1 // (C) Copyright John Maddock 2008.
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6 #define BOOST_TEST_MAIN
7 #include <boost/test/unit_test.hpp>
8 #include <boost/test/floating_point_comparison.hpp>
9 #include <boost/math/tools/precision.hpp>
10 #include <math.h> // ldexpf
11 #include <iostream>
12 #include <iomanip>
13
14 #ifdef TEST_STD
15 #include <cmath>
16 namespace tr1 = std::tr1;
17 #else
18 #include <boost/math/tr1.hpp>
19 namespace tr1 = boost::math::tr1;
20 #endif
21
22 #ifdef _MSC_VER
23 # pragma warning (disable : 4100) // unreferenced formal parameter
24 // Can't just comment parameter out because reference or not depends on macro define.
25 #endif
26
test_values(float,const char * name)27 void test_values(float, const char* name)
28 {
29 std::cout << "Testing type " << name << std::endl;
30 #ifndef TEST_LD
31 //
32 // First the C99 math functions:
33 //
34 float eps = boost::math::tools::epsilon<float>();
35 BOOST_CHECK_CLOSE(tr1::acoshf(std::cosh(0.5f)), 0.5f, 5000 * eps);
36 BOOST_CHECK_CLOSE(tr1::asinhf(std::sinh(0.5f)), 0.5f, 5000 * eps);
37 BOOST_CHECK_CLOSE(tr1::atanhf(std::tanh(0.5f)), 0.5f, 5000 * eps);
38
39 BOOST_CHECK_CLOSE(tr1::cbrtf(1.5f * 1.5f * 1.5f), 1.5f, 5000 * eps);
40
41 BOOST_CHECK(tr1::copysignf(1.0f, 1.0f) == 1.0f);
42 BOOST_CHECK(tr1::copysignf(1.0f, -1.0f) == -1.0f);
43 BOOST_CHECK(tr1::copysignf(-1.0f, 1.0f) == 1.0f);
44 BOOST_CHECK(tr1::copysignf(-1.0f, -1.0f) == -1.0f);
45
46 BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(0.125)), static_cast<float>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
47 BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(0.5)), static_cast<float>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
48 BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(1)), static_cast<float>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
49 BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(5)), static_cast<float>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
50 BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(-0.125)), static_cast<float>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
51 BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(-0.5)), static_cast<float>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
52 BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(0)), static_cast<float>(1), eps * 1000);
53
54 BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(0.125)), static_cast<float>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
55 BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(0.5)), static_cast<float>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
56 BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(1)), static_cast<float>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
57 BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(5)), static_cast<float>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
58 BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(-0.125)), static_cast<float>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
59 BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(-0.5)), static_cast<float>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
60 BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(0)), static_cast<float>(0), eps * 1000);
61
62 BOOST_CHECK_CLOSE(tr1::log1pf(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
63 BOOST_CHECK_CLOSE(tr1::expm1f(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
64 BOOST_CHECK_CLOSE(tr1::log1pf(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
65 BOOST_CHECK_CLOSE(tr1::expm1f(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
66
67 BOOST_CHECK_EQUAL(tr1::fmaxf(0.1f, -0.1f), 0.1f);
68 BOOST_CHECK_EQUAL(tr1::fminf(0.1f, -0.1f), -0.1f);
69
70 BOOST_CHECK_CLOSE(tr1::hypotf(1.0f, 3.0f), std::sqrt(10.0f), eps * 500);
71
72 BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(3.5)), static_cast<float>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
73 BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(0.125)), static_cast<float>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
74 BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(-0.125)), static_cast<float>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
75 BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(-3.125)), static_cast<float>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
76 BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(-53249.0/1024)), static_cast<float>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
77
78 BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(3.5)), static_cast<float>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
79 BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(0.125)), static_cast<float>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
80 BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(-0.125)), static_cast<float>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
81 BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(-3.125)), static_cast<float>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
82
83 #ifdef BOOST_HAS_LONG_LONG
84 BOOST_CHECK(tr1::llroundf(2.5f) == 3LL);
85 BOOST_CHECK(tr1::llroundf(2.25f) == 2LL);
86 #endif
87 BOOST_CHECK(tr1::lroundf(2.5f) == 3L);
88 BOOST_CHECK(tr1::lroundf(2.25f) == 2L);
89 BOOST_CHECK(tr1::roundf(2.5f) == 3.0f);
90 BOOST_CHECK(tr1::roundf(2.25f) == 2.0f);
91
92 BOOST_CHECK(tr1::nextafterf(1.0f, 2.0f) > 1.0f);
93 BOOST_CHECK(tr1::nextafterf(1.0f, -2.0f) < 1.0f);
94 BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, 2.0f), -2.0f) == 1.0f);
95 BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, -2.0f), 2.0f) == 1.0f);
96 BOOST_CHECK(tr1::nextafterf(1.0f, 2.0f) > 1.0f);
97 BOOST_CHECK(tr1::nextafterf(1.0f, -2.0f) < 1.0f);
98 BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, 2.0f), -2.0f) == 1.0f);
99 BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, -2.0f), 2.0f) == 1.0f);
100
101 BOOST_CHECK(tr1::truncf(2.5f) == 2.0f);
102 BOOST_CHECK(tr1::truncf(2.25f) == 2.0f);
103
104 //
105 // And again but without the "f" suffix on the function names:
106 //
107 BOOST_CHECK_CLOSE(tr1::acosh(std::cosh(0.5f)), 0.5f, 5000 * eps);
108 BOOST_CHECK_CLOSE(tr1::asinh(std::sinh(0.5f)), 0.5f, 5000 * eps);
109 BOOST_CHECK_CLOSE(tr1::atanh(std::tanh(0.5f)), 0.5f, 5000 * eps);
110
111 BOOST_CHECK_CLOSE(tr1::cbrt(1.5f * 1.5f * 1.5f), 1.5f, 5000 * eps);
112
113 BOOST_CHECK(tr1::copysign(1.0f, 1.0f) == 1.0f);
114 BOOST_CHECK(tr1::copysign(1.0f, -1.0f) == -1.0f);
115 BOOST_CHECK(tr1::copysign(-1.0f, 1.0f) == 1.0f);
116 BOOST_CHECK(tr1::copysign(-1.0f, -1.0f) == -1.0f);
117
118 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0.125)), static_cast<float>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
119 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0.5)), static_cast<float>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
120 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(1)), static_cast<float>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
121 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(5)), static_cast<float>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
122 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(-0.125)), static_cast<float>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
123 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(-0.5)), static_cast<float>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
124 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0)), static_cast<float>(1), eps * 1000);
125
126 BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0.125)), static_cast<float>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
127 BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0.5)), static_cast<float>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
128 BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(1)), static_cast<float>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
129 BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(5)), static_cast<float>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
130 BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(-0.125)), static_cast<float>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
131 BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(-0.5)), static_cast<float>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
132 BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0)), static_cast<float>(0), eps * 1000);
133
134 BOOST_CHECK_CLOSE(tr1::log1p(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
135 BOOST_CHECK_CLOSE(tr1::expm1(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
136 BOOST_CHECK_CLOSE(tr1::log1p(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
137 BOOST_CHECK_CLOSE(tr1::expm1(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
138
139 BOOST_CHECK_EQUAL(tr1::fmax(0.1f, -0.1f), 0.1f);
140 BOOST_CHECK_EQUAL(tr1::fmin(0.1f, -0.1f), -0.1f);
141
142 BOOST_CHECK_CLOSE(tr1::hypot(1.0f, 3.0f), std::sqrt(10.0f), eps * 500);
143
144 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(3.5)), static_cast<float>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
145 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(0.125)), static_cast<float>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
146 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-0.125)), static_cast<float>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
147 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-3.125)), static_cast<float>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
148 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-53249.0/1024)), static_cast<float>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
149
150 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(3.5)), static_cast<float>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
151 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(0.125)), static_cast<float>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
152 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(-0.125)), static_cast<float>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
153 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(-3.125)), static_cast<float>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
154
155 #ifdef BOOST_HAS_LONG_LONG
156 BOOST_CHECK(tr1::llround(2.5f) == 3LL);
157 BOOST_CHECK(tr1::llround(2.25f) == 2LL);
158 #endif
159 BOOST_CHECK(tr1::lround(2.5f) == 3L);
160 BOOST_CHECK(tr1::lround(2.25f) == 2L);
161 BOOST_CHECK(tr1::round(2.5f) == 3.0f);
162 BOOST_CHECK(tr1::round(2.25f) == 2.0f);
163
164 BOOST_CHECK(tr1::nextafter(1.0f, 2.0f) > 1.0f);
165 BOOST_CHECK(tr1::nextafter(1.0f, -2.0f) < 1.0f);
166 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, 2.0f), -2.0f) == 1.0f);
167 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, -2.0f), 2.0f) == 1.0f);
168 BOOST_CHECK(tr1::nextafter(1.0f, 2.0f) > 1.0f);
169 BOOST_CHECK(tr1::nextafter(1.0f, -2.0f) < 1.0f);
170 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, 2.0f), -2.0f) == 1.0f);
171 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, -2.0f), 2.0f) == 1.0f);
172
173 BOOST_CHECK(tr1::trunc(2.5f) == 2.0f);
174 BOOST_CHECK(tr1::trunc(2.25f) == 2.0f);
175
176 //
177 // Now for the TR1 math functions:
178 //
179 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(4, 5, static_cast<float>(0.5L)), static_cast<float>(88.31510416666666666666666666666666666667L), eps * 100);
180 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 0, static_cast<float>(2.5L)), static_cast<float>(-0.8802526766660982969576719576719576719577L), eps * 100);
181 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 1, static_cast<float>(4.5L)), static_cast<float>(1.564311458042689732142857142857142857143L), eps * 100);
182 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 6, static_cast<float>(8.5L)), static_cast<float>(20.51596541066649098875661375661375661376L), eps * 100);
183 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 12, static_cast<float>(12.5L)), static_cast<float>(-199.5560968456234671241181657848324514991L), eps * 100);
184 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(50, 40, static_cast<float>(12.5L)), static_cast<float>(-4.996769495006119488583146995907246595400e16L), eps * 100);
185
186 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
187 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(0.5L)), static_cast<float>(-0.3307291666666666666666666666666666666667L), eps * 100);
188 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(0.5L)), static_cast<float>(-0.5183392237103174603174603174603174603175L), eps * 100);
189 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(0.5L)), static_cast<float>(0.3120174870800154148915399248893113634676L), eps * 100);
190 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(0.5L)), static_cast<float>(-0.3181388060269979064951118308575628226834L), eps * 100);
191
192 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(-0.5L)), static_cast<float>(1.5L), eps * 100);
193 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(-0.5L)), static_cast<float>(3.835937500000000000000000000000000000000L), eps * 100);
194 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(-0.5L)), static_cast<float>(7.950934709821428571428571428571428571429L), eps * 100);
195 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(-0.5L)), static_cast<float>(76.12915699869631476833699787070874048223L), eps * 100);
196 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(-0.5L)), static_cast<float>(2307.428631277506570629232863491518399720L), eps * 100);
197
198 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(4.5L)), static_cast<float>(-3.500000000000000000000000000000000000000L), eps * 100);
199 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(4.5L)), static_cast<float>(0.08593750000000000000000000000000000000000L), eps * 100);
200 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(4.5L)), static_cast<float>(-1.036928013392857142857142857142857142857L), eps * 100);
201 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(4.5L)), static_cast<float>(1.437239150257817378525582974722170737587L), eps * 100);
202 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(4.5L)), static_cast<float>(-0.7795068145562651416494321484050019245248L), eps * 100);
203
204 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(4, 2, static_cast<float>(0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
205 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(7, 5, static_cast<float>(0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
206 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(4, 2, static_cast<float>(-0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
207 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(7, 5, static_cast<float>(-0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
208
209 BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
210 BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(4, static_cast<float>(0.5L)), static_cast<float>(-0.2890625000000000000000000000000000000000L), eps * 100);
211 BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(7, static_cast<float>(0.5L)), static_cast<float>(0.2231445312500000000000000000000000000000L), eps * 100);
212 BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(40, static_cast<float>(0.5L)), static_cast<float>(-0.09542943523261546936538467572384923220258L), eps * 100);
213
214 float sv = eps / 1024;
215 BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(1), static_cast<float>(1)), static_cast<float>(1), eps * 20 * 100);
216 BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(1), static_cast<float>(4)), static_cast<float>(0.25), eps * 20 * 100);
217 BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), static_cast<float>(1)), static_cast<float>(0.25), eps * 20 * 100);
218 BOOST_CHECK_CLOSE(tr1::betaf(sv, static_cast<float>(4)), 1/sv, eps * 20 * 100);
219 BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), sv), 1/sv, eps * 20 * 100);
220 BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), static_cast<float>(20)), static_cast<float>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);
221 BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(0.0125L), static_cast<float>(0.000023L)), static_cast<float>(43558.24045647538375006349016083320744662L), eps * 20 * 100);
222
223 BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
224 BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(0.125)), static_cast<float>(1.5769867712158131421244030532288080803822271060839), eps * 5000);
225 BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(0.25)), static_cast<float>(1.5962422221317835101489690714979498795055744578951), eps * 5000);
226 BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(300)/1024), static_cast<float>(1.6062331054696636704261124078746600894998873503208), eps * 5000);
227 BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(400)/1024), static_cast<float>(1.6364782007562008756208066125715722889067992997614), eps * 5000);
228 BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(-0.5)), static_cast<float>(1.6857503548125960428712036577990769895008008941411), eps * 5000);
229 BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(-0.75)), static_cast<float>(1.9109897807518291965531482187613425592531451316788), eps * 5000);
230
231 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-1)), static_cast<float>(1), eps * 5000);
232 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
233 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(100) / 1024), static_cast<float>(1.5670445330545086723323795143598956428788609133377), eps * 5000);
234 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(200) / 1024), static_cast<float>(1.5557071588766556854463404816624361127847775545087), eps * 5000);
235 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(300) / 1024), static_cast<float>(1.5365278991162754883035625322482669608948678755743), eps * 5000);
236 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(400) / 1024), static_cast<float>(1.5090417763083482272165682786143770446401437564021), eps * 5000);
237 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-0.5)), static_cast<float>(1.4674622093394271554597952669909161360253617523272), eps * 5000);
238 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-600) / 1024), static_cast<float>(1.4257538571071297192428217218834579920545946473778), eps * 5000);
239 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-800) / 1024), static_cast<float>(1.2927868476159125056958680222998765985004489572909), eps * 5000);
240 BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-900) / 1024), static_cast<float>(1.1966864890248739524112920627353824133420353430982), eps * 5000);
241
242 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0.2), static_cast<float>(0)), static_cast<float>(1.586867847454166237308008033828114192951), eps * 5000);
243 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0.4), static_cast<float>(0)), static_cast<float>(1.639999865864511206865258329748601457626), eps * 5000);
244 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(1.57079632679489661923132169163975144209858469968755291048747), eps * 5000);
245 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(2.221441469079183123507940495030346849307), eps * 5000);
246 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0.3), static_cast<float>(-4)), static_cast<float>(0.712708870925620061597924858162260293305195624270730660081949), eps * 5000);
247 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.5), static_cast<float>(-1e+05)), static_cast<float>(0.00496944596485066055800109163256108604615568144080386919012831), eps * 5000);
248 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.75), static_cast<float>(-1e+10)), static_cast<float>(0.0000157080225184890546939710019277357161497407143903832703317801), eps * 5000);
249 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.875), static_cast<float>(1) / 1024), static_cast<float>(2.18674503176462374414944618968850352696579451638002110619287), eps * 5000);
250 BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.875), static_cast<float>(1023)/1024), static_cast<float>(101.045289804941384100960063898569538919135722087486350366997), eps * 5000);
251
252 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(2.25), static_cast<float>(1)/(1024*1024)), static_cast<float>(2.34379212133481347189068464680335815256364262507955635911656e-15), eps * 5000);
253 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(0.0583514045989371500460946536220735787163510569634133670181210), eps * 5000);
254 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-5) + static_cast<float>(1)/1024, static_cast<float>(2.125)), static_cast<float>(0.0267920938009571023702933210070984416052633027166975342895062), eps * 5000);
255 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(597.577606961369169607937419869926705730305175364662688426534), eps * 5000);
256 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474005665181350367684623930576333542989766867888186478185e35), eps * 5000);
257 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(50)), static_cast<float>(1.07153277202900671531087024688681954238311679648319534644743e20), eps * 5000);
258 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694757392660413922181531984160871678224178890247540320), eps * 5000);
259 BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694672763190927440969155740243346136463461655104698748), eps * 5000);
260
261 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(2457)/1024, static_cast<float>(1)/1024), static_cast<float>(3.80739920118603335646474073457326714709615200130620574875292e-9), eps * 5000);
262 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(0.0281933076257506091621579544064767140470089107926550720453038), eps * 5000);
263 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(3217)/1024), static_cast<float>(-2.55820064470647911823175836997490971806135336759164272675969), eps * 5000);
264 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(2.449843111985605522111159013846599118397e-03), eps * 5000);
265 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.5), static_cast<float>(1e+04)), static_cast<float>(0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
266 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.5), static_cast<float>(1e+06)), static_cast<float>(-0.000747424248595630177396350688505919533097973148718960064663632), eps * 5000);
267 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.125), static_cast<float>(1e+06)), static_cast<float>(-0.000776600124835704280633640911329691642748783663198207360238214), eps * 5000);
268 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.875), static_cast<float>(1e+06)), static_cast<float>(-0.000466322721115193071631008581529503095819705088484386434589780), eps * 5000);
269 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(0.5), static_cast<float>(101)), static_cast<float>(0.0358874487875643822020496677692429287863419555699447066226409), eps * 5000);
270 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(0.00244984311198560552211115901384659911839737686676766460822577), eps * 5000);
271 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(1e+06)), static_cast<float>(0.000279243200433579511095229508894156656558211060453622750659554), eps * 5000);
272 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-0.5), static_cast<float>(101)), static_cast<float>(0.0708184798097594268482290389188138201440114881159344944791454), eps * 5000);
273 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474013160494695750009004222225969090304185981836460288562e35), eps * 5000);
274 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(15)), static_cast<float>(-0.0902239288885423309568944543848111461724911781719692852541489), eps * 5000);
275 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547064914615137807616774867984047583596945624129838091326863), eps * 5000);
276 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(10486074) / (1024*1024), static_cast<float>(2e+04)), static_cast<float>(-0.00556783614400875611650958980796060611309029233226596737701688), eps * 5000);
277 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547613660316806551338637153942604550779513947674222863858713), eps * 5000);
278
279 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(0.5), static_cast<float>(0.875)), static_cast<float>(0.558532231646608646115729767013630967055657943463362504577189), eps * 5000);
280 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(0.5), static_cast<float>(1.125)), static_cast<float>(0.383621010650189547146769320487006220295290256657827220786527), eps * 5000);
281 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(2.25), static_cast<float>(std::ldexp(1.0, -30))), static_cast<float>(5.62397392719283271332307799146649700147907612095185712015604e20), eps * 5000);
282 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(1.30623288775012596319554857587765179889689223531159532808379), eps * 5000);
283 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(0.0000733045300798502164644836879577484533096239574909573072142667), eps * 5000);
284 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(-5.5), static_cast<float>(100)), static_cast<float>(5.41274555306792267322084448693957747924412508020839543293369e-45), eps * 5000);
285 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(10240)/1024, static_cast<float>(1)/1024), static_cast<float>(2.35522579263922076203415803966825431039900000000993410734978e38), eps * 5000);
286 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(10240)/1024, static_cast<float>(10)), static_cast<float>(0.00161425530039067002345725193091329085443750382929208307802221), eps * 5000);
287 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(144793)/1024, static_cast<float>(100)), static_cast<float>(1.39565245860302528069481472855619216759142225046370312329416e-6), eps * 5000);
288 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(144793)/1024, static_cast<float>(200)), static_cast<float>(9.11950412043225432171915100042647230802198254567007382956336e-68), eps * 5000);
289
290 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(0.5), static_cast<float>(1) / (1024*1024)), static_cast<float>(-817.033790261762580469303126467917092806755460418223776544122), eps * 5000);
291 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(-2.61489440328417468776474188539366752698192046890955453259866), eps * 5000);
292 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-5.5), static_cast<float>(3.125)), static_cast<float>(-0.0274994493896489729948109971802244976377957234563871795364056), eps * 5000);
293 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(-0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
294 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(-1.50382374389531766117868938966858995093408410498915220070230e38), eps * 5000);
295 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(0.0583041891319026009955779707640455341990844522293730214223545), eps * 5000);
296 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(141.75), static_cast<float>(1e+02)), static_cast<float>(-5.38829231428696507293191118661269920130838607482708483122068e9), eps * 5000);
297 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(141.75), static_cast<float>(2e+04)), static_cast<float>(-0.00376577888677186194728129112270988602876597726657372330194186), eps * 5000);
298 BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-141.75), static_cast<float>(1e+02)), static_cast<float>(-3.81009803444766877495905954105669819951653361036342457919021e9), eps * 5000);
299
300 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
301 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
302 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-1.2261911708835170708130609674719067527242483502207), eps * 5000);
303 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.875), static_cast<float>(-4)), static_cast<float>(-5.3190556182262405182189463092940736859067548232647), eps * 5000);
304 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(-0.625), static_cast<float>(8)), static_cast<float>(9.0419973860310100524448893214394562615252527557062), eps * 5000);
305 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.875), static_cast<float>(1e-05)), static_cast<float>(0.000010000000000127604166668510945638036143355898993088), eps * 5000);
306 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(10)/1024, static_cast<float>(1e+05)), static_cast<float>(100002.38431454899771096037307519328741455615271038), eps * 5000);
307 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(1), static_cast<float>(1e-20)), static_cast<float>(1.0000000000000000000000000000000000000000166666667e-20), eps * 5000);
308 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(1e-20), static_cast<float>(1e-20)), static_cast<float>(1.000000000000000e-20), eps * 5000);
309 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(400)/1024, static_cast<float>(1e+20)), static_cast<float>(1.0418143796499216839719289963154558027005142709763e20), eps * 5000);
310 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(2)), static_cast<float>(2.1765877052210673672479877957388515321497888026770), eps * 5000);
311 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(4)), static_cast<float>(4.2543274975235836861894752787874633017836785640477), eps * 5000);
312 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(6)), static_cast<float>(6.4588766202317746302999080620490579800463614807916), eps * 5000);
313 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(10)), static_cast<float>(10.697409951222544858346795279378531495869386960090), eps * 5000);
314 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-2)), static_cast<float>(-2.1765877052210673672479877957388515321497888026770), eps * 5000);
315 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-4)), static_cast<float>(-4.2543274975235836861894752787874633017836785640477), eps * 5000);
316 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-6)), static_cast<float>(-6.4588766202317746302999080620490579800463614807916), eps * 5000);
317 BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-10)), static_cast<float>(-10.697409951222544858346795279378531495869386960090), eps * 5000);
318
319 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
320 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
321 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-0.84147098480789650665250232163029899962256306079837), eps * 5000);
322 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(900) / 1024, static_cast<float>(-4)), static_cast<float>(-3.1756145986492562317862928524528520686391383168377), eps * 5000);
323 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(-600) / 1024, static_cast<float>(8)), static_cast<float>(7.2473147180505693037677015377802777959345489333465), eps * 5000);
324 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(800) / 1024, static_cast<float>(1e-05)), static_cast<float>(9.999999999898274739584436515967055859383969942432E-6), eps * 5000);
325 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(100) / 1024, static_cast<float>(1e+05)), static_cast<float>(99761.153306972066658135668386691227343323331995888), eps * 5000);
326 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(-0.5), static_cast<float>(1e+10)), static_cast<float>(9.3421545766487137036576748555295222252286528414669e9), eps * 5000);
327 BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(400) / 1024, ldexp(static_cast<float>(1), 66)), static_cast<float>(7.0886102721911705466476846969992069994308167515242e19), eps * 5000);
328
329 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1), static_cast<float>(-1)), static_cast<float>(-1.557407724654902230506974807458360173087), eps * 5000);
330 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.4), static_cast<float>(0), static_cast<float>(-4)), static_cast<float>(-4.153623371196831087495427530365430979011), eps * 5000);
331 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(-0.6), static_cast<float>(0), static_cast<float>(8)), static_cast<float>(8.935930619078575123490612395578518914416), eps * 5000);
332 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.501246705365439492445236118603525029757890291780157969500480), eps * 5000);
333 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.5), eps * 5000);
334 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(-2), static_cast<float>(0.5)), static_cast<float>(0.437501067017546278595664813509803743009132067629603474488486), eps * 5000);
335 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.25), static_cast<float>(0.5)), static_cast<float>(0.510269830229213412212501938035914557628394166585442994564135), eps * 5000);
336 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.5)), static_cast<float>(0.533293253875952645421201146925578536430596894471541312806165), eps * 5000);
337 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.75)), static_cast<float>(0.871827580412760575085768367421866079353646112288567703061975), eps * 5000);
338 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1), static_cast<float>(0.25)), static_cast<float>(0.255341921221036266504482236490473678204201638800822621740476), eps * 5000);
339 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(2), static_cast<float>(0.25)), static_cast<float>(0.261119051639220165094943572468224137699644963125853641716219), eps * 5000);
340 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1023)/1024, static_cast<float>(1.5)), static_cast<float>(13.2821612239764190363647953338544569682942329604483733197131), eps * 5000);
341 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(-1)), static_cast<float>(-1.228014414316220642611298946293865487807), eps * 5000);
342 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(1e+10)), static_cast<float>(1.536591003599172091573590441336982730551e+10), eps * 5000);
343 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.75), static_cast<float>(-1e+05), static_cast<float>(10)), static_cast<float>(0.0347926099493147087821620459290460547131012904008557007934290), eps * 5000);
344 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(10)), static_cast<float>(0.000109956202759561502329123384755016959364346382187364656768212), eps * 5000);
345 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1e+20)), static_cast<float>(1.00000626665567332602765201107198822183913978895904937646809e15), eps * 5000);
346 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1608)/1024), static_cast<float>(0.0000157080616044072676127333183571107873332593142625043567690379), eps * 5000);
347 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), 1-static_cast<float>(1) / 1024, static_cast<float>(1e+20)), static_cast<float>(6.43274293944380717581167058274600202023334985100499739678963e21), eps * 5000);
348 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(50), static_cast<float>(0.1)), static_cast<float>(0.124573770342749525407523258569507331686458866564082916835900), eps * 5000);
349 BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(1.125), static_cast<float>(1)), static_cast<float>(1.77299767784815770192352979665283069318388205110727241629752), eps * 5000);
350
351 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(1)/1024), static_cast<float>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000);
352 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(0.125)), static_cast<float>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000);
353 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(0.5)), static_cast<float>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000);
354 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(1)), static_cast<float>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000);
355 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(50.5)), static_cast<float>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000);
356 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-1)/1024), static_cast<float>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000);
357 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-0.125)), static_cast<float>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000);
358 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-0.5)), static_cast<float>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000);
359 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-1)), static_cast<float>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000);
360 BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-50.5)), static_cast<float>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000);
361
362 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(0, static_cast<float>(1)), static_cast<float>(1.L), 100 * eps);
363 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(1)), static_cast<float>(2.L), 100 * eps);
364 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(2)), static_cast<float>(4.L), 100 * eps);
365 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(10)), static_cast<float>(20), 100 * eps);
366 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(100)), static_cast<float>(200), 100 * eps);
367 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(1e6)), static_cast<float>(2e6), 100 * eps);
368 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(30)), static_cast<float>(5.896624628001300E+17L), 100 * eps);
369 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(1000)), static_cast<float>(1.023976960161280E+33L), 100 * eps);
370 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
371 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(-10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
372 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-10)), static_cast<float>(-7.880000000000000E+3L), 100 * eps);
373 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-1000)), static_cast<float>(-7.999988000000000E+9L), 100 * eps);
374 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-1000000)), static_cast<float>(-7.999999999988000E+18L), 100 * eps);
375
376 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0.125)), static_cast<float>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000);
377 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1023) / static_cast<float>(1024)), static_cast<float>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000);
378 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1025) / static_cast<float>(1024)), static_cast<float>(1024.5772867695045940578681624248887776501597556226L), eps * 5000);
379 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0.5)), static_cast<float>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000);
380 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1.125)), static_cast<float>(8.5862412945105752999607544082693023591996301183069L), eps * 5000);
381 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(2)), static_cast<float>(1.6449340668482264364724151666460251892189499012068L), eps * 5000);
382 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(3.5)), static_cast<float>(1.1267338673170566464278124918549842722219969574036L), eps * 5000);
383 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(4)), static_cast<float>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000);
384 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(4 + static_cast<float>(1) / 1024), static_cast<float>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000);
385 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(4.5)), static_cast<float>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000);
386 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(6.5)), static_cast<float>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000);
387 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(7.5)), static_cast<float>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000);
388 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(8.125)), static_cast<float>(1.0037305205308161603183307711439385250181080293472L), eps * 5000);
389 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(16.125)), static_cast<float>(1.0000140128224754088474783648500235958510030511915L), eps * 5000);
390 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0)), static_cast<float>(-0.5L), eps * 5000);
391 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-0.125)), static_cast<float>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000);
392 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-1)), static_cast<float>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000);
393 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-2)), static_cast<float>(0L), eps * 5000);
394 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-2.5)), static_cast<float>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000 * 3);
395 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-3)), static_cast<float>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000);
396 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-4)), static_cast<float>(0), eps * 5000);
397 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-20)), static_cast<float>(0), eps * 5000 * 100);
398 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-21)), static_cast<float>(-281.46014492753623188405797101449275362318840579710L), eps * 5000 * 100);
399 BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-30.125)), static_cast<float>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000 * 100);
400
401 BOOST_CHECK_CLOSE(tr1::sph_besself(0, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.9999657468461303487880990241993035937654e0), eps * 5000 * 100);
402 BOOST_CHECK_CLOSE(tr1::sph_besself(0, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.9999483203249623334100130061926184665364e0), eps * 5000 * 100);
403 BOOST_CHECK_CLOSE(tr1::sph_besself(2, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.1370120120703995134662099191103188366059e-4), eps * 5000 * 100);
404 BOOST_CHECK_CLOSE(tr1::sph_besself(2, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.2067173265753174063228459655801741280461e-4), eps * 5000 * 100);
405 BOOST_CHECK_CLOSE(tr1::sph_besself(7, static_cast<float>(0.1252804412841796875e3)), static_cast<float>(0.7887555711993028736906736576314283291289e-2), eps * 5000 * 100);
406 BOOST_CHECK_CLOSE(tr1::sph_besself(7, static_cast<float>(0.25554705810546875e3)), static_cast<float>(-0.1463292767579579943284849187188066532514e-2), eps * 5000 * 100);
407
408 BOOST_CHECK_CLOSE(tr1::sph_neumannf(0, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.2249212131304610409189209411089291558038e1), eps * 5000 * 100);
409 BOOST_CHECK_CLOSE(tr1::sph_neumannf(0, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1213309779166084571756446746977955970241e1), eps * 5000 * 100);
410 BOOST_CHECK_CLOSE(tr1::sph_neumannf(2, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.4541702641837159203058389758895634766256e2), eps * 5000 * 100);
411 BOOST_CHECK_CLOSE(tr1::sph_neumannf(2, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1156112621471167110574129561700037138981e2), eps * 5000 * 100);
412 BOOST_CHECK_CLOSE(tr1::sph_neumannf(10, static_cast<float>(0.1097540378570556640625e1)), static_cast<float>(-0.2427889658115064857278886600528596240123e9), eps * 5000 * 100);
413 BOOST_CHECK_CLOSE(tr1::sph_neumannf(10, static_cast<float>(0.30944411754608154296875e1)), static_cast<float>(-0.3394649246350136450439882104151313759251e4), eps * 5000 * 100);
414
415 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendref(3, 2, static_cast<float>(0.5)), static_cast<float>(0.2061460599687871330692286791802688341213L), eps * 5000);
416 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendref(40, 15, static_cast<float>(0.75)), static_cast<float>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000);
417
418 //
419 // Now all over again but without the "f" suffix on the function names this time:
420 //
421 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(4, 5, static_cast<float>(0.5L)), static_cast<float>(88.31510416666666666666666666666666666667L), eps * 100);
422 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 0, static_cast<float>(2.5L)), static_cast<float>(-0.8802526766660982969576719576719576719577L), eps * 100);
423 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 1, static_cast<float>(4.5L)), static_cast<float>(1.564311458042689732142857142857142857143L), eps * 100);
424 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 6, static_cast<float>(8.5L)), static_cast<float>(20.51596541066649098875661375661375661376L), eps * 100);
425 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 12, static_cast<float>(12.5L)), static_cast<float>(-199.5560968456234671241181657848324514991L), eps * 100);
426 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(50, 40, static_cast<float>(12.5L)), static_cast<float>(-4.996769495006119488583146995907246595400e16L), eps * 100);
427
428 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
429 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(0.5L)), static_cast<float>(-0.3307291666666666666666666666666666666667L), eps * 100);
430 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(0.5L)), static_cast<float>(-0.5183392237103174603174603174603174603175L), eps * 100);
431 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(0.5L)), static_cast<float>(0.3120174870800154148915399248893113634676L), eps * 100);
432 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(0.5L)), static_cast<float>(-0.3181388060269979064951118308575628226834L), eps * 100);
433
434 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(-0.5L)), static_cast<float>(1.5L), eps * 100);
435 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(-0.5L)), static_cast<float>(3.835937500000000000000000000000000000000L), eps * 100);
436 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(-0.5L)), static_cast<float>(7.950934709821428571428571428571428571429L), eps * 100);
437 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(-0.5L)), static_cast<float>(76.12915699869631476833699787070874048223L), eps * 100);
438 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(-0.5L)), static_cast<float>(2307.428631277506570629232863491518399720L), eps * 100);
439
440 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(4.5L)), static_cast<float>(-3.500000000000000000000000000000000000000L), eps * 100);
441 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(4.5L)), static_cast<float>(0.08593750000000000000000000000000000000000L), eps * 100);
442 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(4.5L)), static_cast<float>(-1.036928013392857142857142857142857142857L), eps * 100);
443 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(4.5L)), static_cast<float>(1.437239150257817378525582974722170737587L), eps * 100);
444 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(4.5L)), static_cast<float>(-0.7795068145562651416494321484050019245248L), eps * 100);
445
446 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<float>(0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
447 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<float>(0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
448 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<float>(-0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
449 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<float>(-0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
450
451 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
452 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(4, static_cast<float>(0.5L)), static_cast<float>(-0.2890625000000000000000000000000000000000L), eps * 100);
453 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(7, static_cast<float>(0.5L)), static_cast<float>(0.2231445312500000000000000000000000000000L), eps * 100);
454 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(40, static_cast<float>(0.5L)), static_cast<float>(-0.09542943523261546936538467572384923220258L), eps * 100);
455
456 BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(1), static_cast<float>(1)), static_cast<float>(1), eps * 20 * 100);
457 BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(1), static_cast<float>(4)), static_cast<float>(0.25), eps * 20 * 100);
458 BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), static_cast<float>(1)), static_cast<float>(0.25), eps * 20 * 100);
459 BOOST_CHECK_CLOSE(tr1::beta(sv, static_cast<float>(4)), 1/sv, eps * 20 * 100);
460 BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), sv), 1/sv, eps * 20 * 100);
461 BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), static_cast<float>(20)), static_cast<float>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);
462 BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(0.0125L), static_cast<float>(0.000023L)), static_cast<float>(43558.24045647538375006349016083320744662L), eps * 20 * 100);
463
464 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
465 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0.125)), static_cast<float>(1.5769867712158131421244030532288080803822271060839), eps * 5000);
466 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0.25)), static_cast<float>(1.5962422221317835101489690714979498795055744578951), eps * 5000);
467 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(300)/1024), static_cast<float>(1.6062331054696636704261124078746600894998873503208), eps * 5000);
468 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(400)/1024), static_cast<float>(1.6364782007562008756208066125715722889067992997614), eps * 5000);
469 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(-0.5)), static_cast<float>(1.6857503548125960428712036577990769895008008941411), eps * 5000);
470 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(-0.75)), static_cast<float>(1.9109897807518291965531482187613425592531451316788), eps * 5000);
471
472 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-1)), static_cast<float>(1), eps * 5000);
473 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
474 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(100) / 1024), static_cast<float>(1.5670445330545086723323795143598956428788609133377), eps * 5000);
475 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(200) / 1024), static_cast<float>(1.5557071588766556854463404816624361127847775545087), eps * 5000);
476 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(300) / 1024), static_cast<float>(1.5365278991162754883035625322482669608948678755743), eps * 5000);
477 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(400) / 1024), static_cast<float>(1.5090417763083482272165682786143770446401437564021), eps * 5000);
478 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-0.5)), static_cast<float>(1.4674622093394271554597952669909161360253617523272), eps * 5000);
479 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-600) / 1024), static_cast<float>(1.4257538571071297192428217218834579920545946473778), eps * 5000);
480 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-800) / 1024), static_cast<float>(1.2927868476159125056958680222998765985004489572909), eps * 5000);
481 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-900) / 1024), static_cast<float>(1.1966864890248739524112920627353824133420353430982), eps * 5000);
482
483 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.2), static_cast<float>(0)), static_cast<float>(1.586867847454166237308008033828114192951), eps * 5000);
484 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.4), static_cast<float>(0)), static_cast<float>(1.639999865864511206865258329748601457626), eps * 5000);
485 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(1.57079632679489661923132169163975144209858469968755291048747), eps * 5000);
486 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(2.221441469079183123507940495030346849307), eps * 5000);
487 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.3), static_cast<float>(-4)), static_cast<float>(0.712708870925620061597924858162260293305195624270730660081949), eps * 5000);
488 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.5), static_cast<float>(-1e+05)), static_cast<float>(0.00496944596485066055800109163256108604615568144080386919012831), eps * 5000);
489 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.75), static_cast<float>(-1e+10)), static_cast<float>(0.0000157080225184890546939710019277357161497407143903832703317801), eps * 5000);
490 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.875), static_cast<float>(1) / 1024), static_cast<float>(2.18674503176462374414944618968850352696579451638002110619287), eps * 5000);
491 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.875), static_cast<float>(1023)/1024), static_cast<float>(101.045289804941384100960063898569538919135722087486350366997), eps * 5000);
492
493 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(2.25), static_cast<float>(1)/(1024*1024)), static_cast<float>(2.34379212133481347189068464680335815256364262507955635911656e-15), eps * 5000);
494 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(0.0583514045989371500460946536220735787163510569634133670181210), eps * 5000);
495 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-5) + static_cast<float>(1)/1024, static_cast<float>(2.125)), static_cast<float>(0.0267920938009571023702933210070984416052633027166975342895062), eps * 5000);
496 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(597.577606961369169607937419869926705730305175364662688426534), eps * 5000);
497 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474005665181350367684623930576333542989766867888186478185e35), eps * 5000);
498 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(50)), static_cast<float>(1.07153277202900671531087024688681954238311679648319534644743e20), eps * 5000);
499 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694757392660413922181531984160871678224178890247540320), eps * 5000);
500 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694672763190927440969155740243346136463461655104698748), eps * 5000);
501
502 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(2457)/1024, static_cast<float>(1)/1024), static_cast<float>(3.80739920118603335646474073457326714709615200130620574875292e-9), eps * 5000);
503 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(0.0281933076257506091621579544064767140470089107926550720453038), eps * 5000);
504 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(3217)/1024), static_cast<float>(-2.55820064470647911823175836997490971806135336759164272675969), eps * 5000);
505 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(2.449843111985605522111159013846599118397e-03), eps * 5000);
506 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(1e+04)), static_cast<float>(0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
507 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(1e+06)), static_cast<float>(-0.000747424248595630177396350688505919533097973148718960064663632), eps * 5000);
508 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.125), static_cast<float>(1e+06)), static_cast<float>(-0.000776600124835704280633640911329691642748783663198207360238214), eps * 5000);
509 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.875), static_cast<float>(1e+06)), static_cast<float>(-0.000466322721115193071631008581529503095819705088484386434589780), eps * 5000);
510 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(0.5), static_cast<float>(101)), static_cast<float>(0.0358874487875643822020496677692429287863419555699447066226409), eps * 5000);
511 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(0.00244984311198560552211115901384659911839737686676766460822577), eps * 5000);
512 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+06)), static_cast<float>(0.000279243200433579511095229508894156656558211060453622750659554), eps * 5000);
513 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-0.5), static_cast<float>(101)), static_cast<float>(0.0708184798097594268482290389188138201440114881159344944791454), eps * 5000);
514 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474013160494695750009004222225969090304185981836460288562e35), eps * 5000);
515 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(15)), static_cast<float>(-0.0902239288885423309568944543848111461724911781719692852541489), eps * 5000);
516 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547064914615137807616774867984047583596945624129838091326863), eps * 5000);
517 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(10486074) / (1024*1024), static_cast<float>(2e+04)), static_cast<float>(-0.00556783614400875611650958980796060611309029233226596737701688), eps * 5000);
518 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547613660316806551338637153942604550779513947674222863858713), eps * 5000);
519
520 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(0.5), static_cast<float>(0.875)), static_cast<float>(0.558532231646608646115729767013630967055657943463362504577189), eps * 5000);
521 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(0.5), static_cast<float>(1.125)), static_cast<float>(0.383621010650189547146769320487006220295290256657827220786527), eps * 5000);
522 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(2.25), static_cast<float>(std::ldexp(1.0, -30))), static_cast<float>(5.62397392719283271332307799146649700147907612095185712015604e20), eps * 5000);
523 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(1.30623288775012596319554857587765179889689223531159532808379), eps * 5000);
524 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(0.0000733045300798502164644836879577484533096239574909573072142667), eps * 5000);
525 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(-5.5), static_cast<float>(100)), static_cast<float>(5.41274555306792267322084448693957747924412508020839543293369e-45), eps * 5000);
526 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(10240)/1024, static_cast<float>(1)/1024), static_cast<float>(2.35522579263922076203415803966825431039900000000993410734978e38), eps * 5000);
527 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(10240)/1024, static_cast<float>(10)), static_cast<float>(0.00161425530039067002345725193091329085443750382929208307802221), eps * 5000);
528 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(144793)/1024, static_cast<float>(100)), static_cast<float>(1.39565245860302528069481472855619216759142225046370312329416e-6), eps * 5000);
529 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(144793)/1024, static_cast<float>(200)), static_cast<float>(9.11950412043225432171915100042647230802198254567007382956336e-68), eps * 5000);
530
531 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(0.5), static_cast<float>(1) / (1024*1024)), static_cast<float>(-817.033790261762580469303126467917092806755460418223776544122), eps * 5000);
532 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(-2.61489440328417468776474188539366752698192046890955453259866), eps * 5000);
533 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-5.5), static_cast<float>(3.125)), static_cast<float>(-0.0274994493896489729948109971802244976377957234563871795364056), eps * 5000);
534 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(-0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
535 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(-1.50382374389531766117868938966858995093408410498915220070230e38), eps * 5000);
536 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(0.0583041891319026009955779707640455341990844522293730214223545), eps * 5000);
537 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(141.75), static_cast<float>(1e+02)), static_cast<float>(-5.38829231428696507293191118661269920130838607482708483122068e9), eps * 5000);
538 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(141.75), static_cast<float>(2e+04)), static_cast<float>(-0.00376577888677186194728129112270988602876597726657372330194186), eps * 5000);
539 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-141.75), static_cast<float>(1e+02)), static_cast<float>(-3.81009803444766877495905954105669819951653361036342457919021e9), eps * 5000);
540
541 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
542 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
543 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-1.2261911708835170708130609674719067527242483502207), eps * 5000);
544 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.875), static_cast<float>(-4)), static_cast<float>(-5.3190556182262405182189463092940736859067548232647), eps * 5000);
545 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(-0.625), static_cast<float>(8)), static_cast<float>(9.0419973860310100524448893214394562615252527557062), eps * 5000);
546 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.875), static_cast<float>(1e-05)), static_cast<float>(0.000010000000000127604166668510945638036143355898993088), eps * 5000);
547 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(10)/1024, static_cast<float>(1e+05)), static_cast<float>(100002.38431454899771096037307519328741455615271038), eps * 5000);
548 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(1), static_cast<float>(1e-20)), static_cast<float>(1.0000000000000000000000000000000000000000166666667e-20), eps * 5000);
549 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(1e-20), static_cast<float>(1e-20)), static_cast<float>(1.000000000000000e-20), eps * 5000);
550 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(400)/1024, static_cast<float>(1e+20)), static_cast<float>(1.0418143796499216839719289963154558027005142709763e20), eps * 5000);
551 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(2)), static_cast<float>(2.1765877052210673672479877957388515321497888026770), eps * 5000);
552 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(4)), static_cast<float>(4.2543274975235836861894752787874633017836785640477), eps * 5000);
553 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(6)), static_cast<float>(6.4588766202317746302999080620490579800463614807916), eps * 5000);
554 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(10)), static_cast<float>(10.697409951222544858346795279378531495869386960090), eps * 5000);
555 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-2)), static_cast<float>(-2.1765877052210673672479877957388515321497888026770), eps * 5000);
556 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-4)), static_cast<float>(-4.2543274975235836861894752787874633017836785640477), eps * 5000);
557 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-6)), static_cast<float>(-6.4588766202317746302999080620490579800463614807916), eps * 5000);
558 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-10)), static_cast<float>(-10.697409951222544858346795279378531495869386960090), eps * 5000);
559
560 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
561 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
562 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-0.84147098480789650665250232163029899962256306079837), eps * 5000);
563 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(900) / 1024, static_cast<float>(-4)), static_cast<float>(-3.1756145986492562317862928524528520686391383168377), eps * 5000);
564 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(-600) / 1024, static_cast<float>(8)), static_cast<float>(7.2473147180505693037677015377802777959345489333465), eps * 5000);
565 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(800) / 1024, static_cast<float>(1e-05)), static_cast<float>(9.999999999898274739584436515967055859383969942432E-6), eps * 5000);
566 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(100) / 1024, static_cast<float>(1e+05)), static_cast<float>(99761.153306972066658135668386691227343323331995888), eps * 5000);
567 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(-0.5), static_cast<float>(1e+10)), static_cast<float>(9.3421545766487137036576748555295222252286528414669e9), eps * 5000);
568 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(400) / 1024, static_cast<float>(ldexp(static_cast<double>(1), 66))), static_cast<float>(7.0886102721911705466476846969992069994308167515242e19), eps * 5000);
569
570 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(1), static_cast<float>(-1)), static_cast<float>(-1.557407724654902230506974807458360173087), eps * 5000);
571 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.4), static_cast<float>(0), static_cast<float>(-4)), static_cast<float>(-4.153623371196831087495427530365430979011), eps * 5000);
572 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(-0.6), static_cast<float>(0), static_cast<float>(8)), static_cast<float>(8.935930619078575123490612395578518914416), eps * 5000);
573 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.25), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.501246705365439492445236118603525029757890291780157969500480), eps * 5000);
574 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.5), eps * 5000);
575 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(-2), static_cast<float>(0.5)), static_cast<float>(0.437501067017546278595664813509803743009132067629603474488486), eps * 5000);
576 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0.25), static_cast<float>(0.5)), static_cast<float>(0.510269830229213412212501938035914557628394166585442994564135), eps * 5000);
577 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.5)), static_cast<float>(0.533293253875952645421201146925578536430596894471541312806165), eps * 5000);
578 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.75)), static_cast<float>(0.871827580412760575085768367421866079353646112288567703061975), eps * 5000);
579 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(1), static_cast<float>(0.25)), static_cast<float>(0.255341921221036266504482236490473678204201638800822621740476), eps * 5000);
580 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(2), static_cast<float>(0.25)), static_cast<float>(0.261119051639220165094943572468224137699644963125853641716219), eps * 5000);
581 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(1023)/1024, static_cast<float>(1.5)), static_cast<float>(13.2821612239764190363647953338544569682942329604483733197131), eps * 5000);
582 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(-1)), static_cast<float>(-1.228014414316220642611298946293865487807), eps * 5000);
583 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(1e+10)), static_cast<float>(1.536591003599172091573590441336982730551e+10), eps * 5000);
584 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.75), static_cast<float>(-1e+05), static_cast<float>(10)), static_cast<float>(0.0347926099493147087821620459290460547131012904008557007934290), eps * 5000);
585 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(10)), static_cast<float>(0.000109956202759561502329123384755016959364346382187364656768212), eps * 5000);
586 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1e+20)), static_cast<float>(1.00000626665567332602765201107198822183913978895904937646809e15), eps * 5000);
587 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1608)/1024), static_cast<float>(0.0000157080616044072676127333183571107873332593142625043567690379), eps * 5000);
588 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), 1-static_cast<float>(1) / 1024, static_cast<float>(1e+20)), static_cast<float>(6.43274293944380717581167058274600202023334985100499739678963e21), eps * 5000);
589 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.25), static_cast<float>(50), static_cast<float>(0.1)), static_cast<float>(0.124573770342749525407523258569507331686458866564082916835900), eps * 5000);
590 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.25), static_cast<float>(1.125), static_cast<float>(1)), static_cast<float>(1.77299767784815770192352979665283069318388205110727241629752), eps * 5000);
591
592 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(1)/1024), static_cast<float>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000);
593 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(0.125)), static_cast<float>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000);
594 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(0.5)), static_cast<float>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000);
595 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(1)), static_cast<float>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000);
596 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(50.5)), static_cast<float>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000);
597 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-1)/1024), static_cast<float>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000);
598 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-0.125)), static_cast<float>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000);
599 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-0.5)), static_cast<float>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000);
600 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-1)), static_cast<float>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000);
601 BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-50.5)), static_cast<float>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000);
602
603 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(0, static_cast<float>(1)), static_cast<float>(1.L), 100 * eps);
604 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(1)), static_cast<float>(2.L), 100 * eps);
605 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(2)), static_cast<float>(4.L), 100 * eps);
606 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(10)), static_cast<float>(20), 100 * eps);
607 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(100)), static_cast<float>(200), 100 * eps);
608 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(1e6)), static_cast<float>(2e6), 100 * eps);
609 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(30)), static_cast<float>(5.896624628001300E+17L), 100 * eps);
610 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(1000)), static_cast<float>(1.023976960161280E+33L), 100 * eps);
611 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
612 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(-10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
613 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<float>(-10)), static_cast<float>(-7.880000000000000E+3L), 100 * eps);
614 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<float>(-1000)), static_cast<float>(-7.999988000000000E+9L), 100 * eps);
615 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<float>(-1000000)), static_cast<float>(-7.999999999988000E+18L), 100 * eps);
616
617 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(0.125)), static_cast<float>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000);
618 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(1023) / static_cast<float>(1024)), static_cast<float>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000);
619 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(1025) / static_cast<float>(1024)), static_cast<float>(1024.5772867695045940578681624248887776501597556226L), eps * 5000);
620 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(0.5)), static_cast<float>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000);
621 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(1.125)), static_cast<float>(8.5862412945105752999607544082693023591996301183069L), eps * 5000);
622 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(2)), static_cast<float>(1.6449340668482264364724151666460251892189499012068L), eps * 5000);
623 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(3.5)), static_cast<float>(1.1267338673170566464278124918549842722219969574036L), eps * 5000);
624 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(4)), static_cast<float>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000);
625 BOOST_CHECK_CLOSE(tr1::riemann_zeta(4 + static_cast<float>(1) / 1024), static_cast<float>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000);
626 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(4.5)), static_cast<float>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000);
627 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(6.5)), static_cast<float>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000);
628 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(7.5)), static_cast<float>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000);
629 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(8.125)), static_cast<float>(1.0037305205308161603183307711439385250181080293472L), eps * 5000);
630 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(16.125)), static_cast<float>(1.0000140128224754088474783648500235958510030511915L), eps * 5000);
631 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(0)), static_cast<float>(-0.5L), eps * 5000);
632 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-0.125)), static_cast<float>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000);
633 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-1)), static_cast<float>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000);
634 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-2)), static_cast<float>(0L), eps * 5000);
635 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-2.5)), static_cast<float>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000 * 3);
636 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-3)), static_cast<float>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000);
637 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-4)), static_cast<float>(0), eps * 5000);
638 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-20)), static_cast<float>(0), eps * 5000 * 100);
639 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-21)), static_cast<float>(-281.46014492753623188405797101449275362318840579710L), eps * 5000 * 100);
640 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-30.125)), static_cast<float>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000 * 100);
641
642 BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.9999657468461303487880990241993035937654e0), eps * 5000 * 100);
643 BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.9999483203249623334100130061926184665364e0), eps * 5000 * 100);
644 BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.1370120120703995134662099191103188366059e-4), eps * 5000 * 100);
645 BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.2067173265753174063228459655801741280461e-4), eps * 5000 * 100);
646 BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<float>(0.1252804412841796875e3)), static_cast<float>(0.7887555711993028736906736576314283291289e-2), eps * 5000 * 100);
647 BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<float>(0.25554705810546875e3)), static_cast<float>(-0.1463292767579579943284849187188066532514e-2), eps * 5000 * 100);
648
649 BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.2249212131304610409189209411089291558038e1), eps * 5000 * 100);
650 BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1213309779166084571756446746977955970241e1), eps * 5000 * 100);
651 BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.4541702641837159203058389758895634766256e2), eps * 5000 * 100);
652 BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1156112621471167110574129561700037138981e2), eps * 5000 * 100);
653 BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<float>(0.1097540378570556640625e1)), static_cast<float>(-0.2427889658115064857278886600528596240123e9), eps * 5000 * 100);
654 BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<float>(0.30944411754608154296875e1)), static_cast<float>(-0.3394649246350136450439882104151313759251e4), eps * 5000 * 100);
655
656 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(3, 2, static_cast<float>(0.5)), static_cast<float>(0.2061460599687871330692286791802688341213L), eps * 5000);
657 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(40, 15, static_cast<float>(0.75)), static_cast<float>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000);
658 #endif
659 }
660
test_values(double,const char * name)661 void test_values(double, const char* name)
662 {
663 std::cout << "Testing type " << name << std::endl;
664
665 #ifndef TEST_LD
666 double eps = boost::math::tools::epsilon<double>();
667 BOOST_CHECK_CLOSE(tr1::acosh(std::cosh(0.5)), 0.5, 500 * eps);
668 BOOST_CHECK_CLOSE(tr1::asinh(std::sinh(0.5)), 0.5, 500 * eps);
669 BOOST_CHECK_CLOSE(tr1::atanh(std::tanh(0.5)), 0.5, 500 * eps);
670
671 BOOST_CHECK_CLOSE(tr1::cbrt(1.5 * 1.5 * 1.5), 1.5, 500 * eps);
672
673 BOOST_CHECK(tr1::copysign(1.0, 1.0) == 1.0);
674 BOOST_CHECK(tr1::copysign(1.0, -1.0) == -1.0);
675 BOOST_CHECK(tr1::copysign(-1.0, 1.0) == 1.0);
676 BOOST_CHECK(tr1::copysign(-1.0, -1.0) == -1.0);
677
678 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(0.125)), static_cast<double>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
679 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(0.5)), static_cast<double>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
680 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(1)), static_cast<double>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
681 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(5)), static_cast<double>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
682 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(-0.125)), static_cast<double>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
683 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(-0.5)), static_cast<double>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
684 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(0)), static_cast<double>(1), eps * 1000);
685
686 BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(0.125)), static_cast<double>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
687 BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(0.5)), static_cast<double>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
688 BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(1)), static_cast<double>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
689 BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(5)), static_cast<double>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
690 BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(-0.125)), static_cast<double>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
691 BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(-0.5)), static_cast<double>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
692 BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(0)), static_cast<double>(0), eps * 1000);
693
694 BOOST_CHECK_CLOSE(tr1::log1p(static_cast<double>(0.582029759883880615234375e0)), static_cast<double>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
695 BOOST_CHECK_CLOSE(tr1::expm1(static_cast<double>(0.582029759883880615234375e0)), static_cast<double>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
696 BOOST_CHECK_CLOSE(tr1::log1p(static_cast<double>(-0.2047410048544406890869140625e-1)), static_cast<double>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
697 BOOST_CHECK_CLOSE(tr1::expm1(static_cast<double>(-0.2047410048544406890869140625e-1)), static_cast<double>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
698
699 BOOST_CHECK_EQUAL(tr1::fmax(0.1, -0.1), 0.1);
700 BOOST_CHECK_EQUAL(tr1::fmin(0.1, -0.1), -0.1);
701
702 BOOST_CHECK_CLOSE(tr1::hypot(1.0, 3.0), std::sqrt(10.0), eps * 500);
703
704 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(3.5)), static_cast<double>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
705 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(0.125)), static_cast<double>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
706 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(-0.125)), static_cast<double>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
707 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(-3.125)), static_cast<double>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
708 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(-53249.0/1024)), static_cast<double>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
709
710 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(3.5)), static_cast<double>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
711 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(0.125)), static_cast<double>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
712 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(-0.125)), static_cast<double>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
713 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(-3.125)), static_cast<double>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
714
715 #ifdef BOOST_HAS_LONG_LONG
716 BOOST_CHECK(tr1::llround(2.5) == 3LL);
717 BOOST_CHECK(tr1::llround(2.25) == 2LL);
718 #endif
719 BOOST_CHECK(tr1::lround(2.5) == 3L);
720 BOOST_CHECK(tr1::lround(2.25) == 2L);
721 BOOST_CHECK(tr1::round(2.5) == 3.0);
722 BOOST_CHECK(tr1::round(2.25) == 2.0);
723
724 BOOST_CHECK(tr1::nextafter(1.0, 2.0) > 1.0);
725 BOOST_CHECK(tr1::nextafter(1.0, -2.0) < 1.0);
726 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, 2.0), -2.0) == 1.0);
727 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, -2.0), 2.0) == 1.0);
728 BOOST_CHECK(tr1::nextafter(1.0, 2.0) > 1.0);
729 BOOST_CHECK(tr1::nextafter(1.0, -2.0) < 1.0);
730 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, 2.0), -2.0) == 1.0);
731 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, -2.0), 2.0) == 1.0);
732
733 BOOST_CHECK(tr1::trunc(2.5) == 2.0);
734 BOOST_CHECK(tr1::trunc(2.25) == 2.0);
735
736 //
737 // Now the TR1 functions:
738 //
739 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(4, 5, static_cast<double>(0.5L)), static_cast<double>(88.31510416666666666666666666666666666667L), eps * 100);
740 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 0, static_cast<double>(2.5L)), static_cast<double>(-0.8802526766660982969576719576719576719577L), eps * 100);
741 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 1, static_cast<double>(4.5L)), static_cast<double>(1.564311458042689732142857142857142857143L), eps * 100);
742 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 6, static_cast<double>(8.5L)), static_cast<double>(20.51596541066649098875661375661375661376L), eps * 100);
743 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 12, static_cast<double>(12.5L)), static_cast<double>(-199.5560968456234671241181657848324514991L), eps * 100);
744 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(50, 40, static_cast<double>(12.5L)), static_cast<double>(-4.996769495006119488583146995907246595400e16L), eps * 100);
745
746 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<double>(0.5L)), static_cast<double>(0.5L), eps * 100);
747 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<double>(0.5L)), static_cast<double>(-0.3307291666666666666666666666666666666667L), eps * 100);
748 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<double>(0.5L)), static_cast<double>(-0.5183392237103174603174603174603174603175L), eps * 100);
749 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<double>(0.5L)), static_cast<double>(0.3120174870800154148915399248893113634676L), eps * 100);
750 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<double>(0.5L)), static_cast<double>(-0.3181388060269979064951118308575628226834L), eps * 100);
751
752 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<double>(-0.5L)), static_cast<double>(1.5L), eps * 100);
753 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<double>(-0.5L)), static_cast<double>(3.835937500000000000000000000000000000000L), eps * 100);
754 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<double>(-0.5L)), static_cast<double>(7.950934709821428571428571428571428571429L), eps * 100);
755 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<double>(-0.5L)), static_cast<double>(76.12915699869631476833699787070874048223L), eps * 100);
756 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<double>(-0.5L)), static_cast<double>(2307.428631277506570629232863491518399720L), eps * 100);
757
758 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<double>(4.5L)), static_cast<double>(-3.500000000000000000000000000000000000000L), eps * 100);
759 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<double>(4.5L)), static_cast<double>(0.08593750000000000000000000000000000000000L), eps * 100);
760 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<double>(4.5L)), static_cast<double>(-1.036928013392857142857142857142857142857L), eps * 100);
761 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<double>(4.5L)), static_cast<double>(1.437239150257817378525582974722170737587L), eps * 100);
762 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<double>(4.5L)), static_cast<double>(-0.7795068145562651416494321484050019245248L), eps * 100);
763
764 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<double>(0.5L)), static_cast<double>(4.218750000000000000000000000000000000000L), eps * 100);
765 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<double>(0.5L)), static_cast<double>(5696.789530152175143607977274672800795328L), eps * 100);
766 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<double>(-0.5L)), static_cast<double>(4.218750000000000000000000000000000000000L), eps * 100);
767 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<double>(-0.5L)), static_cast<double>(5696.789530152175143607977274672800795328L), eps * 100);
768
769 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(1, static_cast<double>(0.5L)), static_cast<double>(0.5L), eps * 100);
770 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(4, static_cast<double>(0.5L)), static_cast<double>(-0.2890625000000000000000000000000000000000L), eps * 100);
771 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(7, static_cast<double>(0.5L)), static_cast<double>(0.2231445312500000000000000000000000000000L), eps * 100);
772 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(40, static_cast<double>(0.5L)), static_cast<double>(-0.09542943523261546936538467572384923220258L), eps * 100);
773
774 double sv = eps / 1024;
775
776 BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(1), static_cast<double>(1)), static_cast<double>(1), eps * 20 * 100);
777 BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(1), static_cast<double>(4)), static_cast<double>(0.25), eps * 20 * 100);
778 BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(4), static_cast<double>(1)), static_cast<double>(0.25), eps * 20 * 100);
779 BOOST_CHECK_CLOSE(tr1::beta(sv, static_cast<double>(4)), 1/sv, eps * 20 * 100);
780 BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(4), sv), 1/sv, eps * 20 * 100);
781 BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(4), static_cast<double>(20)), static_cast<double>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);
782 BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(0.0125L), static_cast<double>(0.000023L)), static_cast<double>(43558.24045647538375006349016083320744662L), eps * 20 * 100);
783
784 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(0)), static_cast<double>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
785 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(0.125)), static_cast<double>(1.5769867712158131421244030532288080803822271060839), eps * 5000);
786 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(0.25)), static_cast<double>(1.5962422221317835101489690714979498795055744578951), eps * 5000);
787 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(300)/1024), static_cast<double>(1.6062331054696636704261124078746600894998873503208), eps * 5000);
788 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(400)/1024), static_cast<double>(1.6364782007562008756208066125715722889067992997614), eps * 5000);
789 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(-0.5)), static_cast<double>(1.6857503548125960428712036577990769895008008941411), eps * 5000);
790 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(-0.75)), static_cast<double>(1.9109897807518291965531482187613425592531451316788), eps * 5000);
791
792 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-1)), static_cast<double>(1), eps * 5000);
793 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(0)), static_cast<double>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
794 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(100) / 1024), static_cast<double>(1.5670445330545086723323795143598956428788609133377), eps * 5000);
795 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(200) / 1024), static_cast<double>(1.5557071588766556854463404816624361127847775545087), eps * 5000);
796 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(300) / 1024), static_cast<double>(1.5365278991162754883035625322482669608948678755743), eps * 5000);
797 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(400) / 1024), static_cast<double>(1.5090417763083482272165682786143770446401437564021), eps * 5000);
798 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-0.5)), static_cast<double>(1.4674622093394271554597952669909161360253617523272), eps * 5000);
799 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-600) / 1024), static_cast<double>(1.4257538571071297192428217218834579920545946473778), eps * 5000);
800 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-800) / 1024), static_cast<double>(1.2927868476159125056958680222998765985004489572909), eps * 5000);
801 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-900) / 1024), static_cast<double>(1.1966864890248739524112920627353824133420353430982), eps * 5000);
802
803 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0.2), static_cast<double>(0)), static_cast<double>(1.586867847454166237308008033828114192951), eps * 5000);
804 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0.4), static_cast<double>(0)), static_cast<double>(1.639999865864511206865258329748601457626), eps * 5000);
805 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0), static_cast<double>(0)), static_cast<double>(1.57079632679489661923132169163975144209858469968755291048747), eps * 5000);
806 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0), static_cast<double>(0.5)), static_cast<double>(2.221441469079183123507940495030346849307), eps * 5000);
807 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0.3), static_cast<double>(-4)), static_cast<double>(0.712708870925620061597924858162260293305195624270730660081949), eps * 5000);
808 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.5), static_cast<double>(-1e+05)), static_cast<double>(0.00496944596485066055800109163256108604615568144080386919012831), eps * 5000);
809 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.75), static_cast<double>(-1e+10)), static_cast<double>(0.0000157080225184890546939710019277357161497407143903832703317801), eps * 5000);
810 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.875), static_cast<double>(1) / 1024), static_cast<double>(2.18674503176462374414944618968850352696579451638002110619287), eps * 5000);
811 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.875), static_cast<double>(1023)/1024), static_cast<double>(101.045289804941384100960063898569538919135722087486350366997), eps * 5000);
812
813 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(2.25), static_cast<double>(1)/(1024*1024)), static_cast<double>(2.34379212133481347189068464680335815256364262507955635911656e-15), eps * 5000);
814 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(5.5), static_cast<double>(3.125)), static_cast<double>(0.0583514045989371500460946536220735787163510569634133670181210), eps * 5000);
815 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-5) + static_cast<double>(1)/1024, static_cast<double>(2.125)), static_cast<double>(0.0267920938009571023702933210070984416052633027166975342895062), eps * 5000);
816 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-5.5), static_cast<double>(10)), static_cast<double>(597.577606961369169607937419869926705730305175364662688426534), eps * 5000);
817 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-10486074)/(1024*1024), static_cast<double>(1)/1024), static_cast<double>(1.41474005665181350367684623930576333542989766867888186478185e35), eps * 5000);
818 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-10486074)/(1024*1024), static_cast<double>(50)), static_cast<double>(1.07153277202900671531087024688681954238311679648319534644743e20), eps * 5000);
819 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(144794)/1024, static_cast<double>(100)), static_cast<double>(2066.27694757392660413922181531984160871678224178890247540320), eps * 5000);
820 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-144794)/1024, static_cast<double>(100)), static_cast<double>(2066.27694672763190927440969155740243346136463461655104698748), eps * 5000);
821
822 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(2457)/1024, static_cast<double>(1)/1024), static_cast<double>(3.80739920118603335646474073457326714709615200130620574875292e-9), eps * 5000);
823 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.5), static_cast<double>(3217)/1024), static_cast<double>(0.0281933076257506091621579544064767140470089107926550720453038), eps * 5000);
824 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(3217)/1024), static_cast<double>(-2.55820064470647911823175836997490971806135336759164272675969), eps * 5000);
825 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(1e+04)), static_cast<double>(2.449843111985605522111159013846599118397e-03), eps * 5000);
826 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.5), static_cast<double>(1e+04)), static_cast<double>(0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
827 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.5), static_cast<double>(1e+06)), static_cast<double>(-0.000747424248595630177396350688505919533097973148718960064663632), eps * 5000);
828 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.125), static_cast<double>(1e+06)), static_cast<double>(-0.000776600124835704280633640911329691642748783663198207360238214), eps * 5000);
829 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.875), static_cast<double>(1e+06)), static_cast<double>(-0.000466322721115193071631008581529503095819705088484386434589780), eps * 5000);
830 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(0.5), static_cast<double>(101)), static_cast<double>(0.0358874487875643822020496677692429287863419555699447066226409), eps * 5000);
831 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(1e+04)), static_cast<double>(0.00244984311198560552211115901384659911839737686676766460822577), eps * 5000);
832 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(1e+06)), static_cast<double>(0.000279243200433579511095229508894156656558211060453622750659554), eps * 5000);
833 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-0.5), static_cast<double>(101)), static_cast<double>(0.0708184798097594268482290389188138201440114881159344944791454), eps * 5000);
834 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1)/1024), static_cast<double>(1.41474013160494695750009004222225969090304185981836460288562e35), eps * 5000);
835 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(15)), static_cast<double>(-0.0902239288885423309568944543848111461724911781719692852541489), eps * 5000);
836 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(10486074) / (1024*1024), static_cast<double>(1e+02)), static_cast<double>(-0.0547064914615137807616774867984047583596945624129838091326863), eps * 5000);
837 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(10486074) / (1024*1024), static_cast<double>(2e+04)), static_cast<double>(-0.00556783614400875611650958980796060611309029233226596737701688), eps * 5000);
838 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1e+02)), static_cast<double>(-0.0547613660316806551338637153942604550779513947674222863858713), eps * 5000);
839
840 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(0.5), static_cast<double>(0.875)), static_cast<double>(0.558532231646608646115729767013630967055657943463362504577189), eps * 5000);
841 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(0.5), static_cast<double>(1.125)), static_cast<double>(0.383621010650189547146769320487006220295290256657827220786527), eps * 5000);
842 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(2.25), static_cast<double>(std::ldexp(1.0, -30))), static_cast<double>(5.62397392719283271332307799146649700147907612095185712015604e20), eps * 5000);
843 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(5.5), static_cast<double>(3217)/1024), static_cast<double>(1.30623288775012596319554857587765179889689223531159532808379), eps * 5000);
844 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(-5.5), static_cast<double>(10)), static_cast<double>(0.0000733045300798502164644836879577484533096239574909573072142667), eps * 5000);
845 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(-5.5), static_cast<double>(100)), static_cast<double>(5.41274555306792267322084448693957747924412508020839543293369e-45), eps * 5000);
846 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(10240)/1024, static_cast<double>(1)/1024), static_cast<double>(2.35522579263922076203415803966825431039900000000993410734978e38), eps * 5000);
847 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(10240)/1024, static_cast<double>(10)), static_cast<double>(0.00161425530039067002345725193091329085443750382929208307802221), eps * 5000);
848 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(144793)/1024, static_cast<double>(100)), static_cast<double>(1.39565245860302528069481472855619216759142225046370312329416e-6), eps * 5000);
849 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(144793)/1024, static_cast<double>(200)), static_cast<double>(9.11950412043225432171915100042647230802198254567007382956336e-68), eps * 5000);
850
851 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(0.5), static_cast<double>(1) / (1024*1024)), static_cast<double>(-817.033790261762580469303126467917092806755460418223776544122), eps * 5000);
852 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(5.5), static_cast<double>(3.125)), static_cast<double>(-2.61489440328417468776474188539366752698192046890955453259866), eps * 5000);
853 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-5.5), static_cast<double>(3.125)), static_cast<double>(-0.0274994493896489729948109971802244976377957234563871795364056), eps * 5000);
854 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-5.5), static_cast<double>(1e+04)), static_cast<double>(-0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
855 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1)/1024), static_cast<double>(-1.50382374389531766117868938966858995093408410498915220070230e38), eps * 5000);
856 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1e+02)), static_cast<double>(0.0583041891319026009955779707640455341990844522293730214223545), eps * 5000);
857 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(141.75), static_cast<double>(1e+02)), static_cast<double>(-5.38829231428696507293191118661269920130838607482708483122068e9), eps * 5000);
858 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(141.75), static_cast<double>(2e+04)), static_cast<double>(-0.00376577888677186194728129112270988602876597726657372330194186), eps * 5000);
859 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-141.75), static_cast<double>(1e+02)), static_cast<double>(-3.81009803444766877495905954105669819951653361036342457919021e9), eps * 5000);
860
861 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0), static_cast<double>(0)), static_cast<double>(0), eps * 5000);
862 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0), static_cast<double>(-10)), static_cast<double>(-10), eps * 5000);
863 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(-1), static_cast<double>(-1)), static_cast<double>(-1.2261911708835170708130609674719067527242483502207), eps * 5000);
864 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.875), static_cast<double>(-4)), static_cast<double>(-5.3190556182262405182189463092940736859067548232647), eps * 5000);
865 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(-0.625), static_cast<double>(8)), static_cast<double>(9.0419973860310100524448893214394562615252527557062), eps * 5000);
866 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.875), static_cast<double>(1e-05)), static_cast<double>(0.000010000000000127604166668510945638036143355898993088), eps * 5000);
867 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(10)/1024, static_cast<double>(1e+05)), static_cast<double>(100002.38431454899771096037307519328741455615271038), eps * 5000);
868 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(1), static_cast<double>(1e-20)), static_cast<double>(1.0000000000000000000000000000000000000000166666667e-20), eps * 5000);
869 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(1e-20), static_cast<double>(1e-20)), static_cast<double>(1.000000000000000e-20), eps * 5000);
870 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(400)/1024, static_cast<double>(1e+20)), static_cast<double>(1.0418143796499216839719289963154558027005142709763e20), eps * 5000);
871 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(2)), static_cast<double>(2.1765877052210673672479877957388515321497888026770), eps * 5000);
872 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(4)), static_cast<double>(4.2543274975235836861894752787874633017836785640477), eps * 5000);
873 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(6)), static_cast<double>(6.4588766202317746302999080620490579800463614807916), eps * 5000);
874 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(10)), static_cast<double>(10.697409951222544858346795279378531495869386960090), eps * 5000);
875 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-2)), static_cast<double>(-2.1765877052210673672479877957388515321497888026770), eps * 5000);
876 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-4)), static_cast<double>(-4.2543274975235836861894752787874633017836785640477), eps * 5000);
877 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-6)), static_cast<double>(-6.4588766202317746302999080620490579800463614807916), eps * 5000);
878 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-10)), static_cast<double>(-10.697409951222544858346795279378531495869386960090), eps * 5000);
879
880 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(0), static_cast<double>(0)), static_cast<double>(0), eps * 5000);
881 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(0), static_cast<double>(-10)), static_cast<double>(-10), eps * 5000);
882 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(-1), static_cast<double>(-1)), static_cast<double>(-0.84147098480789650665250232163029899962256306079837), eps * 5000);
883 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(900) / 1024, static_cast<double>(-4)), static_cast<double>(-3.1756145986492562317862928524528520686391383168377), eps * 5000);
884 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(-600) / 1024, static_cast<double>(8)), static_cast<double>(7.2473147180505693037677015377802777959345489333465), eps * 5000);
885 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(800) / 1024, static_cast<double>(1e-05)), static_cast<double>(9.999999999898274739584436515967055859383969942432E-6), eps * 5000);
886 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(100) / 1024, static_cast<double>(1e+05)), static_cast<double>(99761.153306972066658135668386691227343323331995888), eps * 5000);
887 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(-0.5), static_cast<double>(1e+10)), static_cast<double>(9.3421545766487137036576748555295222252286528414669e9), eps * 5000);
888 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(400) / 1024, ldexp(static_cast<double>(1), 66)), static_cast<double>(7.0886102721911705466476846969992069994308167515242e19), eps * 5000);
889
890 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(1), static_cast<double>(-1)), static_cast<double>(-1.557407724654902230506974807458360173087), eps * 5000);
891 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.4), static_cast<double>(0), static_cast<double>(-4)), static_cast<double>(-4.153623371196831087495427530365430979011), eps * 5000);
892 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(-0.6), static_cast<double>(0), static_cast<double>(8)), static_cast<double>(8.935930619078575123490612395578518914416), eps * 5000);
893 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.25), static_cast<double>(0), static_cast<double>(0.5)), static_cast<double>(0.501246705365439492445236118603525029757890291780157969500480), eps * 5000);
894 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0), static_cast<double>(0.5)), static_cast<double>(0.5), eps * 5000);
895 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(-2), static_cast<double>(0.5)), static_cast<double>(0.437501067017546278595664813509803743009132067629603474488486), eps * 5000);
896 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0.25), static_cast<double>(0.5)), static_cast<double>(0.510269830229213412212501938035914557628394166585442994564135), eps * 5000);
897 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0.75), static_cast<double>(0.5)), static_cast<double>(0.533293253875952645421201146925578536430596894471541312806165), eps * 5000);
898 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0.75), static_cast<double>(0.75)), static_cast<double>(0.871827580412760575085768367421866079353646112288567703061975), eps * 5000);
899 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(1), static_cast<double>(0.25)), static_cast<double>(0.255341921221036266504482236490473678204201638800822621740476), eps * 5000);
900 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(2), static_cast<double>(0.25)), static_cast<double>(0.261119051639220165094943572468224137699644963125853641716219), eps * 5000);
901 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(1023)/1024, static_cast<double>(1.5)), static_cast<double>(13.2821612239764190363647953338544569682942329604483733197131), eps * 5000);
902 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.5), static_cast<double>(0.5), static_cast<double>(-1)), static_cast<double>(-1.228014414316220642611298946293865487807), eps * 5000);
903 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.5), static_cast<double>(0.5), static_cast<double>(1e+10)), static_cast<double>(1.536591003599172091573590441336982730551e+10), eps * 5000);
904 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.75), static_cast<double>(-1e+05), static_cast<double>(10)), static_cast<double>(0.0347926099493147087821620459290460547131012904008557007934290), eps * 5000);
905 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), static_cast<double>(-1e+10), static_cast<double>(10)), static_cast<double>(0.000109956202759561502329123384755016959364346382187364656768212), eps * 5000);
906 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), static_cast<double>(-1e+10), static_cast<double>(1e+20)), static_cast<double>(1.00000626665567332602765201107198822183913978895904937646809e15), eps * 5000);
907 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), static_cast<double>(-1e+10), static_cast<double>(1608)/1024), static_cast<double>(0.0000157080616044072676127333183571107873332593142625043567690379), eps * 5000);
908 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), 1-static_cast<double>(1) / 1024, static_cast<double>(1e+20)), static_cast<double>(6.43274293944380717581167058274600202023334985100499739678963e21), eps * 5000);
909 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.25), static_cast<double>(50), static_cast<double>(0.1)), static_cast<double>(0.124573770342749525407523258569507331686458866564082916835900), eps * 5000);
910 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.25), static_cast<double>(1.125), static_cast<double>(1)), static_cast<double>(1.77299767784815770192352979665283069318388205110727241629752), eps * 5000);
911
912 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(1)/1024), static_cast<double>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000);
913 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(0.125)), static_cast<double>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000);
914 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(0.5)), static_cast<double>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000);
915 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(1)), static_cast<double>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000);
916 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(50.5)), static_cast<double>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000);
917 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-1)/1024), static_cast<double>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000);
918 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-0.125)), static_cast<double>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000);
919 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-0.5)), static_cast<double>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000);
920 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-1)), static_cast<double>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000);
921 BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-50.5)), static_cast<double>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000);
922
923 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(0, static_cast<double>(1)), static_cast<double>(1.L), 100 * eps);
924 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(1)), static_cast<double>(2.L), 100 * eps);
925 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(2)), static_cast<double>(4.L), 100 * eps);
926 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(10)), static_cast<double>(20), 100 * eps);
927 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(100)), static_cast<double>(200), 100 * eps);
928 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(1e6)), static_cast<double>(2e6), 100 * eps);
929 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(30)), static_cast<double>(5.896624628001300E+17L), 100 * eps);
930 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(1000)), static_cast<double>(1.023976960161280E+33L), 100 * eps);
931 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(10)), static_cast<double>(8.093278209760000E+12L), 100 * eps);
932 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(-10)), static_cast<double>(8.093278209760000E+12L), 100 * eps);
933 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<double>(-10)), static_cast<double>(-7.880000000000000E+3L), 100 * eps);
934 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<double>(-1000)), static_cast<double>(-7.999988000000000E+9L), 100 * eps);
935 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<double>(-1000000)), static_cast<double>(-7.999999999988000E+18L), 100 * eps);
936
937 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(0.125)), static_cast<double>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000);
938 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(1023) / static_cast<double>(1024)), static_cast<double>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000);
939 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(1025) / static_cast<double>(1024)), static_cast<double>(1024.5772867695045940578681624248887776501597556226L), eps * 5000);
940 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(0.5)), static_cast<double>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000);
941 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(1.125)), static_cast<double>(8.5862412945105752999607544082693023591996301183069L), eps * 5000);
942 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(2)), static_cast<double>(1.6449340668482264364724151666460251892189499012068L), eps * 5000);
943 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(3.5)), static_cast<double>(1.1267338673170566464278124918549842722219969574036L), eps * 5000);
944 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(4)), static_cast<double>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000);
945 BOOST_CHECK_CLOSE(tr1::riemann_zeta(4 + static_cast<double>(1) / 1024), static_cast<double>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000);
946 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(4.5)), static_cast<double>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000);
947 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(6.5)), static_cast<double>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000);
948 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(7.5)), static_cast<double>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000);
949 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(8.125)), static_cast<double>(1.0037305205308161603183307711439385250181080293472L), eps * 5000);
950 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(16.125)), static_cast<double>(1.0000140128224754088474783648500235958510030511915L), eps * 5000);
951 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(0)), static_cast<double>(-0.5L), eps * 5000);
952 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-0.125)), static_cast<double>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000);
953 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-1)), static_cast<double>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000);
954 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-2)), static_cast<double>(0L), eps * 5000);
955 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-2.5)), static_cast<double>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000 * 3);
956 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-3)), static_cast<double>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000);
957 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-4)), static_cast<double>(0), eps * 5000);
958 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-20)), static_cast<double>(0), eps * 5000 * 100);
959 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-21)), static_cast<double>(-281.46014492753623188405797101449275362318840579710L), eps * 5000 * 100);
960 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-30.125)), static_cast<double>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000 * 100);
961
962 BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<double>(0.1433600485324859619140625e-1)), static_cast<double>(0.9999657468461303487880990241993035937654e0), eps * 5000 * 100);
963 BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<double>(0.1760916970670223236083984375e-1)), static_cast<double>(0.9999483203249623334100130061926184665364e0), eps * 5000 * 100);
964 BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<double>(0.1433600485324859619140625e-1)), static_cast<double>(0.1370120120703995134662099191103188366059e-4), eps * 5000 * 100);
965 BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<double>(0.1760916970670223236083984375e-1)), static_cast<double>(0.2067173265753174063228459655801741280461e-4), eps * 5000 * 100);
966 BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<double>(0.1252804412841796875e3)), static_cast<double>(0.7887555711993028736906736576314283291289e-2), eps * 5000 * 100);
967 BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<double>(0.25554705810546875e3)), static_cast<double>(-0.1463292767579579943284849187188066532514e-2), eps * 5000 * 100);
968
969 BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<double>(0.408089816570281982421875e0)), static_cast<double>(-0.2249212131304610409189209411089291558038e1), eps * 5000 * 100);
970 BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<double>(0.6540834903717041015625e0)), static_cast<double>(-0.1213309779166084571756446746977955970241e1), eps * 5000 * 100);
971 BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<double>(0.408089816570281982421875e0)), static_cast<double>(-0.4541702641837159203058389758895634766256e2), eps * 5000 * 100);
972 BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<double>(0.6540834903717041015625e0)), static_cast<double>(-0.1156112621471167110574129561700037138981e2), eps * 5000 * 100);
973 BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<double>(0.1097540378570556640625e1)), static_cast<double>(-0.2427889658115064857278886600528596240123e9), eps * 5000 * 100);
974 BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<double>(0.30944411754608154296875e1)), static_cast<double>(-0.3394649246350136450439882104151313759251e4), eps * 5000 * 100);
975
976 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(3, 2, static_cast<double>(0.5)), static_cast<double>(0.2061460599687871330692286791802688341213L), eps * 5000);
977 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(40, 15, static_cast<double>(0.75)), static_cast<double>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000);
978 #endif
979 }
980
test_values(long double,const char * name)981 void test_values(long double, const char* name)
982 {
983 #ifdef TEST_LD
984 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
985 std::cout << "Testing type " << name << std::endl;
986
987 long double eps = boost::math::tools::epsilon<long double>();
988 BOOST_CHECK_CLOSE(tr1::acoshl(std::cosh(0.5L)), 0.5L, 5000 * eps);
989 BOOST_CHECK_CLOSE(tr1::asinhl(std::sinh(0.5L)), 0.5L, 5000 * eps);
990 BOOST_CHECK_CLOSE(tr1::atanhl(std::tanh(0.5L)), 0.5L, 5000 * eps);
991
992 BOOST_CHECK_CLOSE(tr1::cbrtl(1.5L * 1.5L * 1.5L), 1.5L, 5000 * eps);
993
994 BOOST_CHECK(tr1::copysignl(1.0L, 1.0L) == 1.0L);
995 BOOST_CHECK(tr1::copysignl(1.0L, -1.0L) == -1.0L);
996 BOOST_CHECK(tr1::copysignl(-1.0L, 1.0L) == 1.0L);
997 BOOST_CHECK(tr1::copysignl(-1.0L, -1.0L) == -1.0L);
998
999 BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(0.125)), static_cast<long double>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
1000 BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(0.5)), static_cast<long double>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
1001 BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(1)), static_cast<long double>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
1002 BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(5)), static_cast<long double>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
1003 BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(-0.125)), static_cast<long double>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
1004 BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(-0.5)), static_cast<long double>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
1005 BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(0)), static_cast<long double>(1), eps * 1000);
1006
1007 BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(0.125)), static_cast<long double>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1008 BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(0.5)), static_cast<long double>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1009 BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(1)), static_cast<long double>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
1010 BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(5)), static_cast<long double>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
1011 BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(-0.125)), static_cast<long double>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1012 BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(-0.5)), static_cast<long double>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1013 BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(0)), static_cast<long double>(0), eps * 1000);
1014
1015 BOOST_CHECK_CLOSE(tr1::log1pl(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
1016 BOOST_CHECK_CLOSE(tr1::expm1l(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
1017 BOOST_CHECK_CLOSE(tr1::log1pl(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
1018 BOOST_CHECK_CLOSE(tr1::expm1l(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
1019
1020 BOOST_CHECK_EQUAL(tr1::fmaxl(0.1L, -0.1L), 0.1L);
1021 BOOST_CHECK_EQUAL(tr1::fminl(0.1L, -0.1L), -0.1L);
1022
1023 BOOST_CHECK_CLOSE(tr1::hypotl(1.0L, 3.0L), std::sqrt(10.0L), eps * 500);
1024
1025 BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(3.5)), static_cast<long double>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
1026 BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(0.125)), static_cast<long double>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
1027 BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(-0.125)), static_cast<long double>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
1028 BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(-3.125)), static_cast<long double>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
1029 BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(-53249.0/1024)), static_cast<long double>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
1030
1031 BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(3.5)), static_cast<long double>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
1032 BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(0.125)), static_cast<long double>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
1033 BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(-0.125)), static_cast<long double>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
1034 BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(-3.125)), static_cast<long double>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
1035
1036 #ifdef BOOST_HAS_LONG_LONG
1037 BOOST_CHECK(tr1::llroundl(2.5L) == 3LL);
1038 BOOST_CHECK(tr1::llroundl(2.25L) == 2LL);
1039 #endif
1040 BOOST_CHECK(tr1::lroundl(2.5L) == 3L);
1041 BOOST_CHECK(tr1::lroundl(2.25L) == 2L);
1042 BOOST_CHECK(tr1::roundl(2.5L) == 3.0L);
1043 BOOST_CHECK(tr1::roundl(2.25L) == 2.0L);
1044
1045 BOOST_CHECK(tr1::nextafterl(1.0L, 2.0L) > 1.0L);
1046 BOOST_CHECK(tr1::nextafterl(1.0L, -2.0L) < 1.0L);
1047 BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, 2.0L), -2.0L) == 1.0L);
1048 BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, -2.0L), 2.0L) == 1.0L);
1049 BOOST_CHECK(tr1::nextafterl(1.0L, 2.0L) > 1.0L);
1050 BOOST_CHECK(tr1::nextafterl(1.0L, -2.0L) < 1.0L);
1051 BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, 2.0L), -2.0L) == 1.0L);
1052 BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, -2.0L), 2.0L) == 1.0L);
1053
1054 BOOST_CHECK(tr1::truncl(2.5L) == 2.0L);
1055 BOOST_CHECK(tr1::truncl(2.25L) == 2.0L);
1056
1057 //
1058 // And again but without the "l" suffix on the function names:
1059 //
1060 BOOST_CHECK_CLOSE(tr1::acosh(std::cosh(0.5L)), 0.5L, 5000 * eps);
1061 BOOST_CHECK_CLOSE(tr1::asinh(std::sinh(0.5L)), 0.5L, 5000 * eps);
1062 BOOST_CHECK_CLOSE(tr1::atanh(std::tanh(0.5L)), 0.5L, 5000 * eps);
1063
1064 BOOST_CHECK_CLOSE(tr1::cbrt(1.5L * 1.5L * 1.5L), 1.5L, 5000 * eps);
1065
1066 BOOST_CHECK(tr1::copysign(1.0L, 1.0L) == 1.0L);
1067 BOOST_CHECK(tr1::copysign(1.0L, -1.0L) == -1.0L);
1068 BOOST_CHECK(tr1::copysign(-1.0L, 1.0L) == 1.0L);
1069 BOOST_CHECK(tr1::copysign(-1.0L, -1.0L) == -1.0L);
1070
1071 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(0.125)), static_cast<long double>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
1072 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(0.5)), static_cast<long double>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
1073 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(1)), static_cast<long double>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
1074 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(5)), static_cast<long double>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
1075 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(-0.125)), static_cast<long double>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
1076 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(-0.5)), static_cast<long double>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
1077 BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(0)), static_cast<long double>(1), eps * 1000);
1078
1079 BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(0.125)), static_cast<long double>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1080 BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(0.5)), static_cast<long double>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1081 BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(1)), static_cast<long double>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
1082 BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(5)), static_cast<long double>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
1083 BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(-0.125)), static_cast<long double>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1084 BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(-0.5)), static_cast<long double>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1085 BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(0)), static_cast<long double>(0), eps * 1000);
1086
1087 BOOST_CHECK_CLOSE(tr1::log1p(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
1088 BOOST_CHECK_CLOSE(tr1::expm1(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
1089 BOOST_CHECK_CLOSE(tr1::log1p(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
1090 BOOST_CHECK_CLOSE(tr1::expm1(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
1091
1092 BOOST_CHECK_EQUAL(tr1::fmax(0.1L, -0.1L), 0.1L);
1093 BOOST_CHECK_EQUAL(tr1::fmin(0.1L, -0.1L), -0.1L);
1094
1095 BOOST_CHECK_CLOSE(tr1::hypot(1.0L, 3.0L), std::sqrt(10.0L), eps * 500);
1096
1097 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(3.5)), static_cast<long double>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
1098 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(0.125)), static_cast<long double>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
1099 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(-0.125)), static_cast<long double>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
1100 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(-3.125)), static_cast<long double>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
1101 BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(-53249.0/1024)), static_cast<long double>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
1102
1103 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(3.5)), static_cast<long double>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
1104 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(0.125)), static_cast<long double>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
1105 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(-0.125)), static_cast<long double>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
1106 BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(-3.125)), static_cast<long double>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
1107
1108 #ifdef BOOST_HAS_LONG_LONG
1109 BOOST_CHECK(tr1::llround(2.5L) == 3LL);
1110 BOOST_CHECK(tr1::llround(2.25L) == 2LL);
1111 #endif
1112 BOOST_CHECK(tr1::lround(2.5L) == 3L);
1113 BOOST_CHECK(tr1::lround(2.25L) == 2L);
1114 BOOST_CHECK(tr1::round(2.5L) == 3.0L);
1115 BOOST_CHECK(tr1::round(2.25L) == 2.0L);
1116
1117 BOOST_CHECK(tr1::nextafter(1.0L, 2.0L) > 1.0L);
1118 BOOST_CHECK(tr1::nextafter(1.0L, -2.0L) < 1.0L);
1119 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, 2.0L), -2.0L) == 1.0L);
1120 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, -2.0L), 2.0L) == 1.0L);
1121 BOOST_CHECK(tr1::nextafter(1.0L, 2.0L) > 1.0L);
1122 BOOST_CHECK(tr1::nextafter(1.0L, -2.0L) < 1.0L);
1123 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, 2.0L), -2.0L) == 1.0L);
1124 BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, -2.0L), 2.0L) == 1.0L);
1125
1126 BOOST_CHECK(tr1::trunc(2.5L) == 2.0L);
1127 BOOST_CHECK(tr1::trunc(2.25L) == 2.0L);
1128
1129 //
1130 // Now for the TR1 math functions:
1131 //
1132 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(4L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(88.31510416666666666666666666666666666667L), eps * 100L);
1133 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 0L, static_cast<long double>(2.5L)), static_cast<long double>(-0.8802526766660982969576719576719576719577L), eps * 100L);
1134 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 1L, static_cast<long double>(4.5L)), static_cast<long double>(1.564311458042689732142857142857142857143L), eps * 100L);
1135 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 6L, static_cast<long double>(8.5L)), static_cast<long double>(20.51596541066649098875661375661375661376L), eps * 100L);
1136 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 12L, static_cast<long double>(12.5L)), static_cast<long double>(-199.5560968456234671241181657848324514991L), eps * 100L);
1137 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(50L, 40L, static_cast<long double>(12.5L)), static_cast<long double>(-4.996769495006119488583146995907246595400e16L), eps * 100L);
1138
1139 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1140 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3307291666666666666666666666666666666667L), eps * 100L);
1141 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(7L, static_cast<long double>(0.5L)), static_cast<long double>(-0.5183392237103174603174603174603174603175L), eps * 100L);
1142 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(20L, static_cast<long double>(0.5L)), static_cast<long double>(0.3120174870800154148915399248893113634676L), eps * 100L);
1143 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(50L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3181388060269979064951118308575628226834L), eps * 100L);
1144
1145 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(1L, static_cast<long double>(-0.5L)), static_cast<long double>(1.5L), eps * 100L);
1146 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(4L, static_cast<long double>(-0.5L)), static_cast<long double>(3.835937500000000000000000000000000000000L), eps * 100L);
1147 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(7L, static_cast<long double>(-0.5L)), static_cast<long double>(7.950934709821428571428571428571428571429L), eps * 100L);
1148 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(20L, static_cast<long double>(-0.5L)), static_cast<long double>(76.12915699869631476833699787070874048223L), eps * 100L);
1149 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(50L, static_cast<long double>(-0.5L)), static_cast<long double>(2307.428631277506570629232863491518399720L), eps * 100L);
1150
1151 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(1L, static_cast<long double>(4.5L)), static_cast<long double>(-3.500000000000000000000000000000000000000L), eps * 100L);
1152 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(4L, static_cast<long double>(4.5L)), static_cast<long double>(0.08593750000000000000000000000000000000000L), eps * 100L);
1153 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(7L, static_cast<long double>(4.5L)), static_cast<long double>(-1.036928013392857142857142857142857142857L), eps * 100L);
1154 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(20L, static_cast<long double>(4.5L)), static_cast<long double>(1.437239150257817378525582974722170737587L), eps * 100L);
1155 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(50L, static_cast<long double>(4.5L)), static_cast<long double>(-0.7795068145562651416494321484050019245248L), eps * 100L);
1156
1157 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(4L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1158 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(7L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1159 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(4L, 2L, static_cast<long double>(-0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1160 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(7L, 5L, static_cast<long double>(-0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1161
1162 BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1163 BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.2890625000000000000000000000000000000000L), eps * 100L);
1164 BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(7L, static_cast<long double>(0.5L)), static_cast<long double>(0.2231445312500000000000000000000000000000L), eps * 100L);
1165 BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(40L, static_cast<long double>(0.5L)), static_cast<long double>(-0.09542943523261546936538467572384923220258L), eps * 100L);
1166
1167 long double sv = eps / 1024;
1168 BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(1L), static_cast<long double>(1L)), static_cast<long double>(1L), eps * 20L * 100L);
1169 BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(1L), static_cast<long double>(4L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1170 BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(4L), static_cast<long double>(1L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1171 BOOST_CHECK_CLOSE(tr1::betal(sv, static_cast<long double>(4L)), 1/sv, eps * 20L * 100L);
1172 BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(4L), sv), 1/sv, eps * 20L * 100L);
1173 BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(4L), static_cast<long double>(20L)), static_cast<long double>(0.00002823263692828910220214568040654997176736L), eps * 20L * 100L);
1174 BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(0.0125L), static_cast<long double>(0.000023L)), static_cast<long double>(43558.24045647538375006349016083320744662L), eps * 20L * 100L);
1175
1176 BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1177 BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(0.125L)), static_cast<long double>(1.5769867712158131421244030532288080803822271060839L), eps * 5000L);
1178 BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(0.25L)), static_cast<long double>(1.5962422221317835101489690714979498795055744578951L), eps * 5000L);
1179 BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(300L)/1024L), static_cast<long double>(1.6062331054696636704261124078746600894998873503208L), eps * 5000L);
1180 BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(400L)/1024L), static_cast<long double>(1.6364782007562008756208066125715722889067992997614L), eps * 5000L);
1181 BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(-0.5L)), static_cast<long double>(1.6857503548125960428712036577990769895008008941411L), eps * 5000L);
1182 BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(-0.75L)), static_cast<long double>(1.9109897807518291965531482187613425592531451316788L), eps * 5000L);
1183
1184 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-1L)), static_cast<long double>(1L), eps * 5000L);
1185 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1186 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(100L) / 1024L), static_cast<long double>(1.5670445330545086723323795143598956428788609133377L), eps * 5000L);
1187 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(200L) / 1024L), static_cast<long double>(1.5557071588766556854463404816624361127847775545087L), eps * 5000L);
1188 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(300L) / 1024L), static_cast<long double>(1.5365278991162754883035625322482669608948678755743L), eps * 5000L);
1189 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(400L) / 1024L), static_cast<long double>(1.5090417763083482272165682786143770446401437564021L), eps * 5000L);
1190 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-0.5L)), static_cast<long double>(1.4674622093394271554597952669909161360253617523272L), eps * 5000L);
1191 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-600L) / 1024L), static_cast<long double>(1.4257538571071297192428217218834579920545946473778L), eps * 5000L);
1192 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-800L) / 1024L), static_cast<long double>(1.2927868476159125056958680222998765985004489572909L), eps * 5000L);
1193 BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-900L) / 1024L), static_cast<long double>(1.1966864890248739524112920627353824133420353430982L), eps * 5000L);
1194
1195 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0.2L), static_cast<long double>(0L)), static_cast<long double>(1.586867847454166237308008033828114192951L), eps * 5000L);
1196 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0.4L), static_cast<long double>(0L)), static_cast<long double>(1.639999865864511206865258329748601457626L), eps * 5000L);
1197 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(1.57079632679489661923132169163975144209858469968755291048747L), eps * 5000L);
1198 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(2.221441469079183123507940495030346849307L), eps * 5000L);
1199 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0.3L), static_cast<long double>(-4L)), static_cast<long double>(0.712708870925620061597924858162260293305195624270730660081949L), eps * 5000L);
1200 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.5L), static_cast<long double>(-1e+05L)), static_cast<long double>(0.00496944596485066055800109163256108604615568144080386919012831L), eps * 5000L);
1201 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.75L), static_cast<long double>(-1e+10L)), static_cast<long double>(0.0000157080225184890546939710019277357161497407143903832703317801L), eps * 5000L);
1202 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.875L), static_cast<long double>(1L) / 1024L), static_cast<long double>(2.18674503176462374414944618968850352696579451638002110619287L), eps * 5000L);
1203 BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.875L), static_cast<long double>(1023L)/1024L), static_cast<long double>(101.045289804941384100960063898569538919135722087486350366997L), eps * 5000L);
1204
1205 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(2.25L), static_cast<long double>(1L)/(1024*1024L)), static_cast<long double>(2.34379212133481347189068464680335815256364262507955635911656e-15L), eps * 5000L);
1206 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(0.0583514045989371500460946536220735787163510569634133670181210L), eps * 5000L);
1207 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-5L) + static_cast<long double>(1L)/1024L, static_cast<long double>(2.125L)), static_cast<long double>(0.0267920938009571023702933210070984416052633027166975342895062L), eps * 5000L);
1208 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(597.577606961369169607937419869926705730305175364662688426534L), eps * 5000L);
1209 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474005665181350367684623930576333542989766867888186478185e35L), eps * 5000L);
1210 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(50L)), static_cast<long double>(1.07153277202900671531087024688681954238311679648319534644743e20L), eps * 5000L);
1211 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694757392660413922181531984160871678224178890247540320L), eps * 5000L);
1212 BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694672763190927440969155740243346136463461655104698748L), eps * 5000L);
1213
1214 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(2457L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(3.80739920118603335646474073457326714709615200130620574875292e-9L), eps * 50000L);
1215 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(0.0281933076257506091621579544064767140470089107926550720453038L), eps * 5000L);
1216 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(-2.55820064470647911823175836997490971806135336759164272675969L), eps * 5000L);
1217 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(2.449843111985605522111159013846599118397e-03L), eps * 50000L);
1218 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1219 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000747424248595630177396350688505919533097973148718960064663632L), eps * 50000L);
1220 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.125L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000776600124835704280633640911329691642748783663198207360238214L), eps * 50000L);
1221 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.875L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000466322721115193071631008581529503095819705088484386434589780L), eps * 50000L);
1222 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0358874487875643822020496677692429287863419555699447066226409L), eps * 5000L);
1223 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00244984311198560552211115901384659911839737686676766460822577L), eps * 50000L);
1224 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(0.000279243200433579511095229508894156656558211060453622750659554L), eps * 50000L);
1225 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0708184798097594268482290389188138201440114881159344944791454L), eps * 5000L);
1226 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474013160494695750009004222225969090304185981836460288562e35L), eps * 5000L);
1227 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(15L)), static_cast<long double>(-0.0902239288885423309568944543848111461724911781719692852541489L), eps * 5000L);
1228 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547064914615137807616774867984047583596945624129838091326863L), eps * 5000L);
1229 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00556783614400875611650958980796060611309029233226596737701688L), eps * 5000L);
1230 BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547613660316806551338637153942604550779513947674222863858713L), eps * 5000L);
1231
1232 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(0.5L), static_cast<long double>(0.875L)), static_cast<long double>(0.558532231646608646115729767013630967055657943463362504577189L), eps * 5000L);
1233 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(0.5L), static_cast<long double>(1.125L)), static_cast<long double>(0.383621010650189547146769320487006220295290256657827220786527L), eps * 5000L);
1234 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(2.25L), static_cast<long double>(std::ldexp(1.0L, -30L))), static_cast<long double>(5.62397392719283271332307799146649700147907612095185712015604e20L), eps * 5000L);
1235 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(1.30623288775012596319554857587765179889689223531159532808379L), eps * 5000L);
1236 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(0.0000733045300798502164644836879577484533096239574909573072142667L), eps * 5000L);
1237 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(-5.5L), static_cast<long double>(100L)), static_cast<long double>(5.41274555306792267322084448693957747924412508020839543293369e-45L), eps * 5000L);
1238 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(10240L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(2.35522579263922076203415803966825431039900000000993410734978e38L), eps * 5000L);
1239 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(10240L)/1024L, static_cast<long double>(10L)), static_cast<long double>(0.00161425530039067002345725193091329085443750382929208307802221L), eps * 5000L);
1240 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(144793L)/1024L, static_cast<long double>(100L)), static_cast<long double>(1.39565245860302528069481472855619216759142225046370312329416e-6L), eps * 5000L);
1241 BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(144793L)/1024L, static_cast<long double>(200L)), static_cast<long double>(9.11950412043225432171915100042647230802198254567007382956336e-68L), eps * 7000L);
1242
1243 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(0.5L), static_cast<long double>(1L) / (1024*1024L)), static_cast<long double>(-817.033790261762580469303126467917092806755460418223776544122L), eps * 5000L);
1244 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-2.61489440328417468776474188539366752698192046890955453259866L), eps * 5000L);
1245 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-0.0274994493896489729948109971802244976377957234563871795364056L), eps * 5000L);
1246 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(-0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1247 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(-1.50382374389531766117868938966858995093408410498915220070230e38L), eps * 5000L);
1248 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(0.0583041891319026009955779707640455341990844522293730214223545L), eps * 5000L);
1249 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-5.38829231428696507293191118661269920130838607482708483122068e9L), eps * 5000L);
1250 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(141.75L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00376577888677186194728129112270988602876597726657372330194186L), eps * 50000L);
1251 BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-3.81009803444766877495905954105669819951653361036342457919021e9L), eps * 5000L);
1252
1253 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1254 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1255 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-1.2261911708835170708130609674719067527242483502207L), eps * 5000L);
1256 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.875L), static_cast<long double>(-4L)), static_cast<long double>(-5.3190556182262405182189463092940736859067548232647L), eps * 5000L);
1257 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(-0.625L), static_cast<long double>(8L)), static_cast<long double>(9.0419973860310100524448893214394562615252527557062L), eps * 5000L);
1258 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.875L), static_cast<long double>(1e-05L)), static_cast<long double>(0.000010000000000127604166668510945638036143355898993088L), eps * 5000L);
1259 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(10L)/1024L, static_cast<long double>(1e+05L)), static_cast<long double>(100002.38431454899771096037307519328741455615271038L), eps * 5000L);
1260 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(1L), static_cast<long double>(1e-20L)), static_cast<long double>(1.0000000000000000000000000000000000000000166666667e-20L), eps * 5000L);
1261 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(1e-20L), static_cast<long double>(1e-20L)), static_cast<long double>(1.000000000000000e-20L), eps * 5000L);
1262 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(400L)/1024L, static_cast<long double>(1e+20L)), static_cast<long double>(1.0418143796499216839719289963154558027005142709763e20L), eps * 5000L);
1263 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(2L)), static_cast<long double>(2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1264 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(4L)), static_cast<long double>(4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1265 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(6L)), static_cast<long double>(6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1266 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(10L)), static_cast<long double>(10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1267 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-2L)), static_cast<long double>(-2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1268 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-4L)), static_cast<long double>(-4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1269 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-6L)), static_cast<long double>(-6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1270 BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-10L)), static_cast<long double>(-10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1271
1272 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1273 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1274 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-0.84147098480789650665250232163029899962256306079837L), eps * 5000L);
1275 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(900L) / 1024L, static_cast<long double>(-4L)), static_cast<long double>(-3.1756145986492562317862928524528520686391383168377L), eps * 5000L);
1276 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(-600L) / 1024L, static_cast<long double>(8L)), static_cast<long double>(7.2473147180505693037677015377802777959345489333465L), eps * 5000L);
1277 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(800L) / 1024L, static_cast<long double>(1e-05L)), static_cast<long double>(9.999999999898274739584436515967055859383969942432E-6L), eps * 5000L);
1278 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(100L) / 1024L, static_cast<long double>(1e+05L)), static_cast<long double>(99761.153306972066658135668386691227343323331995888L), eps * 5000L);
1279 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(-0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(9.3421545766487137036576748555295222252286528414669e9L), eps * 5000L);
1280 BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(400L) / 1024L, ldexp(static_cast<long double>(1L), 66L)), static_cast<long double>(7.0886102721911705466476846969992069994308167515242e19L), eps * 5000L);
1281
1282 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(-1L)), static_cast<long double>(-1.557407724654902230506974807458360173087L), eps * 5000L);
1283 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.4L), static_cast<long double>(0L), static_cast<long double>(-4L)), static_cast<long double>(-4.153623371196831087495427530365430979011L), eps * 5000L);
1284 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(-0.6L), static_cast<long double>(0L), static_cast<long double>(8L)), static_cast<long double>(8.935930619078575123490612395578518914416L), eps * 5000L);
1285 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.25L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.501246705365439492445236118603525029757890291780157969500480L), eps * 5000L);
1286 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 5000L);
1287 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(-2L), static_cast<long double>(0.5L)), static_cast<long double>(0.437501067017546278595664813509803743009132067629603474488486L), eps * 5000L);
1288 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.25L), static_cast<long double>(0.5L)), static_cast<long double>(0.510269830229213412212501938035914557628394166585442994564135L), eps * 5000L);
1289 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.5L)), static_cast<long double>(0.533293253875952645421201146925578536430596894471541312806165L), eps * 5000L);
1290 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.75L)), static_cast<long double>(0.871827580412760575085768367421866079353646112288567703061975L), eps * 5000L);
1291 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(0.25L)), static_cast<long double>(0.255341921221036266504482236490473678204201638800822621740476L), eps * 5000L);
1292 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(2L), static_cast<long double>(0.25L)), static_cast<long double>(0.261119051639220165094943572468224137699644963125853641716219L), eps * 5000L);
1293 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(1023L)/1024L, static_cast<long double>(1.5L)), static_cast<long double>(13.2821612239764190363647953338544569682942329604483733197131L), eps * 5000L);
1294 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(-1L)), static_cast<long double>(-1.228014414316220642611298946293865487807L), eps * 5000L);
1295 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(1.536591003599172091573590441336982730551e+10L), eps * 5000L);
1296 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.75L), static_cast<long double>(-1e+05L), static_cast<long double>(10L)), static_cast<long double>(0.0347926099493147087821620459290460547131012904008557007934290L), eps * 5000L);
1297 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(10L)), static_cast<long double>(0.000109956202759561502329123384755016959364346382187364656768212L), eps * 5000L);
1298 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1e+20L)), static_cast<long double>(1.00000626665567332602765201107198822183913978895904937646809e15L), eps * 5000L);
1299 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1608L)/1024L), static_cast<long double>(0.0000157080616044072676127333183571107873332593142625043567690379L), eps * 5000L);
1300 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), 1-static_cast<long double>(1L) / 1024L, static_cast<long double>(1e+20L)), static_cast<long double>(6.43274293944380717581167058274600202023334985100499739678963e21L), eps * 5000L);
1301 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.25L), static_cast<long double>(50L), static_cast<long double>(0.1L)), static_cast<long double>(0.124573770342749525407523258569507331686458866564082916835900L), eps * 5000L);
1302 BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.25L), static_cast<long double>(1.125L), static_cast<long double>(1L)), static_cast<long double>(1.77299767784815770192352979665283069318388205110727241629752L), eps * 5000L);
1303
1304 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(1L)/1024L), static_cast<long double>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000L);
1305 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(0.125L)), static_cast<long double>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000L);
1306 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(0.5L)), static_cast<long double>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000L);
1307 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(1L)), static_cast<long double>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000L);
1308 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(50.5L)), static_cast<long double>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000L);
1309 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-1L)/1024L), static_cast<long double>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000L);
1310 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-0.125L)), static_cast<long double>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000L);
1311 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-0.5L)), static_cast<long double>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000L);
1312 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-1L)), static_cast<long double>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000L);
1313 BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-50.5L)), static_cast<long double>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000L);
1314
1315 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(0L, static_cast<long double>(1L)), static_cast<long double>(1.L), 100L * eps);
1316 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(1L)), static_cast<long double>(2.L), 100L * eps);
1317 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(2L)), static_cast<long double>(4.L), 100L * eps);
1318 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(10L)), static_cast<long double>(20L), 100L * eps);
1319 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(100L)), static_cast<long double>(200L), 100L * eps);
1320 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(1e6L)), static_cast<long double>(2e6L), 100L * eps);
1321 //BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(30L)), static_cast<long double>(5.896624628001300E+17L), 1000L * eps);
1322 //BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(1000L)), static_cast<long double>(1.023976960161280E+33L), 1000L * eps);
1323 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1324 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(-10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1325 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(3L, static_cast<long double>(-10L)), static_cast<long double>(-7.880000000000000E+3L), 100L * eps);
1326 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(3L, static_cast<long double>(-1000L)), static_cast<long double>(-7.999988000000000E+9L), 100L * eps);
1327 BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(3L, static_cast<long double>(-1000000L)), static_cast<long double>(-7.999999999988000E+18L), 100L * eps);
1328
1329 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(0.125L)), static_cast<long double>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000L);
1330 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(1023L) / static_cast<long double>(1024L)), static_cast<long double>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000L);
1331 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(1025L) / static_cast<long double>(1024L)), static_cast<long double>(1024.5772867695045940578681624248887776501597556226L), eps * 5000L);
1332 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(0.5L)), static_cast<long double>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000L);
1333 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(1.125L)), static_cast<long double>(8.5862412945105752999607544082693023591996301183069L), eps * 5000L);
1334 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(2L)), static_cast<long double>(1.6449340668482264364724151666460251892189499012068L), eps * 5000L);
1335 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(3.5L)), static_cast<long double>(1.1267338673170566464278124918549842722219969574036L), eps * 5000L);
1336 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(4L)), static_cast<long double>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000L);
1337 BOOST_CHECK_CLOSE(tr1::riemann_zetal(4L + static_cast<long double>(1L) / 1024L), static_cast<long double>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000L);
1338 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(4.5L)), static_cast<long double>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000L);
1339 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(6.5L)), static_cast<long double>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000L);
1340 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(7.5L)), static_cast<long double>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000L);
1341 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(8.125L)), static_cast<long double>(1.0037305205308161603183307711439385250181080293472L), eps * 5000L);
1342 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(16.125L)), static_cast<long double>(1.0000140128224754088474783648500235958510030511915L), eps * 5000L);
1343 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(0L)), static_cast<long double>(-0.5L), eps * 5000L);
1344 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-0.125L)), static_cast<long double>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000L);
1345 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-1L)), static_cast<long double>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000L);
1346 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-2L)), static_cast<long double>(0L), eps * 5000L);
1347 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-2.5L)), static_cast<long double>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000L * 3L);
1348 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-3L)), static_cast<long double>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000L);
1349 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-4L)), static_cast<long double>(0L), eps * 5000L);
1350 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-20L)), static_cast<long double>(0L), eps * 5000L * 100L);
1351 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-21L)), static_cast<long double>(-281.46014492753623188405797101449275362318840579710L), eps * 5000L * 100L);
1352 BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-30.125L)), static_cast<long double>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000L * 100L);
1353
1354 BOOST_CHECK_CLOSE(tr1::sph_bessell(0L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.9999657468461303487880990241993035937654e0L), eps * 5000L * 100L);
1355 BOOST_CHECK_CLOSE(tr1::sph_bessell(0L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.9999483203249623334100130061926184665364e0L), eps * 5000L * 100L);
1356 BOOST_CHECK_CLOSE(tr1::sph_bessell(2L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.1370120120703995134662099191103188366059e-4L), eps * 5000L * 100L);
1357 BOOST_CHECK_CLOSE(tr1::sph_bessell(2L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.2067173265753174063228459655801741280461e-4L), eps * 5000L * 100L);
1358 BOOST_CHECK_CLOSE(tr1::sph_bessell(7L, static_cast<long double>(0.1252804412841796875e3L)), static_cast<long double>(0.7887555711993028736906736576314283291289e-2L), eps * 50000L * 100L);
1359 BOOST_CHECK_CLOSE(tr1::sph_bessell(7L, static_cast<long double>(0.25554705810546875e3L)), static_cast<long double>(-0.1463292767579579943284849187188066532514e-2L), eps * 5000L * 100L);
1360
1361 BOOST_CHECK_CLOSE(tr1::sph_neumannl(0L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.2249212131304610409189209411089291558038e1L), eps * 5000L * 100L);
1362 BOOST_CHECK_CLOSE(tr1::sph_neumannl(0L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1213309779166084571756446746977955970241e1L), eps * 5000L * 100L);
1363 BOOST_CHECK_CLOSE(tr1::sph_neumannl(2L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.4541702641837159203058389758895634766256e2L), eps * 5000L * 100L);
1364 BOOST_CHECK_CLOSE(tr1::sph_neumannl(2L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1156112621471167110574129561700037138981e2L), eps * 5000L * 100L);
1365 BOOST_CHECK_CLOSE(tr1::sph_neumannl(10L, static_cast<long double>(0.1097540378570556640625e1L)), static_cast<long double>(-0.2427889658115064857278886600528596240123e9L), eps * 5000L * 100L);
1366 BOOST_CHECK_CLOSE(tr1::sph_neumannl(10L, static_cast<long double>(0.30944411754608154296875e1L)), static_cast<long double>(-0.3394649246350136450439882104151313759251e4L), eps * 5000L * 100L);
1367
1368 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendrel(3L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(0.2061460599687871330692286791802688341213L), eps * 5000L);
1369 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendrel(40L, 15L, static_cast<long double>(0.75L)), static_cast<long double>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000L);
1370
1371 //
1372 // Now all over again but without the "f" suffix on the function names this time:
1373 //
1374 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(4L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(88.31510416666666666666666666666666666667L), eps * 100L);
1375 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 0L, static_cast<long double>(2.5L)), static_cast<long double>(-0.8802526766660982969576719576719576719577L), eps * 100L);
1376 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 1L, static_cast<long double>(4.5L)), static_cast<long double>(1.564311458042689732142857142857142857143L), eps * 100L);
1377 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 6L, static_cast<long double>(8.5L)), static_cast<long double>(20.51596541066649098875661375661375661376L), eps * 100L);
1378 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 12L, static_cast<long double>(12.5L)), static_cast<long double>(-199.5560968456234671241181657848324514991L), eps * 100L);
1379 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(50L, 40L, static_cast<long double>(12.5L)), static_cast<long double>(-4.996769495006119488583146995907246595400e16L), eps * 100L);
1380
1381 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1382 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3307291666666666666666666666666666666667L), eps * 100L);
1383 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7L, static_cast<long double>(0.5L)), static_cast<long double>(-0.5183392237103174603174603174603174603175L), eps * 100L);
1384 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20L, static_cast<long double>(0.5L)), static_cast<long double>(0.3120174870800154148915399248893113634676L), eps * 100L);
1385 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3181388060269979064951118308575628226834L), eps * 100L);
1386
1387 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1L, static_cast<long double>(-0.5L)), static_cast<long double>(1.5L), eps * 100L);
1388 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4L, static_cast<long double>(-0.5L)), static_cast<long double>(3.835937500000000000000000000000000000000L), eps * 100L);
1389 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7L, static_cast<long double>(-0.5L)), static_cast<long double>(7.950934709821428571428571428571428571429L), eps * 100L);
1390 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20L, static_cast<long double>(-0.5L)), static_cast<long double>(76.12915699869631476833699787070874048223L), eps * 100L);
1391 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50L, static_cast<long double>(-0.5L)), static_cast<long double>(2307.428631277506570629232863491518399720L), eps * 100L);
1392
1393 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1L, static_cast<long double>(4.5L)), static_cast<long double>(-3.500000000000000000000000000000000000000L), eps * 100L);
1394 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4L, static_cast<long double>(4.5L)), static_cast<long double>(0.08593750000000000000000000000000000000000L), eps * 100L);
1395 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7L, static_cast<long double>(4.5L)), static_cast<long double>(-1.036928013392857142857142857142857142857L), eps * 100L);
1396 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20L, static_cast<long double>(4.5L)), static_cast<long double>(1.437239150257817378525582974722170737587L), eps * 100L);
1397 BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50L, static_cast<long double>(4.5L)), static_cast<long double>(-0.7795068145562651416494321484050019245248L), eps * 100L);
1398
1399 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1400 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1401 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4L, 2L, static_cast<long double>(-0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1402 BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7L, 5L, static_cast<long double>(-0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1403
1404 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1405 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.2890625000000000000000000000000000000000L), eps * 100L);
1406 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(7L, static_cast<long double>(0.5L)), static_cast<long double>(0.2231445312500000000000000000000000000000L), eps * 100L);
1407 BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(40L, static_cast<long double>(0.5L)), static_cast<long double>(-0.09542943523261546936538467572384923220258L), eps * 100L);
1408
1409 BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(1L), static_cast<long double>(1L)), static_cast<long double>(1L), eps * 20L * 100L);
1410 BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(1L), static_cast<long double>(4L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1411 BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(4L), static_cast<long double>(1L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1412 BOOST_CHECK_CLOSE(tr1::beta(sv, static_cast<long double>(4L)), 1/sv, eps * 20L * 100L);
1413 BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(4L), sv), 1/sv, eps * 20L * 100L);
1414 BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(4L), static_cast<long double>(20L)), static_cast<long double>(0.00002823263692828910220214568040654997176736L), eps * 20L * 100L);
1415 BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(0.0125L), static_cast<long double>(0.000023L)), static_cast<long double>(43558.24045647538375006349016083320744662L), eps * 20L * 100L);
1416
1417 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1418 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(0.125L)), static_cast<long double>(1.5769867712158131421244030532288080803822271060839L), eps * 5000L);
1419 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(0.25L)), static_cast<long double>(1.5962422221317835101489690714979498795055744578951L), eps * 5000L);
1420 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(300L)/1024L), static_cast<long double>(1.6062331054696636704261124078746600894998873503208L), eps * 5000L);
1421 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(400L)/1024L), static_cast<long double>(1.6364782007562008756208066125715722889067992997614L), eps * 5000L);
1422 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(-0.5L)), static_cast<long double>(1.6857503548125960428712036577990769895008008941411L), eps * 5000L);
1423 BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(-0.75L)), static_cast<long double>(1.9109897807518291965531482187613425592531451316788L), eps * 5000L);
1424
1425 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-1L)), static_cast<long double>(1L), eps * 5000L);
1426 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1427 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(100L) / 1024L), static_cast<long double>(1.5670445330545086723323795143598956428788609133377L), eps * 5000L);
1428 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(200L) / 1024L), static_cast<long double>(1.5557071588766556854463404816624361127847775545087L), eps * 5000L);
1429 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(300L) / 1024L), static_cast<long double>(1.5365278991162754883035625322482669608948678755743L), eps * 5000L);
1430 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(400L) / 1024L), static_cast<long double>(1.5090417763083482272165682786143770446401437564021L), eps * 5000L);
1431 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-0.5L)), static_cast<long double>(1.4674622093394271554597952669909161360253617523272L), eps * 5000L);
1432 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-600L) / 1024L), static_cast<long double>(1.4257538571071297192428217218834579920545946473778L), eps * 5000L);
1433 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-800L) / 1024L), static_cast<long double>(1.2927868476159125056958680222998765985004489572909L), eps * 5000L);
1434 BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-900L) / 1024L), static_cast<long double>(1.1966864890248739524112920627353824133420353430982L), eps * 5000L);
1435
1436 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0.2L), static_cast<long double>(0L)), static_cast<long double>(1.586867847454166237308008033828114192951L), eps * 5000L);
1437 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0.4L), static_cast<long double>(0L)), static_cast<long double>(1.639999865864511206865258329748601457626L), eps * 5000L);
1438 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(1.57079632679489661923132169163975144209858469968755291048747L), eps * 5000L);
1439 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(2.221441469079183123507940495030346849307L), eps * 5000L);
1440 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0.3L), static_cast<long double>(-4L)), static_cast<long double>(0.712708870925620061597924858162260293305195624270730660081949L), eps * 5000L);
1441 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.5L), static_cast<long double>(-1e+05L)), static_cast<long double>(0.00496944596485066055800109163256108604615568144080386919012831L), eps * 5000L);
1442 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.75L), static_cast<long double>(-1e+10L)), static_cast<long double>(0.0000157080225184890546939710019277357161497407143903832703317801L), eps * 5000L);
1443 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.875L), static_cast<long double>(1L) / 1024L), static_cast<long double>(2.18674503176462374414944618968850352696579451638002110619287L), eps * 5000L);
1444 BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.875L), static_cast<long double>(1023L)/1024L), static_cast<long double>(101.045289804941384100960063898569538919135722087486350366997L), eps * 5000L);
1445
1446 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(2.25L), static_cast<long double>(1L)/(1024*1024L)), static_cast<long double>(2.34379212133481347189068464680335815256364262507955635911656e-15L), eps * 5000L);
1447 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(0.0583514045989371500460946536220735787163510569634133670181210L), eps * 5000L);
1448 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-5L) + static_cast<long double>(1L)/1024L, static_cast<long double>(2.125L)), static_cast<long double>(0.0267920938009571023702933210070984416052633027166975342895062L), eps * 5000L);
1449 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(597.577606961369169607937419869926705730305175364662688426534L), eps * 5000L);
1450 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474005665181350367684623930576333542989766867888186478185e35L), eps * 5000L);
1451 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(50L)), static_cast<long double>(1.07153277202900671531087024688681954238311679648319534644743e20L), eps * 5000L);
1452 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694757392660413922181531984160871678224178890247540320L), eps * 5000L);
1453 BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694672763190927440969155740243346136463461655104698748L), eps * 5000L);
1454
1455 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(2457L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(3.80739920118603335646474073457326714709615200130620574875292e-9L), eps * 5000L);
1456 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(0.0281933076257506091621579544064767140470089107926550720453038L), eps * 5000L);
1457 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(-2.55820064470647911823175836997490971806135336759164272675969L), eps * 5000L);
1458 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(2.449843111985605522111159013846599118397e-03L), eps * 50000L);
1459 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1460 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000747424248595630177396350688505919533097973148718960064663632L), eps * 50000L);
1461 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.125L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000776600124835704280633640911329691642748783663198207360238214L), eps * 50000L);
1462 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.875L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000466322721115193071631008581529503095819705088484386434589780L), eps * 50000L);
1463 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0358874487875643822020496677692429287863419555699447066226409L), eps * 5000L);
1464 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00244984311198560552211115901384659911839737686676766460822577L), eps * 50000L);
1465 //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(0.000279243200433579511095229508894156656558211060453622750659554L), eps * 50000L);
1466 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0708184798097594268482290389188138201440114881159344944791454L), eps * 5000L);
1467 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474013160494695750009004222225969090304185981836460288562e35L), eps * 5000L);
1468 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(15L)), static_cast<long double>(-0.0902239288885423309568944543848111461724911781719692852541489L), eps * 5000L);
1469 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547064914615137807616774867984047583596945624129838091326863L), eps * 5000L);
1470 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00556783614400875611650958980796060611309029233226596737701688L), eps * 5000L);
1471 BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547613660316806551338637153942604550779513947674222863858713L), eps * 5000L);
1472
1473 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(0.5L), static_cast<long double>(0.875L)), static_cast<long double>(0.558532231646608646115729767013630967055657943463362504577189L), eps * 5000L);
1474 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(0.5L), static_cast<long double>(1.125L)), static_cast<long double>(0.383621010650189547146769320487006220295290256657827220786527L), eps * 5000L);
1475 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(2.25L), static_cast<long double>(std::ldexp(1.0L, -30L))), static_cast<long double>(5.62397392719283271332307799146649700147907612095185712015604e20L), eps * 5000L);
1476 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(1.30623288775012596319554857587765179889689223531159532808379L), eps * 5000L);
1477 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(0.0000733045300798502164644836879577484533096239574909573072142667L), eps * 5000L);
1478 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(-5.5L), static_cast<long double>(100L)), static_cast<long double>(5.41274555306792267322084448693957747924412508020839543293369e-45L), eps * 5000L);
1479 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(10240L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(2.35522579263922076203415803966825431039900000000993410734978e38L), eps * 5000L);
1480 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(10240L)/1024L, static_cast<long double>(10L)), static_cast<long double>(0.00161425530039067002345725193091329085443750382929208307802221L), eps * 5000L);
1481 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(144793L)/1024L, static_cast<long double>(100L)), static_cast<long double>(1.39565245860302528069481472855619216759142225046370312329416e-6L), eps * 5000L);
1482 BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(144793L)/1024L, static_cast<long double>(200L)), static_cast<long double>(9.11950412043225432171915100042647230802198254567007382956336e-68L), eps * 7000L);
1483
1484 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(0.5L), static_cast<long double>(1L) / (1024*1024L)), static_cast<long double>(-817.033790261762580469303126467917092806755460418223776544122L), eps * 5000L);
1485 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-2.61489440328417468776474188539366752698192046890955453259866L), eps * 5000L);
1486 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-0.0274994493896489729948109971802244976377957234563871795364056L), eps * 5000L);
1487 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(-0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1488 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(-1.50382374389531766117868938966858995093408410498915220070230e38L), eps * 5000L);
1489 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(0.0583041891319026009955779707640455341990844522293730214223545L), eps * 5000L);
1490 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-5.38829231428696507293191118661269920130838607482708483122068e9L), eps * 5000L);
1491 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(141.75L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00376577888677186194728129112270988602876597726657372330194186L), eps * 50000L);
1492 BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-3.81009803444766877495905954105669819951653361036342457919021e9L), eps * 5000L);
1493
1494 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1495 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1496 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-1.2261911708835170708130609674719067527242483502207L), eps * 5000L);
1497 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.875L), static_cast<long double>(-4L)), static_cast<long double>(-5.3190556182262405182189463092940736859067548232647L), eps * 5000L);
1498 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(-0.625L), static_cast<long double>(8L)), static_cast<long double>(9.0419973860310100524448893214394562615252527557062L), eps * 5000L);
1499 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.875L), static_cast<long double>(1e-05L)), static_cast<long double>(0.000010000000000127604166668510945638036143355898993088L), eps * 5000L);
1500 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(10L)/1024L, static_cast<long double>(1e+05L)), static_cast<long double>(100002.38431454899771096037307519328741455615271038L), eps * 5000L);
1501 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(1L), static_cast<long double>(1e-20L)), static_cast<long double>(1.0000000000000000000000000000000000000000166666667e-20L), eps * 5000L);
1502 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(1e-20L), static_cast<long double>(1e-20L)), static_cast<long double>(1.000000000000000e-20L), eps * 5000L);
1503 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(400L)/1024L, static_cast<long double>(1e+20L)), static_cast<long double>(1.0418143796499216839719289963154558027005142709763e20L), eps * 5000L);
1504 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(2L)), static_cast<long double>(2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1505 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(4L)), static_cast<long double>(4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1506 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(6L)), static_cast<long double>(6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1507 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(10L)), static_cast<long double>(10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1508 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-2L)), static_cast<long double>(-2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1509 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-4L)), static_cast<long double>(-4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1510 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-6L)), static_cast<long double>(-6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1511 BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-10L)), static_cast<long double>(-10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1512
1513 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1514 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1515 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-0.84147098480789650665250232163029899962256306079837L), eps * 5000L);
1516 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(900L) / 1024L, static_cast<long double>(-4L)), static_cast<long double>(-3.1756145986492562317862928524528520686391383168377L), eps * 5000L);
1517 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(-600L) / 1024L, static_cast<long double>(8L)), static_cast<long double>(7.2473147180505693037677015377802777959345489333465L), eps * 5000L);
1518 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(800L) / 1024L, static_cast<long double>(1e-05L)), static_cast<long double>(9.999999999898274739584436515967055859383969942432E-6L), eps * 5000L);
1519 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(100L) / 1024L, static_cast<long double>(1e+05L)), static_cast<long double>(99761.153306972066658135668386691227343323331995888L), eps * 5000L);
1520 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(-0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(9.3421545766487137036576748555295222252286528414669e9L), eps * 5000L);
1521 BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(400L) / 1024L, ldexp(static_cast<long double>(1L), 66L)), static_cast<long double>(7.0886102721911705466476846969992069994308167515242e19L), eps * 5000L);
1522
1523 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(-1L)), static_cast<long double>(-1.557407724654902230506974807458360173087L), eps * 5000L);
1524 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.4L), static_cast<long double>(0L), static_cast<long double>(-4L)), static_cast<long double>(-4.153623371196831087495427530365430979011L), eps * 5000L);
1525 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(-0.6L), static_cast<long double>(0L), static_cast<long double>(8L)), static_cast<long double>(8.935930619078575123490612395578518914416L), eps * 5000L);
1526 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.25L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.501246705365439492445236118603525029757890291780157969500480L), eps * 5000L);
1527 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 5000L);
1528 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(-2L), static_cast<long double>(0.5L)), static_cast<long double>(0.437501067017546278595664813509803743009132067629603474488486L), eps * 5000L);
1529 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0.25L), static_cast<long double>(0.5L)), static_cast<long double>(0.510269830229213412212501938035914557628394166585442994564135L), eps * 5000L);
1530 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.5L)), static_cast<long double>(0.533293253875952645421201146925578536430596894471541312806165L), eps * 5000L);
1531 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.75L)), static_cast<long double>(0.871827580412760575085768367421866079353646112288567703061975L), eps * 5000L);
1532 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(0.25L)), static_cast<long double>(0.255341921221036266504482236490473678204201638800822621740476L), eps * 5000L);
1533 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(2L), static_cast<long double>(0.25L)), static_cast<long double>(0.261119051639220165094943572468224137699644963125853641716219L), eps * 5000L);
1534 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(1023L)/1024L, static_cast<long double>(1.5L)), static_cast<long double>(13.2821612239764190363647953338544569682942329604483733197131L), eps * 5000L);
1535 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(-1L)), static_cast<long double>(-1.228014414316220642611298946293865487807L), eps * 5000L);
1536 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(1.536591003599172091573590441336982730551e+10L), eps * 5000L);
1537 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.75L), static_cast<long double>(-1e+05L), static_cast<long double>(10L)), static_cast<long double>(0.0347926099493147087821620459290460547131012904008557007934290L), eps * 5000L);
1538 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(10L)), static_cast<long double>(0.000109956202759561502329123384755016959364346382187364656768212L), eps * 5000L);
1539 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1e+20L)), static_cast<long double>(1.00000626665567332602765201107198822183913978895904937646809e15L), eps * 5000L);
1540 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1608L)/1024L), static_cast<long double>(0.0000157080616044072676127333183571107873332593142625043567690379L), eps * 5000L);
1541 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), 1-static_cast<long double>(1L) / 1024L, static_cast<long double>(1e+20L)), static_cast<long double>(6.43274293944380717581167058274600202023334985100499739678963e21L), eps * 5000L);
1542 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.25L), static_cast<long double>(50L), static_cast<long double>(0.1L)), static_cast<long double>(0.124573770342749525407523258569507331686458866564082916835900L), eps * 5000L);
1543 BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.25L), static_cast<long double>(1.125L), static_cast<long double>(1L)), static_cast<long double>(1.77299767784815770192352979665283069318388205110727241629752L), eps * 5000L);
1544
1545 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(1L)/1024L), static_cast<long double>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000L);
1546 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(0.125L)), static_cast<long double>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000L);
1547 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(0.5L)), static_cast<long double>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000L);
1548 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(1L)), static_cast<long double>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000L);
1549 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(50.5L)), static_cast<long double>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000L);
1550 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-1L)/1024L), static_cast<long double>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000L);
1551 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-0.125L)), static_cast<long double>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000L);
1552 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-0.5L)), static_cast<long double>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000L);
1553 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-1L)), static_cast<long double>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000L);
1554 BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-50.5L)), static_cast<long double>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000L);
1555
1556 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(0L, static_cast<long double>(1L)), static_cast<long double>(1.L), 100L * eps);
1557 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(1L)), static_cast<long double>(2.L), 100L * eps);
1558 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(2L)), static_cast<long double>(4.L), 100L * eps);
1559 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(10L)), static_cast<long double>(20L), 100L * eps);
1560 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(100L)), static_cast<long double>(200L), 100L * eps);
1561 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(1e6L)), static_cast<long double>(2e6L), 100L * eps);
1562 //BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(30L)), static_cast<long double>(5.896624628001300E+17L), 100L * eps);
1563 //BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(1000L)), static_cast<long double>(1.023976960161280E+33L), 100L * eps);
1564 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1565 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(-10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1566 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3L, static_cast<long double>(-10L)), static_cast<long double>(-7.880000000000000E+3L), 100L * eps);
1567 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3L, static_cast<long double>(-1000L)), static_cast<long double>(-7.999988000000000E+9L), 100L * eps);
1568 BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3L, static_cast<long double>(-1000000L)), static_cast<long double>(-7.999999999988000E+18L), 100L * eps);
1569
1570 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(0.125L)), static_cast<long double>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000L);
1571 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(1023L) / static_cast<long double>(1024L)), static_cast<long double>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000L);
1572 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(1025L) / static_cast<long double>(1024L)), static_cast<long double>(1024.5772867695045940578681624248887776501597556226L), eps * 5000L);
1573 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(0.5L)), static_cast<long double>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000L);
1574 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(1.125L)), static_cast<long double>(8.5862412945105752999607544082693023591996301183069L), eps * 5000L);
1575 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(2L)), static_cast<long double>(1.6449340668482264364724151666460251892189499012068L), eps * 5000L);
1576 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(3.5L)), static_cast<long double>(1.1267338673170566464278124918549842722219969574036L), eps * 5000L);
1577 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(4L)), static_cast<long double>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000L);
1578 BOOST_CHECK_CLOSE(tr1::riemann_zeta(4L + static_cast<long double>(1L) / 1024L), static_cast<long double>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000L);
1579 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(4.5L)), static_cast<long double>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000L);
1580 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(6.5L)), static_cast<long double>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000L);
1581 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(7.5L)), static_cast<long double>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000L);
1582 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(8.125L)), static_cast<long double>(1.0037305205308161603183307711439385250181080293472L), eps * 5000L);
1583 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(16.125L)), static_cast<long double>(1.0000140128224754088474783648500235958510030511915L), eps * 5000L);
1584 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(0L)), static_cast<long double>(-0.5L), eps * 5000L);
1585 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-0.125L)), static_cast<long double>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000L);
1586 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-1L)), static_cast<long double>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000L);
1587 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-2L)), static_cast<long double>(0L), eps * 5000L);
1588 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-2.5L)), static_cast<long double>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000L * 3L);
1589 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-3L)), static_cast<long double>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000L);
1590 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-4L)), static_cast<long double>(0L), eps * 5000L);
1591 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-20L)), static_cast<long double>(0L), eps * 5000L * 100L);
1592 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-21L)), static_cast<long double>(-281.46014492753623188405797101449275362318840579710L), eps * 5000L * 100L);
1593 BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-30.125L)), static_cast<long double>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000L * 100L);
1594
1595 BOOST_CHECK_CLOSE(tr1::sph_bessel(0L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.9999657468461303487880990241993035937654e0L), eps * 5000L * 100L);
1596 BOOST_CHECK_CLOSE(tr1::sph_bessel(0L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.9999483203249623334100130061926184665364e0L), eps * 5000L * 100L);
1597 BOOST_CHECK_CLOSE(tr1::sph_bessel(2L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.1370120120703995134662099191103188366059e-4L), eps * 5000L * 100L);
1598 BOOST_CHECK_CLOSE(tr1::sph_bessel(2L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.2067173265753174063228459655801741280461e-4L), eps * 5000L * 100L);
1599 BOOST_CHECK_CLOSE(tr1::sph_bessel(7L, static_cast<long double>(0.1252804412841796875e3L)), static_cast<long double>(0.7887555711993028736906736576314283291289e-2L), eps * 5000L * 100L);
1600 BOOST_CHECK_CLOSE(tr1::sph_bessel(7L, static_cast<long double>(0.25554705810546875e3L)), static_cast<long double>(-0.1463292767579579943284849187188066532514e-2L), eps * 5000L * 100L);
1601
1602 BOOST_CHECK_CLOSE(tr1::sph_neumann(0L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.2249212131304610409189209411089291558038e1L), eps * 5000L * 100L);
1603 BOOST_CHECK_CLOSE(tr1::sph_neumann(0L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1213309779166084571756446746977955970241e1L), eps * 5000L * 100L);
1604 BOOST_CHECK_CLOSE(tr1::sph_neumann(2L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.4541702641837159203058389758895634766256e2L), eps * 5000L * 100L);
1605 BOOST_CHECK_CLOSE(tr1::sph_neumann(2L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1156112621471167110574129561700037138981e2L), eps * 5000L * 100L);
1606 BOOST_CHECK_CLOSE(tr1::sph_neumann(10L, static_cast<long double>(0.1097540378570556640625e1L)), static_cast<long double>(-0.2427889658115064857278886600528596240123e9L), eps * 5000L * 100L);
1607 BOOST_CHECK_CLOSE(tr1::sph_neumann(10L, static_cast<long double>(0.30944411754608154296875e1L)), static_cast<long double>(-0.3394649246350136450439882104151313759251e4L), eps * 5000L * 100L);
1608
1609 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(3L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(0.2061460599687871330692286791802688341213L), eps * 5000L);
1610 BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(40L, 15L, static_cast<long double>(0.75L)), static_cast<long double>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000L);
1611 #endif
1612 #endif
1613 }
1614
BOOST_AUTO_TEST_CASE(test_main)1615 BOOST_AUTO_TEST_CASE( test_main )
1616 {
1617 #ifndef TEST_LD
1618 test_values(1.0f, "float");
1619 test_values(1.0, "double");
1620 #else
1621 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
1622 test_values(1.0L, "long double");
1623 #endif
1624 #endif
1625
1626 }
1627
1628