Ei_scaled (-1.0)" => [-0.59634736232319407434, $TOL0 ],
591 "gsl_sf_expint_Ei_scaled (1.0/4294967296.0)" => [-21.603494107753930958, $TOL0 ],
592 "gsl_sf_expint_Ei_scaled (1.0)" => [0.69717488323506606877, $TOL0 ],
593 "gsl_sf_expint_Ei_scaled (1000.0)" => [0.0010010020060241207251, $TOL0 ],
594 "gsl_sf_Shi (-1.0)" => [-1.0572508753757285146, $TOL0 ],
595 "gsl_sf_Shi (1.0/4294967296.0)" => [2.3283064365386962891e-10, $TOL0 ],
596 "gsl_sf_Shi (1.0/65536.0)" => [0.00001525878906269737298, $TOL0 ],
597 "gsl_sf_Shi (0.1)" => [0.1000555722250569955, $TOL0 ],
598 "gsl_sf_Shi (1.0)" => [1.0572508753757285146, $TOL0 ],
599 "gsl_sf_Shi (10.0)" => [1246.1144901994233444, $TOL1 ],
600 "gsl_sf_Shi (50.0)" => [5.292818448565845482e+19, $TOL2 ],
601 #"gsl_sf_Shi (300.0)" => [3.248241254044332895e+127, $TOL2 ],
602 "gsl_sf_Chi (-1.0)" => [0.8378669409802082409, $TOL0 ],
603 "gsl_sf_Chi (1.0/4294967296.0)" => [-21.603494113016717041, $TOL0 ],
604 "gsl_sf_Chi (1.0/65536.0)" => [-10.513139223999384429, $TOL0 ],
605 "gsl_sf_Chi (1.0/8.0)" => [-1.4983170827635760646, $TOL0 ],
606 "gsl_sf_Chi (1.0)" => [0.8378669409802082409, $TOL0 ],
607 "gsl_sf_Chi (10.0)" => [1246.1144860424544147, $TOL1 ],
608 "gsl_sf_Chi (50.0)" => [5.292818448565845482e+19, $TOL2 ],
609 #"gsl_sf_Chi (300.0)" => [3.248241254044332895e+127, $TOL2 ],
610 "gsl_sf_expint_3 (1.0e-10)" => [1.0e-10, $TOL0 ],
611 "gsl_sf_expint_3 (1.0e-05)" => [9.9999999999999975e-06, $TOL0 ],
612 "gsl_sf_expint_3 (0.1)" => [0.09997500714119079665122, $TOL0 ],
613 "gsl_sf_expint_3 (0.5)" => [0.48491714311363971332427, $TOL0 ],
614 "gsl_sf_expint_3 (1.0)" => [0.80751118213967145285833, $TOL0 ],
615 "gsl_sf_expint_3 (2.0)" => [0.89295351429387631138208, $TOL0 ],
616 "gsl_sf_expint_3 (5.0)" => [0.89297951156924921121856, $TOL0 ],
617 "gsl_sf_expint_3 (10.0)" => [0.89297951156924921121856, $TOL0 ],
618 "gsl_sf_expint_3 (100.0)" => [0.89297951156924921121856, $TOL0 ],
619 "gsl_sf_Si (-1.0)" => [-0.9460830703671830149, $TOL0 ],
620 "gsl_sf_Si (1.0e-10)" => [1.0e-10, $TOL0 ],
621 "gsl_sf_Si (1.0e-05)" => [9.999999999944444444e-06, $TOL0 ],
622 "gsl_sf_Si (0.1)" => [0.09994446110827695016, $TOL0 ],
623 "gsl_sf_Si (1.0)" => [0.9460830703671830149, $TOL0 ],
624 "gsl_sf_Si (10.0)" => [1.6583475942188740493, $TOL0 ],
625 "gsl_sf_Si (50.0)" => [1.5516170724859358947, $TOL0 ],
626 "gsl_sf_Si (300.0)" => [1.5708810882137495193, $TOL0 ],
627 "gsl_sf_Si (1.0e+20)" => [1.5707963267948966192, $TOL0 ],
628 "gsl_sf_Ci (1.0/4294967296.0)" => [-21.603494113016717041, $TOL0 ],
629 "gsl_sf_Ci (1.0/65536.0)" => [-10.513139224115799751, $TOL0 ],
630 "gsl_sf_Ci (1.0/8.0)" => [-1.5061295845296396649, $TOL0 ],
631 "gsl_sf_Ci (1.0)" => [0.3374039229009681347, $TOL0 ],
632 "gsl_sf_Ci (10.0)" => [-0.04545643300445537263, $TOL0 ],
633 "gsl_sf_Ci (50.0)" => [-0.005628386324116305440, $TOL0 ],
634 "gsl_sf_Ci (300.0)" => [-0.003332199918592111780, $TOL0 ],
635 "gsl_sf_Ci (65536.0)" => [0.000010560248837656279453, $TOL0 ],
636 "gsl_sf_Ci (4294967296.0)" => [-1.0756463261957757485e-10, $SQRT_TOL0 ],
637 "gsl_sf_Ci (1099511627776.0)" => [-3.689865584710764214e-13, 1024.0*$SQRT_TOL0 ],
638 "gsl_sf_atanint (1.0e-10)" => [1.0e-10, $TOL0 ],
639 "gsl_sf_atanint (1.0e-05)" => [9.99999999988888888889e-06, $TOL0 ],
640 "gsl_sf_atanint (0.1)" => [0.09988928686033618404, $TOL0 ],
641 "gsl_sf_atanint (1.0)" => [0.91596559417721901505, $TOL0 ],
642 "gsl_sf_atanint (2.0)" => [1.57601540344632342236, $TOL0 ],
643 "gsl_sf_atanint (10.0)" => [3.71678149306806859029, $TOL0 ],
644 "gsl_sf_atanint (50.0)" => [6.16499047850274874222, $TOL0 ],
645 "gsl_sf_atanint (300.0)" => [8.96281388924518959990, $TOL0 ],
646 "gsl_sf_atanint (1.0e+5)" => [18.084471031038661920, $TOL0 ],
647 "gsl_sf_fermi_dirac_m1 (-10.0)" => [0.00004539786870243439450, $TOL0 ],
648 "gsl_sf_fermi_dirac_m1 ( -1.0)" => [0.26894142136999512075, $TOL0 ],
649 "gsl_sf_fermi_dirac_m1 ( 1.0)" => [0.7310585786300048793, $TOL0 ],
650 "gsl_sf_fermi_dirac_m1 ( 10.0)" => [0.9999546021312975656, $TOL0 ],
651 "gsl_sf_fermi_dirac_0 (-10.0)" => [0.00004539889921686464677, $TOL0 ],
652 "gsl_sf_fermi_dirac_0 ( -1.0)" => [0.31326168751822283405, $TOL0 ],
653 "gsl_sf_fermi_dirac_0 ( 1.0)" => [1.3132616875182228340, $TOL0 ],
654 "gsl_sf_fermi_dirac_0 ( 10.0)" => [10.000045398899216865, $TOL0 ],
655 "gsl_sf_fermi_dirac_1 (-10.0)" => [0.00004539941448447633524, $TOL0 ],
656 "gsl_sf_fermi_dirac_1 ( -2.0)" => [0.13101248471442377127, $TOL0 ],
657 "gsl_sf_fermi_dirac_1 ( -1.0)" => [0.3386479964034521798, $TOL0 ],
658 "gsl_sf_fermi_dirac_1 ( -0.4)" => [0.5825520806897909028, $TOL0 ],
659 "gsl_sf_fermi_dirac_1 ( 0.4)" => [1.1423819861584355337, $TOL0 ],
660 "gsl_sf_fermi_dirac_1 ( 1.0)" => [1.8062860704447742567, $TOL0 ],
661 "gsl_sf_fermi_dirac_1 ( 1.5)" => [2.5581520872227806402, $TOL0 ],
662 "gsl_sf_fermi_dirac_1 ( 2.5)" => [4.689474797599761667, $TOL0 ],
663 "gsl_sf_fermi_dirac_1 ( 10.0)" => [51.64488866743374196, $TOL0 ],
664 "gsl_sf_fermi_dirac_1 ( 12.0)" => [73.64492792264531092, $TOL0 ],
665 "gsl_sf_fermi_dirac_1 ( 20.0)" => [201.64493406478707282, $TOL0 ],
666 "gsl_sf_fermi_dirac_1 ( 50.0)" => [1251.6449340668482264, $TOL0 ],
667 "gsl_sf_fermi_dirac_2 (-10.0)" => [0.00004539967212174776662, $TOL0 ],
668 "gsl_sf_fermi_dirac_2 ( -2.0)" => [0.13313272938565030508, $TOL0 ],
669 "gsl_sf_fermi_dirac_2 ( -1.0)" => [0.3525648792978077590, $TOL0 ],
670 "gsl_sf_fermi_dirac_2 ( -0.4)" => [0.6229402647001272120, $TOL0 ],
671 "gsl_sf_fermi_dirac_2 ( 0.4)" => [1.2915805581060844533, $TOL0 ],
672 "gsl_sf_fermi_dirac_2 ( 1.0)" => [2.1641656128127008622, $TOL0 ],
673 "gsl_sf_fermi_dirac_2 ( 1.5)" => [3.247184513920792475, $TOL0 ],
674 "gsl_sf_fermi_dirac_2 ( 2.5)" => [6.797764392735056317, $TOL0 ],
675 "gsl_sf_fermi_dirac_2 ( 10.0)" => [183.11605273482105278, $TOL3 ],
676 "gsl_sf_fermi_dirac_2 ( 12.0)" => [307.73921494638635166, $TOL4 ],
677 "gsl_sf_fermi_dirac_2 ( 20.0)" => [1366.2320146723590157, $TOL4 ],
678 "gsl_sf_fermi_dirac_2 ( 50.0)" => [20915.580036675744655, $TOL4 ],
679 "gsl_sf_fermi_dirac_2 (200.0)" => [1.3336623201467029786e+06, $TOL4 ],
680 "gsl_sf_fermi_dirac_mhalf (-10.0)" => [0.00004539847236080549532, $TOL0 ],
681 "gsl_sf_fermi_dirac_mhalf ( -2.0)" => [0.12366562180120994266, $TOL0 ],
682 "gsl_sf_fermi_dirac_mhalf ( -1.0)" => [0.29402761761145122022, $TOL0 ],
683 "gsl_sf_fermi_dirac_mhalf ( -0.4)" => [0.4631755336886027800, $TOL0 ],
684 "gsl_sf_fermi_dirac_mhalf ( 0.4)" => [0.7654084737661656915, $TOL0 ],
685 "gsl_sf_fermi_dirac_mhalf ( 1.0)" => [1.0270571254743506890, $TOL0 ],
686 "gsl_sf_fermi_dirac_mhalf ( 1.5)" => [1.2493233478527122008, $TOL0 ],
687 "gsl_sf_fermi_dirac_mhalf ( 2.5)" => [1.6663128834358313625, $TOL0 ],
688 "gsl_sf_fermi_dirac_mhalf ( 10.0)" => [3.552779239536617160, $TOL0 ],
689 "gsl_sf_fermi_dirac_mhalf ( 12.0)" => [3.897268231925439359, $TOL0 ],
690 "gsl_sf_fermi_dirac_mhalf ( 20.0)" => [5.041018507535328603, $TOL0 ],
691 "gsl_sf_fermi_dirac_mhalf ( 50.0)" => [7.977530858581869960, $TOL1 ],
692 "gsl_sf_fermi_dirac_half (-10.0)" => [0.00004539920105264132755, $TOL1 ],
693 "gsl_sf_fermi_dirac_half ( -2.0)" => [0.12929851332007559106, $TOL0 ],
694 "gsl_sf_fermi_dirac_half ( -1.0)" => [0.3277951592607115477, $TOL0 ],
695 "gsl_sf_fermi_dirac_half ( -0.4)" => [0.5522452153690688947, $TOL0 ],
696 "gsl_sf_fermi_dirac_half ( 0.4)" => [1.0386797503389389277, $TOL0 ],
697 "gsl_sf_fermi_dirac_half ( 1.0)" => [1.5756407761513002308, $TOL0 ],
698 "gsl_sf_fermi_dirac_half ( 1.5)" => [2.1448608775831140360, $TOL0 ],
699 "gsl_sf_fermi_dirac_half ( 2.5)" => [3.606975377950373251, $TOL0 ],
700 "gsl_sf_fermi_dirac_half ( 10.0)" => [24.084656964637653615, $TOL0 ],
701 "gsl_sf_fermi_dirac_half ( 12.0)" => [31.540203287044242593, $TOL0 ],
702 "gsl_sf_fermi_dirac_half ( 20.0)" => [67.49151222165892049, $TOL0 ],
703 "gsl_sf_fermi_dirac_half ( 50.0)" => [266.09281252136259343, $TOL1 ],
704 "gsl_sf_fermi_dirac_3half (-10.0)" => [0.00004539956540456176333, $TOL0 ],
705 "gsl_sf_fermi_dirac_3half ( -2.0)" => [0.13224678225177236685, $TOL0 ],
706 "gsl_sf_fermi_dirac_3half ( -1.0)" => [0.3466747947990574170, $TOL0 ],
707 "gsl_sf_fermi_dirac_3half ( -0.4)" => [0.6056120213305040910, $TOL0 ],
708 "gsl_sf_fermi_dirac_3half ( 0.4)" => [1.2258236403963668282, $TOL0 ],
709 "gsl_sf_fermi_dirac_3half ( 1.0)" => [2.0022581487784644573, $TOL0 ],
710 "gsl_sf_fermi_dirac_3half ( 1.5)" => [2.9277494127932173068, $TOL0 ],
711 "gsl_sf_fermi_dirac_3half ( 2.5)" => [5.768879312210516582, $TOL0 ],
712 "gsl_sf_fermi_dirac_3half ( 10.0)" => [101.00510084332600020, $TOL2 ],
713 "gsl_sf_fermi_dirac_3half ( 12.0)" => [156.51518642795728036, $TOL3 ],
714 "gsl_sf_fermi_dirac_3half ( 20.0)" => [546.5630100657601959, $TOL1 ],
715 "gsl_sf_fermi_dirac_3half ( 50.0)" => [5332.353566687145552, 2*$TOL2 ],
716 "gsl_sf_fermi_dirac_int (3, -2.0)" => [0.1342199155038680215, $TOL0 ],
717 "gsl_sf_fermi_dirac_int (3, 0.0)" => [0.9470328294972459176, $TOL0 ],
718 "gsl_sf_fermi_dirac_int (3, 0.1)" => [1.0414170610956165759, $TOL0 ],
719 "gsl_sf_fermi_dirac_int (3, 1.0)" => [2.3982260822489407070, $TOL0 ],
720 "gsl_sf_fermi_dirac_int (3, 3.0)" => [12.621635313399690724, $TOL1 ],
721 "gsl_sf_fermi_dirac_int (3, 100.0)" => [4.174893231066566793e+06, $TOL6 ],
722 #"gsl_sf_fermi_dirac_int (3, 500.0)" => [2.604372285319088354e+09, $TOL1 ],
723 "gsl_sf_fermi_dirac_int (5, -2.0)" => [0.13505242246823676478, $TOL0 ],
724 "gsl_sf_fermi_dirac_int (5, 0.0)" => [0.9855510912974351041, $TOL0 ],
725 "gsl_sf_fermi_dirac_int (5, 0.1)" => [1.0876519750101492782, $TOL0 ],
726 "gsl_sf_fermi_dirac_int (5, 1.0)" => [2.6222337848692390539, $TOL0 ],
727 "gsl_sf_fermi_dirac_int (5, 3.0)" => [17.008801618012113022, $TOL1 ],
728 #"gsl_sf_fermi_dirac_int (5, 100.0)" => [1.3957522531334869874e+09, $TOL1 ],
729 #"gsl_sf_fermi_dirac_int (5, 500.0)" => [2.1705672808114817955e+13, $TOL2 ],
730 "gsl_sf_fermi_dirac_int (7, -2.0)" => [0.1352641105671255851, $TOL0 ],
731 "gsl_sf_fermi_dirac_int (7, 0.0)" => [0.9962330018526478992, $TOL0 ],
732 "gsl_sf_fermi_dirac_int (7, 0.1)" => [1.1005861815180315485, $TOL0 ],
733 "gsl_sf_fermi_dirac_int (7, 1.0)" => [2.6918878172003129203, $TOL0 ],
734 "gsl_sf_fermi_dirac_int (7, 3.0)" => [19.033338976999367642, $TOL2 ],
735 "gsl_sf_fermi_dirac_int (7, 10.0)" => [5654.530932873610014, $TOL3 ],
736 #"gsl_sf_fermi_dirac_int (7, 50.0)" => [1.005005069985066278e+09, $TOL2 ],
737 #"gsl_sf_fermi_dirac_int (7, 500.0)" => [9.691690268341569514e+16, $TOL3 ],
738 "gsl_sf_fermi_dirac_int (9, -2.0)" => [0.1353174385330242691, $TOL0 ],
739 "gsl_sf_fermi_dirac_int (9, 0.0)" => [0.9990395075982715656, $TOL0 ],
740 "gsl_sf_fermi_dirac_int (9, 0.1)" => [1.1039997234712941212, $TOL0 ],
741 "gsl_sf_fermi_dirac_int (9, 1.0)" => [2.7113648898129249947, $TOL0 ],
742 "gsl_sf_fermi_dirac_int (9, 3.0)" => [19.768544008138602223, $TOL2 ],
743 "gsl_sf_fermi_dirac_int (9, 10.0)" => [10388.990167312912478, $TOL4 ],
744 #"gsl_sf_fermi_dirac_int (9, 50.0)" => [2.85466960802601649e+10, $TOL1 ],
745 #"gsl_sf_fermi_dirac_int (9, 500.0)" => [2.69273849842695876e+20, 2*$TOL1 ],
746 "gsl_sf_fermi_dirac_int (10, -2.0)" => [0.13532635396712288092, $TOL0 ],
747 "gsl_sf_fermi_dirac_int (10, 0.0)" => [0.9995171434980607541, $TOL0 ],
748 "gsl_sf_fermi_dirac_int (10, 0.1)" => [1.1045818238852612296, $TOL0 ],
749 "gsl_sf_fermi_dirac_int (10, 1.0)" => [2.7147765350346120647, $TOL0 ],
750 "gsl_sf_fermi_dirac_int (10, 3.0)" => [19.917151938411675171, $TOL1 ],
751 "gsl_sf_fermi_dirac_int (10, 10.0)" => [12790.918595516495955, $TOL3 ],
752 #"gsl_sf_fermi_dirac_int (10, 50.0)" => [1.3147703201869657654e+11, $TOL2 ],
753 #"gsl_sf_fermi_dirac_int (10, 500.0)" => [1.2241331244469204398e+22, $TOL2 ],
754 "gsl_sf_fermi_dirac_int (11, -2.0)" => [0.1353308162894847149, $TOL0 ],
755 "gsl_sf_fermi_dirac_int (11, 0.0)" => [0.9997576851438581909, $TOL0 ],
756 "gsl_sf_fermi_dirac_int (11, 0.1)" => [1.1048751811565850418, $TOL0 ],
757 "gsl_sf_fermi_dirac_int (11, 1.0)" => [2.7165128749007313436, $TOL0 ],
758 "gsl_sf_fermi_dirac_int (11, 3.0)" => [19.997483022044603065, $TOL2 ],
759 "gsl_sf_fermi_dirac_int (11, 10.0)" => [14987.996005901818036, $TOL4 ],
760 #"gsl_sf_fermi_dirac_int (11, 50.0)" => [5.558322924078990628e+11, $TOL2 ],
761 #"gsl_sf_fermi_dirac_int (11, 500.0)" => [5.101293089606198280e+23, $TOL2 ],
762 "gsl_sf_fermi_dirac_int (20, -2.0)" => [0.13533527450327238373, $TOL0 ],
763 "gsl_sf_fermi_dirac_int (20, 0.0)" => [0.9999995232582155428, $TOL0 ],
764 "gsl_sf_fermi_dirac_int (20, 0.1)" => [1.1051703357941368203, $TOL0 ],
765 "gsl_sf_fermi_dirac_int (20, 1.0)" => [2.7182783069905721654, $TOL0 ],
766 "gsl_sf_fermi_dirac_int (20, 3.0)" => [20.085345296028242734, $TOL2 ],
767 "gsl_sf_fermi_dirac_int (20, 10.0)" => [21898.072920149606475, $TOL4 ],
768 #"gsl_sf_fermi_dirac_int (20, 50.0)" => [1.236873256595717618e+16, $TOL2 ],
769 #"gsl_sf_fermi_dirac_int (20, 500.0)" => [9.358938204369557277e+36, $TOL2 ],
770 "gsl_sf_gegenpoly_1 (-0.2, 1.0)" => [-0.4, $TOL0 ],
771 "gsl_sf_gegenpoly_1 ( 0.0, 1.0)" => [2.0, $TOL0 ],
772 "gsl_sf_gegenpoly_1 ( 1.0, 1.0)" => [2.0, $TOL0 ],
773 "gsl_sf_gegenpoly_1 ( 1.0, 0.5)" => [1.0, $TOL0 ],
774 "gsl_sf_gegenpoly_1 ( 5.0, 1.0)" => [10.0, $TOL0 ],
775 "gsl_sf_gegenpoly_1 ( 100.0, 0.5)" => [100.0, $TOL0 ],
776 "gsl_sf_gegenpoly_2 (-0.2, 0.5)" => [0.12, $TOL0 ],
777 "gsl_sf_gegenpoly_2 ( 0.0, 1.0)" => [1.00, $TOL0 ],
778 "gsl_sf_gegenpoly_2 ( 1.0, 1.0)" => [3.00, $TOL0 ],
779 "gsl_sf_gegenpoly_2 ( 1.0, 0.1)" => [-0.96, $TOL0 ],
780 "gsl_sf_gegenpoly_2 ( 5.0, 1.0)" => [55.0, $TOL0 ],
781 "gsl_sf_gegenpoly_2 ( 100.0, 0.5)" => [4950.0, $TOL0 ],
782 "gsl_sf_gegenpoly_3 (-0.2, 0.5)" => [0.112, $TOL0 ],
783 "gsl_sf_gegenpoly_3 ( 0.0, 1.0)" => [-2.0/3.0, $TOL0 ],
784 "gsl_sf_gegenpoly_3 ( 1.0, 1.0)" => [4.000, $TOL0 ],
785 "gsl_sf_gegenpoly_3 ( 1.0, 0.1)" => [-0.392, $TOL0 ],
786 "gsl_sf_gegenpoly_3 ( 5.0, 1.0)" => [220.000, $TOL0 ],
787 "gsl_sf_gegenpoly_3 ( 100.0, 0.5)" => [161600.000, $TOL0 ],
788 "gsl_sf_gegenpoly_n (1, 1.0, 1.0)" => [2.000 , $TOL0 ],
789 "gsl_sf_gegenpoly_n (10, 1.0, 1.0)" => [11.000 , $TOL0 ],
790 "gsl_sf_gegenpoly_n (10, 1.0, 0.1)" => [-0.4542309376 , $TOL0 ],
791 "gsl_sf_gegenpoly_n (10, 5.0, 1.0)" => [9.23780e+4 , $TOL0 ],
792 "gsl_sf_gegenpoly_n (10, 100.0, 0.5)" => [1.5729338392690000e+13, $TOL0 ],
793 #"gsl_sf_gegenpoly_n (1000, 100.0, 1.0)" => [3.3353666135627322e+232, $TOL1 ],
794 #"gsl_sf_gegenpoly_n (100, 2000.0, 1.0)" => [5.8753432034937579e+202, $TOL0 ],
795 #"gsl_sf_gegenpoly_n (103, 207.0, 2.0)" => [1.4210272202235983e+145, $TOL0 ],
796 "gsl_sf_gegenpoly_n (103, -0.4, 0.3)" => [-1.64527498094522e-04, $TOL1 ],
797 "gsl_sf_laguerre_1 (0.5, -1.0)" => [2.5, $TOL0 ],
798 "gsl_sf_laguerre_1 (0.5, 1.0)" => [0.5, $TOL0 ],
799 "gsl_sf_laguerre_1 (1.0, 1.0)" => [1.0, $TOL0 ],
800 "gsl_sf_laguerre_2 ( 0.5, -1.0)" => [4.875, $TOL0 ],
801 "gsl_sf_laguerre_2 ( 0.5, 1.0)" => [-0.125, $TOL0 ],
802 "gsl_sf_laguerre_2 ( 1.0, 1.0)" => [ 0.5, $TOL0 ],
803 "gsl_sf_laguerre_2 (-1.0, 1.0)" => [-0.5, $TOL0 ],
804 "gsl_sf_laguerre_2 (-2.0, 1.0)" => [ 0.5, $TOL0 ],
805 "gsl_sf_laguerre_2 (-3.0, 1.0)" => [ 2.5, $TOL0 ],
806 "gsl_sf_laguerre_3 (0.5, -1.0)" => [8.479166666666666667, $TOL0 ],
807 "gsl_sf_laguerre_3 (0.5, 1.0)" => [-0.6041666666666666667, $TOL0 ],
808 "gsl_sf_laguerre_3 (1.0, 1.0)" => [-0.16666666666666666667, $TOL1 ],
809 "gsl_sf_laguerre_3 ( 2.0, 1.0)" => [2.3333333333333333333, $TOL0 ],
810 "gsl_sf_laguerre_3 (-2.0, 1.0)" => [1.0/3.0, $TOL0 ],
811 "gsl_sf_laguerre_3 (-3.0, 1.0)" => [-1.0/6.0, $TOL0 ],
812 "gsl_sf_laguerre_3 (-4.0, 1.0)" => [-8.0/3.0, $TOL0 ],
813 "gsl_sf_laguerre_n (1, 0.5, 1.0)" => [0.5, 10*$TOL0 ],
814 "gsl_sf_laguerre_n (2, 1.0, 1.0)" => [0.5, $TOL1 ],
815 "gsl_sf_laguerre_n (3, 2.0, 1.0)" => [2.3333333333333333333, $TOL1 ],
816 "gsl_sf_laguerre_n (4, 2.0, 0.5)" => [6.752604166666666667, $TOL1 ],
817 #"gsl_sf_laguerre_n (90, 2.0, 0.5)" => [-48.79047157201507897, $TOL1 ],
818 #"gsl_sf_laguerre_n (90, 2.0, -100.0)" => [2.5295879275042410902e+63, $TOL3 ],
819 #"gsl_sf_laguerre_n (90, 2.0, 100.0)" => [-2.0929042259546928670e+20, $TOL1 ],
820 "gsl_sf_laguerre_n (100, 2.0, 0.5)" => [-28.764832945909097418, $TOL2 ],
821 #"gsl_sf_laguerre_n (1000, 2.0, -0.5)" => [2.4399915170947549589e+21, $TOL3 ],
822 "gsl_sf_laguerre_n (1000, 2.0, 0.5)" => [-306.77440254315317525, $TOL3 ],
823 "gsl_sf_laguerre_n (100000, 2.0, 1.0)" => [5107.73491348319, $TOL4 ],
824 "gsl_sf_laguerre_n (1e5, 2.5, 2.5)" => [-0.41491680394598644969113795e5, 128*$TOL6 ],
825 "gsl_sf_laguerre_n (1e5+1, 2.5, 2.5)" => [-0.41629446949552321027514888e5, 128*$TOL6 ],
826 #"gsl_sf_laguerre_n (1e6+1, 2.5, 2.5)" => [-0.48017961545391273151977118e6, 128*$TOL6 ],
827 #"gsl_sf_laguerre_n (5e6+1, 2.5, 2.5)" => [-0.15174037401611122446089494e7, $TOL6 ],
828 #"gsl_sf_laguerre_n (8e6+1, 2.5, 2.5)" => [ 0.63251509472091810994286362e6, $TEST_SNGL ],
829 #"gsl_sf_laguerre_n (1e7+1, 2.5, 2.5)" => [ 0.15299484685632983178033887e7, $TEST_SNGL ],
830 #"gsl_sf_laguerre_n (1e8+1, 2.5, 2.5)" => [ 0.23645341644922756725290777e8, $TEST_SNGL ],
831 #"gsl_sf_laguerre_n (1e9+1, 2.5, 2.5)" => [-0.17731002248958790286185878e8, 100*$TEST_SNGL ],
832 "gsl_sf_laguerre_n (1, -2.0, 1.0)" => [ -2.0, $TOL0 ],
833 "gsl_sf_laguerre_n (2, -2.0, 1.0)" => [ 0.5, $TOL0 ],
834 "gsl_sf_laguerre_n (3, -2.0, 1.0)" => [ 1.0/3.0, $TOL0 ],
835 "gsl_sf_laguerre_n (10, -2.0, 1.0)" => [-0.04654954805996472663, $TOL2 ],
836 "gsl_sf_laguerre_n (10, -5.0, 1.0)" => [-0.0031385030864197530864, $TOL2 ],
837 "gsl_sf_laguerre_n (10, -9.0, 1.0)" => [-2.480158730158730159e-06, $TOL5 ],
838 "gsl_sf_laguerre_n (10, -11.0, 1.0)" => [2.7182818011463844797, $TOL2 ],
839 "gsl_sf_laguerre_n (10, -11.0, -1.0)" => [0.3678794642857142857, $TOL2 ],
840 "gsl_sf_laguerre_n (100, -2.0, 1.0)" => [ -0.0027339992019526273866, $SQRT_TOL0 ],
841 "gsl_sf_laguerre_n (100, -2.0, -1.0)" => [ 229923.09193402028290, $TOL5 ],
842 "gsl_sf_laguerre_n (100, -10.0, 1.0)" => [ 3.25966665871244092e-11, $TOL6 ],
843 "gsl_sf_laguerre_n (100, -10.0, -1.0)" => [ 0.00016484365618205810025, $TOL6 ],
844 "gsl_sf_laguerre_n (100, -20.0, 1.0)" => [ 5.09567630343671251e-21, $TOL3 ],
845 "gsl_sf_laguerre_n (100, -30.0, 1.0)" => [ 3.46063150272466192e-34, $TOL1 ],
846 "gsl_sf_laguerre_n (100, -50.0, 1.0)" => [ 1.20981872933162889e-65, $TOL1 ],
847 "gsl_sf_laguerre_n (100, -50.0, -1.0)" => [ 8.60763477742332922e-65, $TOL1 ],
848 "gsl_sf_laguerre_n (100, -50.5, 1.0)" => [ 4.84021010426688393e-31, $TOL1 ],
849 "gsl_sf_laguerre_n (100, -50.5, -1.0)" => [ 8.49861345212160618e-33, $TOL1 ],
850 "gsl_sf_laguerre_n (100, -101.0, 1.0)" => [2.7182818284590452354, $TOL1 ],
851 "gsl_sf_laguerre_n (100, -101.0, -1.0)" => [0.3678794411714423216, $TOL1 ],
852 "gsl_sf_laguerre_n (100, -102.0, 1.0)" => [271.8281828459045235, $TOL2 ],
853 "gsl_sf_laguerre_n (100, -102.0, -1.0)" => [37.52370299948711680, $TOL1 ],
854 #"gsl_sf_laguerre_n (100, -110.0, 1.0)" => [1.0666955248998831554e+13, $TOL1 ],
855 #"gsl_sf_laguerre_n (100, -110.0, -1.0)" => [1.7028306108058225871e+12, $TOL1 ],
856 #"gsl_sf_laguerre_n (100, -200.0, 1.0)" => [7.47851889721356628e+58, $TOL1 ],
857 #"gsl_sf_laguerre_n (100, -200.0, -1.0)" => [2.73740299754732273e+58, $TOL1 ],
858 "gsl_sf_laguerre_n (100, -50.0, 10.0)" => [4.504712811317745591e-21, $SQRT_TOL0 ],
859 "gsl_sf_laguerre_n (100, -50.0, -10.0)" => [1.475165520610679937e-11, $TOL1 ],
860 "gsl_sf_laguerre_n (100, 0.0, 0.5)" => [0.18682260367692278801, $TOL2 ],
861 "gsl_sf_laguerre_n (100, 0.0, 10.5)" => [9.1796907354050059874, $TOL2 ],
862 #"gsl_sf_laguerre_n (100, 0.0, -10.5)" => [5.6329215744170606488e24, $TOL2 ],
863 #"gsl_sf_laguerre_n (100, 0.0, 100.5)" => [-3.9844782875811907525e20, $TOL2 ],
864 #"gsl_sf_laguerre_n (100, 0.0, 150)" => [-1.4463204337261709595e31, $TOL2 ],
865 "gsl_sf_lambert_W0 (0.0)" => [ 0.0, $TOL0 ],
866 "gsl_sf_lambert_W0 (1.0)" => [ 0.567143290409783872999969, $TOL0 ],
867 "gsl_sf_lambert_W0 (2.0)" => [ 0.852605502013725491346472, $TOL0 ],
868 "gsl_sf_lambert_W0 (20.0)" => [2.205003278024059970493066, $TOL0 ],
869 "gsl_sf_lambert_W0 (1000.0)" => [5.24960285240159622712606, $TOL0 ],
870 "gsl_sf_lambert_W0 (1.0e+6)" => [11.38335808614005262200016, $TOL0 ],
871 "gsl_sf_lambert_W0 (1.0e+12)" => [24.43500440493491313826305, $TOL0 ],
872 "gsl_sf_lambert_W0 (1.0e+308)" => [702.641362034106812081125, $TOL0 ],
873 "gsl_sf_lambert_W0 (1.6849341956993852953416990)" => [0.775706963944252869680440, $TOL0 ],
874 "gsl_sf_lambert_W0 (-1.0/$M_E - $GSL_DBL_EPSILON)" => [-1.0, 10*$TOL6 ],
875 "gsl_sf_lambert_W0 (-1.0/$M_E + 1.0/(1024.0*1024.0*1024.0))" => [-0.999928845560308370714970, $TOL3],
876 "gsl_sf_lambert_W0 (-1.0/$M_E + 1.0/(1024.0*1024.0))" => [-0.997724730359774141620354, $TOL3 ],
877 "gsl_sf_lambert_W0 (-1.0/$M_E + 1.0/512.0)" => [-0.900335676696088773044678, $TOL0 ],
878 "gsl_sf_lambert_W0 (-1.0/$M_E + 0.25)" => [-0.1349044682661213545487599, $TOL0 ],
879 "gsl_sf_lambert_Wm1 (0.0)" => [ 0.0, $TOL0 ],
880 "gsl_sf_lambert_Wm1 (1.0)" => [ 0.567143290409783872999969, $TOL0 ],
881 "gsl_sf_lambert_Wm1 (2.0)" => [ 0.852605502013725491346472, $TOL0 ],
882 "gsl_sf_lambert_Wm1 (20.0)" => [2.205003278024059970493066, $TOL0 ],
883 "gsl_sf_lambert_Wm1 (-1.0/$M_E - $GSL_DBL_EPSILON)" => [-1.0, 10*$TOL6 ],
884 "gsl_sf_lambert_Wm1 (-1.0/$M_E + 1.0/(1024.0*1024.0*1024.0))" => [-1.000071157815154608049055, $TOL3 ],
885 "gsl_sf_lambert_Wm1 (-1.0/$M_E + 1.0/(1024.0*1024.0))" => [-1.002278726118593023934693, $TOL3 ],
886 "gsl_sf_lambert_Wm1 (-1.0/$M_E + 1.0/512.0)" => [-1.106761200865743124599130, $TOL1 ],
887 "gsl_sf_lambert_Wm1 (-1.0/$M_E + 1.0/64.0)" => [-1.324240940341812125489772, $TOL1 ],
888 "gsl_sf_lambert_Wm1 (-1.0/$M_E + 0.25)" => [-3.345798131120112, $TOL1 ],
889 "gsl_sf_log (0.1)" => [-2.3025850929940456840, $TOL0 ],
890 "gsl_sf_log (1.1)" => [0.09531017980432486004, $TOL1 ],
891 "gsl_sf_log (1000.0)" => [6.907755278982137052, $TOL0 ],
892 "gsl_sf_log_abs (-0.1)" => [-2.3025850929940456840, $TOL0 ],
893 "gsl_sf_log_abs (-1.1)" => [0.09531017980432486004, $TOL1 ],
894 "gsl_sf_log_abs (-1000.0)" => [6.907755278982137052, $TOL0 ],
895 "gsl_sf_log_abs (0.1)" => [-2.3025850929940456840, $TOL0 ],
896 "gsl_sf_log_abs (1.1)" => [0.09531017980432486004, $TOL1 ],
897 "gsl_sf_log_abs (1000.0)" => [6.907755278982137052, $TOL0 ],
898 "gsl_sf_log_1plusx (1.0e-10)" => [9.999999999500000000e-11, $TOL0 ],
899 "gsl_sf_log_1plusx (1.0e-8)" => [9.999999950000000333e-09, $TOL0 ],
900 "gsl_sf_log_1plusx (1.0e-4)" => [0.00009999500033330833533, $TOL0 ],
901 "gsl_sf_log_1plusx (0.1)" => [0.09531017980432486004, $TOL0 ],
902 "gsl_sf_log_1plusx (0.49)" => [0.3987761199573677730, $TOL0 ],
903 "gsl_sf_log_1plusx (-0.49)" => [-0.6733445532637655964, $TOL0 ],
904 "gsl_sf_log_1plusx (1.0)" => [$M_LN2, $TOL0 ],
905 "gsl_sf_log_1plusx (-0.99)" => [-4.605170185988091368, $TOL0 ],
906 "gsl_sf_log_1plusx_mx (1.0e-10)" => [-4.999999999666666667e-21, $TOL0 ],
907 "gsl_sf_log_1plusx_mx (1.0e-8)" => [-4.999999966666666917e-17, $TOL0 ],
908 "gsl_sf_log_1plusx_mx (1.0e-4)" => [-4.999666691664666833e-09, $TOL0 ],
909 "gsl_sf_log_1plusx_mx (0.1)" => [-0.004689820195675139956, $TOL0 ],
910 "gsl_sf_log_1plusx_mx (0.49)" => [-0.09122388004263222704, $TOL0 ],
911 "gsl_sf_log_1plusx_mx (-0.49)" => [-0.18334455326376559639, $TOL0 ],
912 "gsl_sf_log_1plusx_mx (1.0)" => [$M_LN2-1.0, $TOL0 ],
913 "gsl_sf_log_1plusx_mx (-0.99)" => [-3.615170185988091368, $TOL0 ],
914 "gsl_sf_pow_int (2.0, 3)" => [8.0, $TOL0 ],
915 "gsl_sf_pow_int (-2.0, 3)" => [-8.0, $TOL0 ],
916 "gsl_sf_pow_int (2.0, -3)" => [1.0/8.0, $TOL0 ],
917 "gsl_sf_pow_int (-2.0, -3)" => [-1.0/8.0, $TOL0 ],
918 "gsl_sf_pow_int (10.0, 4)" => [1.0e+4, $TOL0 ],
919 "gsl_sf_pow_int (10.0, -4)" => [1.0e-4, $TOL0 ],
920 "gsl_sf_pow_int (-10.0, 4)" => [1.0e+4, $TOL0 ],
921 "gsl_sf_pow_int (-10.0, -4)" => [1.0e-4, $TOL0 ],
922 "gsl_sf_pow_int (10.0, 40)" => [1.0e+40, $TOL0 ],
923 "gsl_sf_pow_int (8.0, -40)" => [7.523163845262640051e-37, $TOL0 ],
924 "gsl_sf_pow_int (-10.0, 40)" => [1.0e+40, $TOL0 ],
925 "gsl_sf_pow_int (-8.0, -40)" => [7.523163845262640051e-37, $TOL0 ],
926 "gsl_sf_pow_int (10.0, 41)" => [1.0e+41, $TOL0 ],
927 "gsl_sf_pow_int (8.0, -41)" => [9.403954806578300064e-38, $TOL0 ],
928 "gsl_sf_pow_int (-10.0, 41)" => [-1.0e+41, $TOL0 ],
929 "gsl_sf_pow_int (-8.0, -41)" => [-9.403954806578300064e-38, $TOL0 ],
930 "gsl_sf_psi_int (1)" => [-0.57721566490153286060, $TOL0 ],
931 "gsl_sf_psi_int (2)" => [0.42278433509846713939, $TOL0 ],
932 "gsl_sf_psi_int (3)" => [0.92278433509846713939, $TOL0 ],
933 "gsl_sf_psi_int (4)" => [1.2561176684318004727, $TOL0 ],
934 "gsl_sf_psi_int (5)" => [1.5061176684318004727, $TOL0 ],
935 "gsl_sf_psi_int (100)" => [4.600161852738087400, $TOL0 ],
936 "gsl_sf_psi_int (110)" => [4.695928024251535633, $TOL0 ],
937 "gsl_sf_psi_int (5000)" => [8.517093188082904107, $TOL0 ],
938 "gsl_sf_psi (5000.0)" => [8.517093188082904107, $TOL0 ],
939 "gsl_sf_psi (5.0)" => [1.5061176684318004727, $TOL0 ],
940 "gsl_sf_psi (-10.5)" => [ 2.3982391295357816134, $TOL0 ],
941 "gsl_sf_psi (-100.5)" => [ 4.615124601338064117, $TOL2 ],
942 "gsl_sf_psi (-1.0e+5-0.5)" => [11.512935464924395337, 4.0*$TOL4 ],
943 "gsl_sf_psi (-262144.0-0.5)" => [12.476653064769611581, 4.0*$TOL4 ],
944 "gsl_sf_psi_1piy (0.8)" => [-0.07088340212750589223, $TOL1 ],
945 "gsl_sf_psi_1piy (1.0)" => [ 0.09465032062247697727, $TOL0 ],
946 "gsl_sf_psi_1piy (5.0)" => [ 1.6127848446157465854, $TOL2 ],
947 "gsl_sf_psi_1piy (100.0)" => [ 4.605178519404762003, $TOL0 ],
948 "gsl_sf_psi_1piy (2000.0)" => [7.600902480375416216, $TOL0 ],
949 "gsl_sf_psi_1piy (-0.8)" => [-0.07088340212750589223, $TOL1 ],
950 "gsl_sf_psi_1piy (-1.0)" => [ 0.09465032062247697727, $TOL0 ],
951 "gsl_sf_psi_1piy (-5.0)" => [ 1.6127848446157465854, $TOL2 ],
952 "gsl_sf_psi_1piy (-100.0)" => [ 4.605178519404762003, $TOL0 ],
953 "gsl_sf_psi_1piy (-2000.0)" => [7.600902480375416216, $TOL0 ],
954 "gsl_sf_psi_1_int (1)" => [1.6449340668482264364, $TOL0 ],
955 "gsl_sf_psi_1_int (2)" => [0.64493406684822643647, $TOL0 ],
956 "gsl_sf_psi_1_int (3)" => [0.39493406684822643647, $TOL0 ],
957 "gsl_sf_psi_1_int (4)" => [0.28382295573711532536, $TOL0 ],
958 "gsl_sf_psi_1_int (1)" => [1.6449340668482264365, $TOL0 ],
959 "gsl_sf_psi_1_int (5)" => [0.22132295573711532536, $TOL0 ],
960 "gsl_sf_psi_1_int (100)" => [0.010050166663333571395, $TOL0 ],
961 "gsl_sf_psi_1_int (110)" => [0.009132356622022545705, $TOL0 ],
962 "gsl_sf_psi_1_int (500)" => [0.0020020013333322666697, $TOL0 ],
963 "gsl_sf_psi_1 (1.0/32.0)" => [1025.5728544782377089, $TOL2 ],
964 "gsl_sf_psi_1 (1.0)" => [1.6449340668482264365, $TOL0 ],
965 "gsl_sf_psi_1 (5.0)" => [0.22132295573711532536, $TOL0 ],
966 "gsl_sf_psi_1 (100.0)" => [0.010050166663333571395, $TOL0 ],
967 "gsl_sf_psi_1 (110.0)" => [0.009132356622022545705, $TOL0 ],
968 "gsl_sf_psi_1 (500.0)" => [0.0020020013333322666697, $TOL0 ],
969 "gsl_sf_psi_1 (-1.0 - 1.0/128.0)" => [16386.648472598746587, $TOL0 ],
970 "gsl_sf_psi_1 (-1.50)" => [9.3792466449891237539, $TOL0 ],
971 "gsl_sf_psi_1 (-10.5)" => [9.7787577398148123845, $TOL0 ],
972 "gsl_sf_psi_1 (-15.5)" => [9.8071247184113896201, $TOL0 ],
973 "gsl_sf_psi_1 (-50.5)" => [9.8499971860824842274, $TOL0 ],
974 "gsl_sf_psi_1 (-1000.5)" => [9.8686054001734414233, $TOL0 ],
975 "gsl_sf_psi_n (1, 1)" => [1.6449340668482264364, $TOL0 ],
976 "gsl_sf_psi_n (1, 2)" => [0.64493406684822643647, $TOL0 ],
977 "gsl_sf_psi_n (1, 3)" => [0.39493406684822643647, $TOL0 ],
978 "gsl_sf_psi_n (1, 4)" => [0.28382295573711532536, $TOL0 ],
979 "gsl_sf_psi_n (1, 5)" => [0.22132295573711532536, $TOL0 ],
980 "gsl_sf_psi_n (1, 100)" => [0.010050166663333571395, $TOL0 ],
981 "gsl_sf_psi_n (1, 110)" => [0.009132356622022545705, $TOL0 ],
982 "gsl_sf_psi_n (1, 500)" => [0.0020020013333322666697, $TOL0 ],
983 "gsl_sf_psi_n (3, 5.0)" => [0.021427828192755075022, $TOL0 ],
984 "gsl_sf_psi_n (3, 500.0)" => [1.6048063999872000683e-08, $TOL0 ],
985 "gsl_sf_psi_n (10, 5.0)" => [-0.08675107579196581317, $TOL1 ],
986 "gsl_sf_psi_n (10, 50.0)" => [-4.101091112731268288e-12, $TOL0 ],
987 "gsl_sf_psi_n (0, -1.5)" => [0.70315664064524318723, $TOL0 ],
988 "gsl_sf_psi_n (1, -1.5)" => [9.3792466449891237539, $TOL0 ],
989 "gsl_sf_synchrotron_1 (0.01)" => [ 0.444972504114210632, $TOL0 ],
990 "gsl_sf_synchrotron_1 (1.0)" => [ 0.651422815355364504, $TOL1 ],
991 "gsl_sf_synchrotron_1 (10.0)" => [ 0.000192238264300868882, $TOL1 ],
992 "gsl_sf_synchrotron_1 (100.0)" => [4.69759366592220221e-43, $TOL1 ],
993 "gsl_sf_synchrotron_2 (0.01)" => [ 0.23098077342226277732, $TOL2 ],
994 "gsl_sf_synchrotron_2 (1.0)" => [ 0.4944750621042082670, $TOL1 ],
995 "gsl_sf_synchrotron_2 (10.0)" => [ 0.00018161187569530204281, $TOL1 ],
996 "gsl_sf_synchrotron_2 (256.0)" => [1.3272635474353774058e-110, $TOL4 ],
997 "gsl_sf_transport_2 (1.0e-10)" => [9.9999999999999999999e-11, $TOL0 ],
998 "gsl_sf_transport_2 (1.0)" => [ 0.97303256135517012845, $TOL0 ],
999 "gsl_sf_transport_2 (3.0)" => [ 2.41105004901695346199, $TOL0 ],
1000 "gsl_sf_transport_2 (10.0)" => [ 3.28432911449795173575, $TOL0 ],
1001 "gsl_sf_transport_2 (100.0)" => [ 3.28986813369645287294, $TOL0 ],
1002 "gsl_sf_transport_2 (1.0e+05)" => [3.28986813369645287294, $TOL0 ],
1003 "gsl_sf_transport_3 (1.0e-10)" => [4.999999999999999999997e-21, $TOL0 ],
1004 "gsl_sf_transport_3 (1.0)" => [ 0.479841006572417499939, $TOL0 ],
1005 "gsl_sf_transport_3 (3.0)" => [ 3.210604662942246772338, $TOL0 ],
1006 "gsl_sf_transport_3 (5.0)" => [ 5.614386613842273228585, $TOL0 ],
1007 "gsl_sf_transport_3 (10.0)" => [ 7.150322712008592975030, $TOL0 ],
1008 "gsl_sf_transport_3 (30.0)" => [ 7.212341416160946511930, $TOL0 ],
1009 "gsl_sf_transport_3 (100.0)" => [ 7.212341418957565712398, $TOL0 ],
1010 "gsl_sf_transport_3 (1.0e+05)" => [7.212341418957565712398, $TOL0 ],
1011 "gsl_sf_transport_4 (1.0e-10)" => [3.33333333333333333333e-31, $TOL0 ],
1012 "gsl_sf_transport_4 (1.0e-07)" => [3.33333333333333166666e-22, $TOL0 ],
1013 "gsl_sf_transport_4 (1.0e-04)" => [3.33333333166666666726e-13, $TOL0 ],
1014 "gsl_sf_transport_4 (0.1)" => [0.000333166726172109903824, $TOL0 ],
1015 "gsl_sf_transport_4 (1.0)" => [0.31724404523442648241, $TOL0 ],
1016 "gsl_sf_transport_4 (3.0)" => [5.96482239737147652446, $TOL0 ],
1017 "gsl_sf_transport_4 (5.0)" => [15.3597843168821829816, $TOL0 ],
1018 "gsl_sf_transport_4 (10.0)" => [25.2736676770304417334, $TOL0 ],
1019 "gsl_sf_transport_4 (30.0)" => [25.9757575220840937469, $TOL0 ],
1020 "gsl_sf_transport_4 (100.0)" => [25.9757576090673165963, $TOL1 ],
1021 "gsl_sf_transport_4 (1.0e+05)" => [25.9757576090673165963, $TOL2 ],
1022 "gsl_sf_transport_5 (1.0e-10)" => [2.49999999999999999999e-41, $TOL0 ],
1023 "gsl_sf_transport_5 (1.0e-07)" => [2.49999999999999861111e-29, $TOL0 ],
1024 "gsl_sf_transport_5 (1.0e-04)" => [2.49999999861111111163e-17, $TOL0 ],
1025 "gsl_sf_transport_5 (0.1)" => [0.000024986116317791487410, $TOL0 ],
1026 "gsl_sf_transport_5 (1.0)" => [0.236615879239094789259153, $TOL0 ],
1027 "gsl_sf_transport_5 (3.0)" => [12.77055769104415951115760, $TOL0 ],
1028 "gsl_sf_transport_5 (5.0)" => [50.26309221817518778543615, $TOL0 ],
1029 "gsl_sf_transport_5 (10.0)" => [116.3807454024207107698556, $TOL0 ],
1030 "gsl_sf_transport_5 (30.0)" => [124.4313279083858954839911, $TOL0 ],
1031 "gsl_sf_transport_5 (100.0)" => [124.4313306172043911597639, $TOL0 ],
1032 "gsl_sf_transport_5 (1.0e+05)" => [124.43133061720439115976, $TOL0 ],
1033 "gsl_sf_sin (-10.0)" => [ 0.5440211108893698134, $TOL0 ],
1034 "gsl_sf_sin (1.0)" => [ 0.8414709848078965067, $TOL0 ],
1035 "gsl_sf_sin (1000.0)" => [ 0.8268795405320025603, $TOL0 ],
1036 "gsl_sf_sin (1048576.75)" => [ 0.8851545351115651914, $TOL1 ],
1037 "gsl_sf_sin (62831853.75)" => [0.6273955953485000827, $TOL3 ],
1038 "gsl_sf_sin (1073741822.5)" => [-0.8284043541754465988, $SQRT_TOL0 ],
1039 "gsl_sf_sin (1073741824.0)" => [-0.6173264150460421708, $SQRT_TOL0 ],
1040 "gsl_sf_sin (1073741825.5)" => [ 0.7410684679436226926, $SQRT_TOL0 ],
1041 "gsl_sf_sin (1099511627776.0)" => [-0.4057050115328287198, 512.0*$SQRT_TOL0 ],
1042 "gsl_sf_cos (-10.0)" => [-0.8390715290764524523, $TOL0 ],
1043 "gsl_sf_cos (1.0)" => [ 0.5403023058681397174, $TOL0 ],
1044 "gsl_sf_cos (1000.0)" => [ 0.5623790762907029911, $TOL1 ],
1045 "gsl_sf_cos (1048576.75)" => [ 0.4652971620066351799, $TOL2 ],
1046 "gsl_sf_cos (62831853.75)" => [ 0.7787006914966116436, $TOL2 ],
1047 "gsl_sf_cos (1073741822.5)" => [-0.5601305436977716102, $SQRT_TOL0 ],
1048 "gsl_sf_cos (1073741824.0)" => [ 0.7867071229411881196, $SQRT_TOL0 ],
1049 "gsl_sf_cos (1099511627776.0)" => [-0.9140040719915570023, 512.0*$SQRT_TOL0 ],
1050 "gsl_sf_sinc (1.0/1024.0)" => [0.9999984312693665404, $TOL0 ],
1051 "gsl_sf_sinc (1.0/2.0 )" => [2.0/$M_PI, $TOL0 ],
1052 "gsl_sf_sinc (80.5 )" => [0.0039541600768172754, $TOL0 ],
1053 "gsl_sf_sinc (100.5 )" => [0.0031672625490924445, $TOL0 ],
1054 "gsl_sf_sinc (1.0e+06 + 0.5)" => [3.18309727028927157e-07, $TOL0 ],
1055 #"gsl_sf_sin_pi_x_e (1000.5)" => [1.0, $TOL0 ],
1056 #"gsl_sf_sin_pi_x_e (10000.0 + 1.0/65536.0)" => [0.00004793689960306688455, $TOL0 ],
1057 #"gsl_sf_sin_pi_x_e (1099511627776.0 + 1 + 0.125)" => [-0.3826834323650897717, $TOL0 ],
1058 "gsl_sf_lnsinh (0.1)" => [ -2.3009189815304652235, $TOL0 ],
1059 "gsl_sf_lnsinh (1.0)" => [ 0.16143936157119563361, $TOL0 ],
1060 "gsl_sf_lnsinh (5.0)" => [ 4.306807418479684201, $TOL0 ],
1061 "gsl_sf_lnsinh (100.0)" => [99.30685281944005469, $TOL0 ],
1062 "gsl_sf_lncosh (0.125)" => [0.007792239318898252791, $TOL0 ],
1063 "gsl_sf_lncosh (1.0)" => [ 0.4337808304830271870, $TOL0 ],
1064 "gsl_sf_lncosh (5.0)" => [ 4.306898218339271555, $TOL0 ],
1065 "gsl_sf_lncosh (100.0)" => [99.30685281944005469, $TOL0 ],
1066 #"gsl_sf_angle_restrict_pos_err (2.0*$M_PI)" => [2*$M_PI, $TOL1 ],
1067 #"gsl_sf_angle_restrict_pos_err (-2.0*$M_PI)" => [2*$DELTA, $TOL1 ],
1068 #"gsl_sf_angle_restrict_pos_err (1e9)" => [0.5773954235013851694, $TOL1 ],
1069 #"gsl_sf_angle_restrict_pos_err (1e12)" => [5.625560548042800009446, $TEST_SNGL ],
1070 #"gsl_sf_angle_restrict_pos_err (-1e9)" => [5.7057898836782013075, $TOL1 ],
1071 #"gsl_sf_angle_restrict_pos_err (-1e12)" => [0.6576247591367864674792517289, 100*$TEST_SNGL ],
1072 #"gsl_sf_angle_restrict_symm_err (1e9)" => [0.5773954235013851694, $TOL1 ],
1073 #"gsl_sf_angle_restrict_symm_err (1e12)" => [-0.6576247591367864674792517289, 100*$TEST_SNGL ],
1074 #"gsl_sf_angle_restrict_symm_err (-1e9)" => [-0.5773954235013851694, $TOL1 ],
1075 #"gsl_sf_angle_restrict_symm_err (-1e12)" => [0.6576247591367864674792517289, 100*$TEST_SNGL ],
1076 "gsl_sf_zeta_int (-61.0)" => [-3.30660898765775767257e+34, $TOL0 ],
1077 "gsl_sf_zeta_int (-8)" => [0.0, $TOL0 ],
1078 "gsl_sf_zeta_int (-6)" => [0.0, $TOL0 ],
1079 "gsl_sf_zeta_int (-5.0)" => [ -0.003968253968253968253968, $TOL0 ],
1080 "gsl_sf_zeta_int (-4)" => [0.0, $TOL0 ],
1081 "gsl_sf_zeta_int (-3)" => [1.0/120.0, $TOL0 ],
1082 "gsl_sf_zeta_int (-2)" => [0.0, $TOL0 ],
1083 "gsl_sf_zeta_int (-1)" => [-1.0/12.0, $TOL0 ],
1084 "gsl_sf_zeta_int ( 5.0)" => [1.0369277551433699263313655, $TOL0 ],
1085 "gsl_sf_zeta_int (31.0)" => [1.0000000004656629065033784, $TOL0 ],
1086 "gsl_sf_zetam1_int (-61.0)" => [-3.30660898765775767257e+34, $TOL0 ],
1087 "gsl_sf_zetam1_int (-5.0)" => [ -1.003968253968253968253968, $TOL0 ],
1088 "gsl_sf_zetam1_int (-8)" => [-1.0, $TOL0 ],
1089 "gsl_sf_zetam1_int (-6)" => [-1.0, $TOL0 ],
1090 "gsl_sf_zetam1_int (-4)" => [-1.0, $TOL0 ],
1091 "gsl_sf_zetam1_int (-3)" => [-119.0/120.0, $TOL0 ],
1092 "gsl_sf_zetam1_int (-2)" => [-1.0, $TOL0 ],
1093 "gsl_sf_zetam1_int (-1)" => [-13.0/12.0, $TOL0 ],
1094 "gsl_sf_zetam1_int ( 5.0)" => [0.0369277551433699263313655, $TOL0 ],
1095 "gsl_sf_zetam1_int (31.0)" => [0.0000000004656629065033784, $TOL0 ],
1096 "gsl_sf_zeta (-151)" => [8.195215221831378294e+143, $TOL2 ],
1097 "gsl_sf_zeta (-51)" => [9.68995788746359406565e+24, 1.226414e+11 ],
1098 "gsl_sf_zeta (-5)" => [-0.003968253968253968253968, $TOL1 ],
1099 "gsl_sf_zeta (-8)" => [0.0, $TOL1 ],
1100 "gsl_sf_zeta (-6)" => [0.0, $TOL1 ],
1101 "gsl_sf_zeta (-4)" => [0.0, $TOL1 ],
1102 "gsl_sf_zeta (-3)" => [1.0/120.0, $TOL1 ],
1103 "gsl_sf_zeta (-2)" => [0.0, $TOL1 ],
1104 "gsl_sf_zeta (-1)" => [-1.0/12.0, $TOL1 ],
1105 "gsl_sf_zeta (-0.5)" => [-0.207886224977354566017307, $TOL1 ],
1106 "gsl_sf_zeta (-1e-10)" => [-0.49999999990810614668948, $TOL1 ],
1107 "gsl_sf_zeta (0.0)" => [ -0.5, $TOL0 ],
1108 "gsl_sf_zeta (1e-10)" => [ -0.50000000009189385333058, $TOL0 ],
1109 "gsl_sf_zeta (0.5)" => [-1.460354508809586812889499, $TOL0 ],
1110 "gsl_sf_zeta (1.0-1.0/1024.0)" => [-1023.4228554489429787, $TOL0 ],
1111 "gsl_sf_zeta (1.0+1.0/1048576)" => [1.0485765772157343441e+06, $TOL5 ],
1112 "gsl_sf_zeta (5.0)" => [1.036927755143369926331365, $TOL0 ],
1113 "gsl_sf_zeta (25.5)" => [1.000000021074106110269959, $TOL0 ],
1114 "gsl_sf_zetam1 (-8)" => [-1.0, $TOL1 ],
1115 "gsl_sf_zetam1 (-6)" => [-1.0, $TOL1 ],
1116 "gsl_sf_zetam1 (-4)" => [-1.0, $TOL1 ],
1117 "gsl_sf_zetam1 (-3)" => [-119.0/120.0, $TOL1 ],
1118 "gsl_sf_zetam1 (-2)" => [-1.0, $TOL1 ],
1119 "gsl_sf_zetam1 (-1)" => [-13.0/12.0, $TOL1 ],
1120 "gsl_sf_zetam1 (-0.5)" => [-1.207886224977354566017307, $TOL1 ],
1121 "gsl_sf_zetam1 (-1e-10)" => [-1.49999999990810614668948, $TOL1 ],
1122 "gsl_sf_zetam1 (0.0)" => [ -1.5, $TOL0 ],
1123 "gsl_sf_zetam1 (1e-10)" => [ -1.50000000009189385333058, $TOL0 ],
1124 "gsl_sf_zetam1 (0.5)" => [-2.460354508809586812889499, $TOL0 ],
1125 "gsl_sf_zetam1 (2.0)" => [ 0.64493406684822643647, $TOL1 ],
1126 "gsl_sf_zetam1 (3.0)" => [ 0.20205690315959428540, $TOL1 ],
1127 "gsl_sf_zetam1 (5.0)" => [ 0.0369277551433699263314, $TOL1 ],
1128 "gsl_sf_zetam1 (9.5)" => [ 0.0014125906121736622712, $TOL1 ],
1129 "gsl_sf_zetam1 (10.5)" => [0.000700842641736155219500, $TOL1 ],
1130 "gsl_sf_zetam1 (12.5)" => [0.000173751733643178193390, $TOL1 ],
1131 "gsl_sf_zetam1 (13.5)" => [0.000086686727462338155188, $TOL1 ],
1132 "gsl_sf_zetam1 (15.5)" => [0.000021619904246069108133, $TOL1 ],
1133 "gsl_sf_zetam1 (16.5)" => [0.000010803124900178547671, $TOL0 ],
1134 "gsl_sf_zetam1 (25.5)" => [0.000000021074106110269959, $TOL0 ],
1135 "gsl_sf_hzeta (2, 1.0)" => [ 1.6449340668482264365, $TOL0 ],
1136 "gsl_sf_hzeta (2, 10.0)" => [ 0.1051663356816857461, $TOL0 ],
1137 "gsl_sf_hzeta (5, 1.0)" => [ 1.0369277551433699263, $TOL0 ],
1138 "gsl_sf_hzeta (5, 10.0)" => [ 0.000030413798676470276, $TOL0 ],
1139 #"gsl_sf_hzeta (9, 0.1)" => [ 1.0000000004253980e+09, $TOL0 ],
1140 "gsl_sf_hzeta (30, 0.5)" => [ 1.0737418240000053e+09, $TOL0 ],
1141 "gsl_sf_hzeta (30, 0.9)" => [ 2.3589824880264765e+01, $TOL1 ],
1142 "gsl_sf_hzeta (75, 0.25)" => [1.4272476927059599e+45, $TOL1 ],
1143 #"gsl_sf_eta_int (-91)" => [-4.945598888750002040e+94, $TOL0 ],
1144 "gsl_sf_eta_int (-51)" => [-4.363969073121683116e+40, $TOL0 ],
1145 "gsl_sf_eta_int (-5)" => [0.25, $TOL0 ],
1146 "gsl_sf_eta_int (-1)" => [0.25, $TOL0 ],
1147 "gsl_sf_eta_int ( 0)" => [0.5, $TOL0 ],
1148 "gsl_sf_eta_int ( 5)" => [0.9721197704469093059, $TOL0 ],
1149 "gsl_sf_eta_int ( 6)" => [0.9855510912974351041, $TOL0 ],
1150 "gsl_sf_eta_int ( 20)" => [0.9999990466115815221, $TOL0 ],
1151 "gsl_sf_eta_int ( 1000)" => [1.0, $TOL0 ],
1152 #"gsl_sf_eta (-51.5)" => [-1.2524184036924703656e+41, $TOL2 ] ,
1153 "gsl_sf_eta (-5)" => [0.25, $TOL0 ],
1154 "gsl_sf_eta (0.5)" => [0.6048986434216303702, $TOL0 ],
1155 "gsl_sf_eta (0.999)" => [0.6929872789683383574, $TOL0 ],
1156 "gsl_sf_eta (1.0)" => [0.6931471805599453094, $TOL0 ],
1157 "gsl_sf_eta (1.0+1.0e-10)" => [0.6931471805759321998, $TOL0 ],
1158 "gsl_sf_eta ( 5)" => [0.9721197704469093059, $TOL0 ],
1159 "gsl_sf_eta ( 5.2)" => [0.9755278712546684682, $TOL0 ],
1160 "gsl_sf_eta ( 6)" => [0.9855510912974351041, $TOL0 ],
1161 "gsl_sf_eta ( 20)" => [0.9999990466115815221, $TOL0 ],
1162 };
1164 my $gsl = Math::GSL->new;
1166 $gsl->verify_results($results, 'Math::GSL::SF');
1168 {
1169 my $result = Math::GSL::SF::gsl_sf_result_struct->new;
1170 my ($status) = gsl_sf_bessel_J0_e(2.0,$result);
1171 ok( defined $result->{err}, '$result->{err}' );
1172 ok( is_similar($result->{val}, gsl_sf_bessel_J0(2.0)) , '$result->{val}' );
1173 };