1package Math::GSL::SF::Test; 2use strict; 3use warnings; 4use Math::GSL::Test qw/:all/; 5use base q{Test::Class}; 6use Test::Most; 7use Math::GSL qw/:all/; 8use Math::GSL::Const qw/:all/; 9use Math::GSL::Errno qw/:all/; 10use Math::GSL::SF qw/:all/; 11use Math::GSL::Poly qw/:all/; 12use Math::GSL::Machine qw/:all/; 13use Math::GSL::Sys qw/$GSL_NAN/; 14use Data::Dumper; 15 16BEGIN { gsl_set_error_handler_off() } 17 18my $factor = 100; 19my $TOL1 = $factor*16.0*$GSL_DBL_EPSILON; 20my $SQRT_TOL0 = 2.0*$GSL_SQRT_DBL_EPSILON; 21my $DELTA = 1.2246467991473531772e-16; 22my $w = 0.8*$GSL_LOG_DBL_MAX; 23my $y = 0.2*$GSL_DBL_MAX; 24 25sub make_fixture : Test(setup) { 26} 27sub teardown : Test(teardown) { 28} 29 30sub TEST_RT66882 : Tests { 31 # This test was losing a small amount of precision with 32 # perls that have DUSELONGDOUBLE, so give it some leeway 33 # Where is the loss of precision coming from? Is it a bug in Perl, GSL or Math::GSL ? 34 # A beer if you figure it out. 35 # why doesn't $TODO work here? 36 local $TODO = "loss of precision on Perls with DUSELONGDOUBLE"; 37 38 # additional diagnostics 39 local %ENV; $ENV{DEBUG} = 1; 40 my $results = { 41 'gsl_sf_fermi_dirac_m1_e(10.0, $r)' => 0.9999546021312975656, 42 }; 43 # TODO: disabling this test temporarily (june 2020, see issue #204) 44 # https://github.com/leto/math--gsl/issues/204 45 # since the TODO test seems not to be recognized on perl 5.20.1 on FreeBSD 46 # 47 # verify_results($results, 'Math::GSL::SF', 1e-16); 48} 49 50sub TEST_ELLINT : Tests { 51 local $TODO = "these functions are not currently available"; 52 my $version= gsl_version(); 53 my ($major, $minor) = split /\./, $version; 54 my $results; 55 56 return; 57 58 # these funcitons no longer have an n param in GSL >=2 59 if ($major < 2 ) { 60 $results = { 61 'gsl_sf_ellint_D_e($M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.375395076351788975665323192, 62 'gsl_sf_ellint_D_e($M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.8731525818926755496456335628, 63 'gsl_sf_ellint_D_e($M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.7854276176694868932799393751, 64 'gsl_sf_ellint_D_e(2*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.305885125424644860264320635, 65 'gsl_sf_ellint_D_e(2*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.418324704155697579394036402, 66 'gsl_sf_ellint_D_e(2*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.263755353901126149206022061, 67 'gsl_sf_ellint_D_e($M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.750790152703577951330646444, 68 'gsl_sf_ellint_D_e($M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.746305163785351099291267125, 69 'gsl_sf_ellint_D_e($M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.570855235338973786559878750, 70 'gsl_sf_ellint_D_e(4*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.195695179982511042396972113, 71 'gsl_sf_ellint_D_e(4*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.074285623415004619188497818, 72 'gsl_sf_ellint_D_e(4*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.877955116776821423913735408, 73 'gsl_sf_ellint_D_e(3*$M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.126185229055366926995969476, 74 'gsl_sf_ellint_D_e(3*$M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.619457745678026648936900687, 75 'gsl_sf_ellint_D_e(3*$M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.356282853008460679839818125, 76 'gsl_sf_ellint_D_e(5*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 9.056675278128222811594967044, 77 'gsl_sf_ellint_D_e(5*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.164629867941048678685303509, 78 'gsl_sf_ellint_D_e(5*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.834610589240099935765900794, 79 'gsl_sf_ellint_D_e(2*$M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 9.501580305407155902661292832, 80 'gsl_sf_ellint_D_e(2*$M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.492610327570702198582534249, 81 'gsl_sf_ellint_D_e(2*$M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.141710470677947573119757500, 82 'gsl_sf_ellint_D_e(7*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 9.946485332686088993727618315, 83 'gsl_sf_ellint_D_e(7*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.820590787200355718479764901, 84 'gsl_sf_ellint_D_e(7*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.448810352115795210473614120, 85 'gsl_sf_ellint_D_e(-$M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.375395076351788975665323192, 86 'gsl_sf_ellint_D_e(-$M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -0.8731525818926755496456335628, 87 'gsl_sf_ellint_D_e(-$M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -0.7854276176694868932799393751, 88 'gsl_sf_ellint_D_e(-2*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.305885125424644860264320635, 89 'gsl_sf_ellint_D_e(-2*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.418324704155697579394036402, 90 'gsl_sf_ellint_D_e(-2*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.263755353901126149206022061, 91 'gsl_sf_ellint_D_e(-$M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.750790152703577951330646444, 92 'gsl_sf_ellint_D_e(-$M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.746305163785351099291267125, 93 'gsl_sf_ellint_D_e(-$M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.570855235338973786559878750, 94 'gsl_sf_ellint_D_e(-4*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.195695179982511042396972113, 95 'gsl_sf_ellint_D_e(-4*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.074285623415004619188497818, 96 'gsl_sf_ellint_D_e(-4*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.877955116776821423913735408, 97 'gsl_sf_ellint_D_e(-3*$M_PI/2.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.126185229055366926995969476, 98 'gsl_sf_ellint_D_e(-3*$M_PI/2.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.619457745678026648936900687, 99 'gsl_sf_ellint_D_e(-3*$M_PI/2.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.356282853008460679839818125, 100 'gsl_sf_ellint_D_e(-5*$M_PI/3, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -9.056675278128222811594967044, 101 'gsl_sf_ellint_D_e(-5*$M_PI/3, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.164629867941048678685303509, 102 'gsl_sf_ellint_D_e(-5*$M_PI/3, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.834610589240099935765900794, 103 'gsl_sf_ellint_D_e(-2*$M_PI, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -9.501580305407155902661292832, 104 'gsl_sf_ellint_D_e(-2*$M_PI, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.492610327570702198582534249, 105 'gsl_sf_ellint_D_e(-2*$M_PI, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.141710470677947573119757500, 106 'gsl_sf_ellint_D_e(-7*$M_PI/3.0, 0.99, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -9.946485332686088993727618315, 107 'gsl_sf_ellint_D_e(-7*$M_PI/3.0, 0.50, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.820590787200355718479764901, 108 'gsl_sf_ellint_D_e(-7*$M_PI/3.0, 0.01, 0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.448810352115795210473614120, 109 }; 110 } else { 111 $results = { 112 'gsl_sf_ellint_D_e($M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.375395076351788975665323192, 113 'gsl_sf_ellint_D_e($M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.8731525818926755496456335628, 114 'gsl_sf_ellint_D_e($M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.7854276176694868932799393751, 115 'gsl_sf_ellint_D_e(2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.305885125424644860264320635, 116 'gsl_sf_ellint_D_e(2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.418324704155697579394036402, 117 'gsl_sf_ellint_D_e(2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.263755353901126149206022061, 118 'gsl_sf_ellint_D_e($M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.750790152703577951330646444, 119 'gsl_sf_ellint_D_e($M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.746305163785351099291267125, 120 'gsl_sf_ellint_D_e($M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.570855235338973786559878750, 121 'gsl_sf_ellint_D_e(4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.195695179982511042396972113, 122 'gsl_sf_ellint_D_e(4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.074285623415004619188497818, 123 'gsl_sf_ellint_D_e(4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.877955116776821423913735408, 124 'gsl_sf_ellint_D_e(3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.126185229055366926995969476, 125 'gsl_sf_ellint_D_e(3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.619457745678026648936900687, 126 'gsl_sf_ellint_D_e(3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.356282853008460679839818125, 127 'gsl_sf_ellint_D_e(5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 9.056675278128222811594967044, 128 'gsl_sf_ellint_D_e(5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.164629867941048678685303509, 129 'gsl_sf_ellint_D_e(5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.834610589240099935765900794, 130 'gsl_sf_ellint_D_e(2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 9.501580305407155902661292832, 131 'gsl_sf_ellint_D_e(2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.492610327570702198582534249, 132 'gsl_sf_ellint_D_e(2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.141710470677947573119757500, 133 'gsl_sf_ellint_D_e(7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 9.946485332686088993727618315, 134 'gsl_sf_ellint_D_e(7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.820590787200355718479764901, 135 'gsl_sf_ellint_D_e(7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.448810352115795210473614120, 136 'gsl_sf_ellint_D_e(-$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.375395076351788975665323192, 137 'gsl_sf_ellint_D_e(-$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -0.8731525818926755496456335628, 138 'gsl_sf_ellint_D_e(-$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -0.7854276176694868932799393751, 139 'gsl_sf_ellint_D_e(-2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.305885125424644860264320635, 140 'gsl_sf_ellint_D_e(-2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.418324704155697579394036402, 141 'gsl_sf_ellint_D_e(-2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.263755353901126149206022061, 142 'gsl_sf_ellint_D_e(-$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.750790152703577951330646444, 143 'gsl_sf_ellint_D_e(-$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.746305163785351099291267125, 144 'gsl_sf_ellint_D_e(-$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.570855235338973786559878750, 145 'gsl_sf_ellint_D_e(-4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.195695179982511042396972113, 146 'gsl_sf_ellint_D_e(-4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.074285623415004619188497818, 147 'gsl_sf_ellint_D_e(-4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.877955116776821423913735408, 148 'gsl_sf_ellint_D_e(-3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.126185229055366926995969476, 149 'gsl_sf_ellint_D_e(-3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.619457745678026648936900687, 150 'gsl_sf_ellint_D_e(-3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.356282853008460679839818125, 151 'gsl_sf_ellint_D_e(-5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -9.056675278128222811594967044, 152 'gsl_sf_ellint_D_e(-5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.164629867941048678685303509, 153 'gsl_sf_ellint_D_e(-5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.834610589240099935765900794, 154 'gsl_sf_ellint_D_e(-2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -9.501580305407155902661292832, 155 'gsl_sf_ellint_D_e(-2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.492610327570702198582534249, 156 'gsl_sf_ellint_D_e(-2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.141710470677947573119757500, 157 'gsl_sf_ellint_D_e(-7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -9.946485332686088993727618315, 158 'gsl_sf_ellint_D_e(-7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.820590787200355718479764901, 159 'gsl_sf_ellint_D_e(-7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.448810352115795210473614120, 160 }; 161 } 162 verify_results($results, "Math::GSL::SF"); 163} 164 165sub TEST_THE_KITCHEN_SINK : Tests { 166 my $results = { 167 'gsl_sf_airy_Ai_e(-5, $Math::GSL::GSL_MODE_DEFAULT, $r)' => 0.3507610090241142, 168 'gsl_sf_airy_Ai_e(-500,$Math::GSL::GSL_MODE_DEFAULT, $r)' => 0.0725901201040411396, 169 'gsl_sf_bessel_J0_e(0.1,$r)' => 0.99750156206604003230, 170 'gsl_sf_bessel_J0_e(2.0,$r)' => 0.22389077914123566805, 171 'gsl_sf_bessel_J0_e(5,$r)' => -0.17759677131433830434739701, 172 'gsl_sf_bessel_J0_e(100,$r)' => 0.019985850304223122424, 173 'gsl_sf_bessel_J0_e(1e10,$r)' => 2.1755917502468917269e-06, 174 'gsl_sf_erf_e(5,$r)' => 0.999999999998463, 175 'gsl_sf_dilog_e(-3.0,$r)' => -1.9393754207667089531, 176 'gsl_sf_dilog_e(-0.5,$r)' => -0.4484142069236462024, 177 'gsl_sf_gamma_e(6.3,$r)' => 201.813275184748, 178 'gsl_sf_dilog_e(-0.001,$r)' => -0.0009997501110486510834, 179 'gsl_sf_dilog_e(0.1,$r)' => 0.1026177910993911, 180 'gsl_sf_dilog_e(0.7,$r)' => 0.8893776242860387386, 181 'gsl_sf_dilog_e(1.0,$r)' => 1.6449340668482260, 182 'gsl_sf_clausen_e($M_PI/20.0,$r)' => 0.4478882448133546, 183 'gsl_sf_clausen_e($M_PI/6.0,$r)' => 0.8643791310538927, 184 'gsl_sf_clausen_e($M_PI/3.0,$r)' => 1.0149416064096535, 185 'gsl_sf_clausen_e( 2.0*$M_PI + $M_PI/3.0,$r)' => 1.0149416064096535, 186 'gsl_sf_clausen_e(100.0*$M_PI + $M_PI/3.0,$r)' => 1.0149416064096535, 187 'gsl_sf_coupling_3j_e(0, 1, 1, 0, 1, -1,$r)' => sqrt(1.0/2.0), 188 'gsl_sf_coupling_3j_e(1, 1, 2, 1, -1, 0,$r)' => sqrt(1.0/6.0), 189 'gsl_sf_coupling_3j_e(2, 4, 6, 0, 2, -2,$r)' => sqrt(8.0/105.0), 190 'gsl_sf_coupling_3j_e(4, 4, 8, 0, 0, 0,$r)' => sqrt(2.0/35.0), 191 'gsl_sf_coupling_3j_e(4, 4, 8, 2, -2, 0,$r)' => 2.0/3.0*sqrt(2.0/35.0), 192 'gsl_sf_coupling_3j_e(4, 4, 8, 4, -4, 0,$r)' => 1.0/(3.0*sqrt(70.0)), 193 'gsl_sf_coupling_3j_e(1, 1, 2, 2, -1, 0,$r)' => 0, 194 'gsl_sf_coupling_3j_e(1, 1, 2, 1, -2, 0,$r)' => 0, 195 'gsl_sf_coupling_3j_e(1, 1, 2, 1, -1, 3,$r)' => 0, 196 'gsl_sf_coupling_3j_e(1, 1, 3, 1, -1, 0,$r)' => 0, 197 'gsl_sf_coupling_3j_e(1, 4, 2, 1, -1, 0,$r)' => 0, 198 'gsl_sf_coupling_3j_e(4, 1, 2, 1, -1, 0,$r)' => 0, 199 'gsl_sf_coupling_6j_e(2, 2, 4, 2, 2, 2,$r)' => 1.0/6.0, 200 'gsl_sf_coupling_6j_e(4, 4, 2, 4, 4, 4,$r)' => -1.0/10.0, 201 'gsl_sf_coupling_6j_e(4, 4, 2, 4, 4, 2,$r)' => 1.0/6.0, 202 'gsl_sf_coupling_6j_e(4, 4, 2, 2, 2, 2,$r)' => -0.5/sqrt(5.0), 203 'gsl_sf_coupling_6j_e(4, 4, 4, 2, 2, 2,$r)' => sqrt(7.0/3.0)/10.0, 204 'gsl_sf_coupling_6j_e(6, 6, 6, 4, 4, 4,$r)' => -sqrt(3.0/5.0)/14.0, 205 'gsl_sf_coupling_6j_e(6, 6, 6, 4, 4, 2,$r)' => -sqrt(3.0/5.0)/7.0, 206 'gsl_sf_coupling_6j_e(2, 2, 4, 2, 2, 7,$r)' => 0, 207 'gsl_sf_coupling_6j_e(2, 2, 4, 2, 7, 2,$r)' => 0, 208 'gsl_sf_coupling_6j_e(2, 2, 4, 7, 2, 2,$r)' => 0, 209 'gsl_sf_coupling_6j_e(2, 2, 7, 2, 2, 2,$r)' => 0, 210 'gsl_sf_coupling_6j_e(2, 7, 4, 2, 2, 2,$r)' => 0, 211 'gsl_sf_coupling_6j_e(7, 2, 4, 2, 2, 2,$r)' => 0, 212 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 2, 1, 1, 2,$r)' => -sqrt(1.0/6.0)/10.0, 213 'gsl_sf_coupling_9j_e(8, 4, 10, 7, 3, 8, 1, 1, 2,$r)' => sqrt(7.0/3.0)/60.0, 214 'gsl_sf_coupling_9j_e(10, 2, 4, 3, 3, 2, 1, 1, 2,$r)' => 0, 215 'gsl_sf_coupling_9j_e(4, 10, 4, 3, 3, 2, 1, 1, 2,$r)' => 0, 216 'gsl_sf_coupling_9j_e(4, 2, 10, 3, 3, 2, 1, 1, 2,$r)' => 0, 217 'gsl_sf_coupling_9j_e(4, 2, 4, 10, 3, 2, 1, 1, 2,$r)' => 0, 218 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 10, 2, 1, 1, 2,$r)' => 0, 219 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 10, 1, 1, 2,$r)' => 0, 220 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 2, 10, 1, 2,$r)' => 0, 221 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 2, 1, 10, 2,$r)' => 0, 222 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 2, 1, 1, 10,$r)' => 0, 223 'gsl_sf_dawson_e(1.0e-15,$r)' => 1.0e-15, 224 'gsl_sf_dawson_e(0.5,$r)' => 0.4244363835020222959, 225 'gsl_sf_dawson_e(2.0,$r)' => 0.30134038892379196603, 226 'gsl_sf_dawson_e(1000.0,$r)' => 0.0005000002500003750009, 227 'gsl_sf_debye_1_e(0.1,$r)' => 0.975277750004723276, 228 'gsl_sf_debye_1_e(1.0,$r)' => 0.777504634112248239, 229 'gsl_sf_debye_1_e(10.0,$r)' => 0.164443465679946027, 230 'gsl_sf_debye_2_e(0.1,$r)' => 0.967083287045302664, 231 'gsl_sf_debye_2_e(1.0,$r)' => 0.70787847562782924, 232 'gsl_sf_debye_2_e(10.0,$r)' => 0.0479714980201218708, 233 'gsl_sf_debye_3_e(0.1,$r)' => 0.962999940487211048, 234 'gsl_sf_debye_3_e(1.0,$r)' => 0.674415564077814667, 235 'gsl_sf_debye_3_e(10.0,$r)' => 0.0192957656903454886, 236 'gsl_sf_debye_4_e(0.1,$r)' => 0.960555486124335944, 237 'gsl_sf_debye_4_e(1.0,$r)' => 0.654874068886737049, 238 'gsl_sf_debye_4_e(10.0,$r)' => 0.00967367556027115896, 239 'gsl_sf_debye_5_e(0.1,$r)' => 0.95892849428310568745, 240 'gsl_sf_debye_5_e(1.0,$r)' => 0.6421002580217790246, 241 'gsl_sf_debye_5_e(10.0,$r)' => 0.005701535852992908538, 242 'gsl_sf_debye_6_e(0.1,$r)' => 0.95776777382605465878, 243 'gsl_sf_debye_6_e(1.0,$r)' => 0.63311142583495107588, 244 'gsl_sf_debye_6_e(10.0,$r)' => 3.7938493294615955279e-3, 245 'gsl_sf_multiply_e(-3.0,2.0,$r)' => -6.0, 246 "gsl_sf_multiply_e($y, 1.0/$y,\$r)" => 1.0, 247 "gsl_sf_multiply_e($y, 0.2,\$r)" => 0.04*$GSL_DBL_MAX, 248 "gsl_sf_multiply_e($y, 4.0,\$r)" => 0.8*$GSL_DBL_MAX, 249 'gsl_sf_ellint_Kcomp_e( 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.3566005233611923760, 250 'gsl_sf_ellint_Kcomp_e( 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.6857503548125960429, 251 'gsl_sf_ellint_Kcomp_e(0.010, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.5708355989121522360, 252 'gsl_sf_ellint_Ecomp_e(0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.0284758090288040010, 253 'gsl_sf_ellint_Ecomp_e(0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.4674622093394271555, 254 'gsl_sf_ellint_Ecomp_e(0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.5707570561503852873, 255 'gsl_sf_ellint_Pcomp_e(0.99, 0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.13792612351836506315593, 256 'gsl_sf_ellint_Pcomp_e(0.50, 0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.60455249360848890075108, 257 'gsl_sf_ellint_Pcomp_e(0.01, 0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.49773208536003801277453, 258 'gsl_sf_ellint_Dcomp_e(0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.375395076351788975665323192, 259 'gsl_sf_ellint_Dcomp_e(0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.8731525818926755496456335628, 260 'gsl_sf_ellint_Dcomp_e(0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.7854276176694868932799393751, 261 'gsl_sf_ellint_F_e($M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.3065333392738766762, 262 'gsl_sf_ellint_F_e($M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.0895506700518854093, 263 'gsl_sf_ellint_F_e($M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.0472129063770918952, 264 'gsl_sf_ellint_E_e($M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.8704819220377943536, 265 'gsl_sf_ellint_E_e($M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.0075555551444720293, 266 'gsl_sf_ellint_E_e($M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.0471821963889481104, 267 'gsl_sf_ellint_P_e($M_PI/3.0, 0.99, 0.5, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.1288726598764099882, 268 'gsl_sf_ellint_P_e($M_PI/3.0, 0.50, 0.5, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.9570574331323584890, 269 'gsl_sf_ellint_P_e($M_PI/3.0, 0.01, 0.5, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.9228868127118118465, 270 'gsl_sf_ellint_RF_e(5.0e-11, 1.0e-10, 1.0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 12.36441982979439, 271 'gsl_sf_ellint_RF_e(1.0, 2.0, 3.0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.7269459354689082, 272 'gsl_sf_ellint_RD_e(5.0e-11, 1.0e-10, 1.0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 34.0932594919337362, 273 'gsl_sf_ellint_RD_e(1.0, 2.0, 3.0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.2904602810289906, 274 'gsl_sf_ellint_RC_e(1.0, 2.0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.7853981633974482, 275 'gsl_sf_ellint_RJ_e(2.0, 3.0, 4.0, 5.0, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 0.1429757966715675, 276 'gsl_sf_ellint_E_e($M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.02847580902880400098389, 277 'gsl_sf_ellint_E_e($M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.46746220933942715545980, 278 'gsl_sf_ellint_E_e($M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.57075705615038528733708, 279 'gsl_sf_ellint_E_e(2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.18646969601981364833972, 280 'gsl_sf_ellint_E_e(2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.92736886353438228163734, 281 'gsl_sf_ellint_E_e(2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.09433191591182246425715, 282 'gsl_sf_ellint_E_e($M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.05695161805760800196777, 283 'gsl_sf_ellint_E_e($M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.93492441867885431091959, 284 'gsl_sf_ellint_E_e($M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.14151411230077057467416, 285 'gsl_sf_ellint_E_e(4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.92743354009540235559582, 286 'gsl_sf_ellint_E_e(4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.94247997382332634020184, 287 'gsl_sf_ellint_E_e(4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.18869630868971868509117, 288 'gsl_sf_ellint_E_e(3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.08542742708641200295166, 289 'gsl_sf_ellint_E_e(3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.40238662801828146637939, 290 'gsl_sf_ellint_E_e(3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.71227116845115586201123, 291 'gsl_sf_ellint_E_e(5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.24342131407742165030750, 292 'gsl_sf_ellint_E_e(5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.86229328221323659255693, 293 'gsl_sf_ellint_E_e(5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.23584602821259303893130, 294 'gsl_sf_ellint_E_e(2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.11390323611521600393555, 295 'gsl_sf_ellint_E_e(2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.86984883735770862183918, 296 'gsl_sf_ellint_E_e(2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 6.28302822460154114934831, 297 'gsl_sf_ellint_E_e(7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.98438515815301035756360, 298 'gsl_sf_ellint_E_e(7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 6.87740439250218065112143, 299 'gsl_sf_ellint_E_e(7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.33021042099048925976532, 300 'gsl_sf_ellint_E_e(-$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.02847580902880400098389, 301 'gsl_sf_ellint_E_e(-$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.46746220933942715545980, 302 'gsl_sf_ellint_E_e(-$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.57075705615038528733708, 303 'gsl_sf_ellint_E_e(-2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.18646969601981364833972, 304 'gsl_sf_ellint_E_e(-2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.92736886353438228163734, 305 'gsl_sf_ellint_E_e(-2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.09433191591182246425715, 306 'gsl_sf_ellint_E_e(-$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.05695161805760800196777, 307 'gsl_sf_ellint_E_e(-$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.93492441867885431091959, 308 'gsl_sf_ellint_E_e(-$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.14151411230077057467416, 309 'gsl_sf_ellint_E_e(-4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.92743354009540235559582, 310 'gsl_sf_ellint_E_e(-4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.94247997382332634020184, 311 'gsl_sf_ellint_E_e(-4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.18869630868971868509117, 312 'gsl_sf_ellint_E_e(-3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.08542742708641200295166, 313 'gsl_sf_ellint_E_e(-3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.40238662801828146637939, 314 'gsl_sf_ellint_E_e(-3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.71227116845115586201123, 315 'gsl_sf_ellint_E_e(-5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.24342131407742165030750, 316 'gsl_sf_ellint_E_e(-5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.86229328221323659255693, 317 'gsl_sf_ellint_E_e(-5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.23584602821259303893130, 318 'gsl_sf_ellint_E_e(-2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.11390323611521600393555, 319 'gsl_sf_ellint_E_e(-2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.86984883735770862183918, 320 'gsl_sf_ellint_E_e(-2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -6.28302822460154114934831, 321 'gsl_sf_ellint_E_e(-7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.98438515815301035756360, 322 'gsl_sf_ellint_E_e(-7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -6.87740439250218065112143, 323 'gsl_sf_ellint_E_e(-7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.33021042099048925976532, 324 'gsl_sf_ellint_F_e($M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.35660052336119237603347, 325 'gsl_sf_ellint_F_e($M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.68575035481259604287120, 326 'gsl_sf_ellint_F_e($M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.57083559891215223602641, 327 'gsl_sf_ellint_F_e(2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.40666770744850807588478, 328 'gsl_sf_ellint_F_e(2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.28195003957330667648585, 329 'gsl_sf_ellint_F_e(2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.09445829144721257687207, 330 'gsl_sf_ellint_F_e($M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 6.71320104672238475206694, 331 'gsl_sf_ellint_F_e($M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.37150070962519208574241, 332 'gsl_sf_ellint_F_e($M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.14167119782430447205281, 333 'gsl_sf_ellint_F_e(4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 8.01973438599626142824910, 334 'gsl_sf_ellint_F_e(4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.46105137967707749499897, 335 'gsl_sf_ellint_F_e(4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.18888410420139636723356, 336 'gsl_sf_ellint_F_e(3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 10.0698015700835771281004, 337 'gsl_sf_ellint_F_e(3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.05725106443778812861361, 338 'gsl_sf_ellint_F_e(3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.71250679673645670807922, 339 'gsl_sf_ellint_F_e(5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 12.1198687541708928279517, 340 'gsl_sf_ellint_F_e(5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.65345074919849876222825, 341 'gsl_sf_ellint_F_e(5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.23612948927151704892488, 342 'gsl_sf_ellint_F_e(2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 13.4264020934447695041339, 343 'gsl_sf_ellint_F_e(2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 6.74300141925038417148481, 344 'gsl_sf_ellint_F_e(2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 6.28334239564860894410562, 345 'gsl_sf_ellint_F_e(7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 14.7329354327186461803160, 346 'gsl_sf_ellint_F_e(7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.83255208930226958074138, 347 'gsl_sf_ellint_F_e(7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.33055530202570083928637, 348 'gsl_sf_ellint_F_e(-$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.35660052336119237603347, 349 'gsl_sf_ellint_F_e(-$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.68575035481259604287120, 350 'gsl_sf_ellint_F_e(-$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.57083559891215223602641, 351 'gsl_sf_ellint_F_e(-2*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.40666770744850807588478, 352 'gsl_sf_ellint_F_e(-2*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.28195003957330667648585, 353 'gsl_sf_ellint_F_e(-2*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.09445829144721257687207, 354 'gsl_sf_ellint_F_e(-$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -6.71320104672238475206694, 355 'gsl_sf_ellint_F_e(-$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.37150070962519208574241, 356 'gsl_sf_ellint_F_e(-$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.14167119782430447205281, 357 'gsl_sf_ellint_F_e(-4*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -8.01973438599626142824910, 358 'gsl_sf_ellint_F_e(-4*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.46105137967707749499897, 359 'gsl_sf_ellint_F_e(-4*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.18888410420139636723356, 360 'gsl_sf_ellint_F_e(-3*$M_PI/2.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -10.0698015700835771281004, 361 'gsl_sf_ellint_F_e(-3*$M_PI/2.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.05725106443778812861361, 362 'gsl_sf_ellint_F_e(-3*$M_PI/2.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.71250679673645670807922, 363 'gsl_sf_ellint_F_e(-5*$M_PI/3, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -12.1198687541708928279517, 364 'gsl_sf_ellint_F_e(-5*$M_PI/3, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.65345074919849876222825, 365 'gsl_sf_ellint_F_e(-5*$M_PI/3, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.23612948927151704892488, 366 'gsl_sf_ellint_F_e(-2*$M_PI, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -13.4264020934447695041339, 367 'gsl_sf_ellint_F_e(-2*$M_PI, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -6.74300141925038417148481, 368 'gsl_sf_ellint_F_e(-2*$M_PI, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -6.28334239564860894410562, 369 'gsl_sf_ellint_F_e(-7*$M_PI/3.0, 0.99, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -14.7329354327186461803160, 370 'gsl_sf_ellint_F_e(-7*$M_PI/3.0, 0.50, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.83255208930226958074138, 371 'gsl_sf_ellint_F_e(-7*$M_PI/3.0, 0.01, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.33055530202570083928637, 372 'gsl_sf_ellint_P_e($M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.61678162163246646783050, 373 'gsl_sf_ellint_P_e($M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.78030349465454812629168, 374 'gsl_sf_ellint_P_e($M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 1.65580719756898353270922, 375 'gsl_sf_ellint_P_e(2*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.88008918207571119911983, 376 'gsl_sf_ellint_P_e(2*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.43655207300356008717867, 377 'gsl_sf_ellint_P_e(2*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 2.23211110528200554950903, 378 'gsl_sf_ellint_P_e($M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.23356324326493293566099, 379 'gsl_sf_ellint_P_e($M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.56060698930909625258336, 380 'gsl_sf_ellint_P_e($M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 3.31161439513796706541844, 381 'gsl_sf_ellint_P_e(4*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 8.58703730445415467220216, 382 'gsl_sf_ellint_P_e(4*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.68466190561463241798805, 383 'gsl_sf_ellint_P_e(4*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.39111768499392858132786, 384 'gsl_sf_ellint_P_e(3*$M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 10.8503448648973994034915, 385 'gsl_sf_ellint_P_e(3*$M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.34091048396364437887504, 386 'gsl_sf_ellint_P_e(3*$M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 4.96742159270695059812767, 387 'gsl_sf_ellint_P_e(5*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 13.1136524253406441347808, 388 'gsl_sf_ellint_P_e(5*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.99715906231265633976204, 389 'gsl_sf_ellint_P_e(5*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 5.54372550041997261492747, 390 'gsl_sf_ellint_P_e(2*$M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 14.4671264865298658713220, 391 'gsl_sf_ellint_P_e(2*$M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.12121397861819250516672, 392 'gsl_sf_ellint_P_e(2*$M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 6.62322879027593413083689, 393 'gsl_sf_ellint_P_e(7*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 15.8206005477190876078631, 394 'gsl_sf_ellint_P_e(7*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 8.24526889492372867057141, 395 'gsl_sf_ellint_P_e(7*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => 7.70273208013189564674630, 396 'gsl_sf_ellint_P_e(-$M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.61678162163246646783050, 397 'gsl_sf_ellint_P_e(-$M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.78030349465454812629168, 398 'gsl_sf_ellint_P_e(-$M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -1.65580719756898353270922, 399 'gsl_sf_ellint_P_e(-2*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.88008918207571119911983, 400 'gsl_sf_ellint_P_e(-2*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.43655207300356008717867, 401 'gsl_sf_ellint_P_e(-2*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -2.23211110528200554950903, 402 'gsl_sf_ellint_P_e(-$M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.23356324326493293566099, 403 'gsl_sf_ellint_P_e(-$M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.56060698930909625258336, 404 'gsl_sf_ellint_P_e(-$M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -3.31161439513796706541844, 405 'gsl_sf_ellint_P_e(-4*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -8.58703730445415467220216, 406 'gsl_sf_ellint_P_e(-4*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.68466190561463241798805, 407 'gsl_sf_ellint_P_e(-4*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.39111768499392858132786, 408 'gsl_sf_ellint_P_e(-3*$M_PI/2.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -10.8503448648973994034915, 409 'gsl_sf_ellint_P_e(-3*$M_PI/2.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.34091048396364437887504, 410 'gsl_sf_ellint_P_e(-3*$M_PI/2.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -4.96742159270695059812767, 411 'gsl_sf_ellint_P_e(-5*$M_PI/3, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -13.1136524253406441347808, 412 'gsl_sf_ellint_P_e(-5*$M_PI/3, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.99715906231265633976204, 413 'gsl_sf_ellint_P_e(-5*$M_PI/3, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -5.54372550041997261492747, 414 'gsl_sf_ellint_P_e(-2*$M_PI, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -14.4671264865298658713220, 415 'gsl_sf_ellint_P_e(-2*$M_PI, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.12121397861819250516672, 416 'gsl_sf_ellint_P_e(-2*$M_PI, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -6.62322879027593413083689, 417 'gsl_sf_ellint_P_e(-7*$M_PI/3.0, 0.99, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -15.8206005477190876078631, 418 'gsl_sf_ellint_P_e(-7*$M_PI/3.0, 0.50, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -8.24526889492372867057141, 419 'gsl_sf_ellint_P_e(-7*$M_PI/3.0, 0.01, -0.1, $Math::GSL::GSL_MODE_DEFAULT,$r)' => -7.70273208013189564674630, 420 'gsl_sf_erfc_e(-10.0,$r)' => 2.0, 421 'gsl_sf_erfc_e(-5.0000002,$r)' => 1.9999999999984625433, 422 'gsl_sf_erfc_e(-5.0,$r)' => 1.9999999999984625402, 423 'gsl_sf_erfc_e(-1.0,$r)' => 1.8427007929497148693, 424 'gsl_sf_erfc_e(-0.5,$r)' => 1.5204998778130465377, 425 'gsl_sf_erfc_e(1.0,$r)' => 0.15729920705028513066, 426 'gsl_sf_erfc_e(3.0,$r)' => 0.000022090496998585441373, 427 'gsl_sf_erfc_e(7.0,$r)' => 4.183825607779414399e-23, 428 'gsl_sf_erfc_e(10.0,$r)' => 2.0884875837625447570e-45, 429 'gsl_sf_log_erfc_e(-1.0,$r)' => log(1.842700792949714869), 430 'gsl_sf_log_erfc_e(-0.1,$r)' => 0.106576400586522485015, 431 'gsl_sf_log_erfc_e(-1e-10,$r)' => 1.1283791670318505967e-10, 432 'gsl_sf_log_erfc_e(0.0,$r)' => log(1.0), 433 'gsl_sf_log_erfc_e(1e-10,$r)' => -1.128379167159174551e-10, 434 'gsl_sf_log_erfc_e(0.001,$r)' => -0.0011290158896213548027, 435 'gsl_sf_log_erfc_e(0.1,$r)' => -0.119304973737395598329, 436 'gsl_sf_log_erfc_e(1.0,$r)' => log(0.15729920705028513066), 437 'gsl_sf_log_erfc_e(10.0,$r)' => log(2.0884875837625447570e-45), 438 'gsl_sf_erf_e(-10.0,$r)' => -1.0000000000000000000, 439 'gsl_sf_erf_e(0.5,$r)' => 0.5204998778130465377, 440 'gsl_sf_erf_e(1.0,$r)' => 0.8427007929497148693, 441 'gsl_sf_erf_e(10.0,$r)' => 1.0000000000000000000, 442 'gsl_sf_erf_Z_e(1.0,$r)' => 0.24197072451914334980, 443 'gsl_sf_erf_Q_e(10.0,$r)' => 7.619853024160526066e-24, 444 'gsl_sf_hazard_e(-20.0,$r)' => 5.5209483621597631896e-88, 445 'gsl_sf_hazard_e(-10.0,$r)' => 7.6945986267064193463e-23, 446 'gsl_sf_hazard_e(-1.0,$r)' => 0.28759997093917836123, 447 'gsl_sf_hazard_e( 0.0,$r)' => 0.79788456080286535588, 448 'gsl_sf_hazard_e( 1.0,$r)' => 1.5251352761609812091, 449 'gsl_sf_hazard_e(10.0,$r)' => 10.098093233962511963, 450 'gsl_sf_hazard_e(20.0,$r)' => 20.049753068527850542, 451 'gsl_sf_hazard_e(30.0,$r)' => 30.033259667433677037, 452 'gsl_sf_hazard_e(50.0,$r)' => 50.019984031905639809, 453 'gsl_sf_hazard_e(80.0,$r)' => 80.012496096798234468, 454 'gsl_sf_hazard_e(150.0,$r)' => 150.00666607420571802, 455 'gsl_sf_hazard_e(300.0,$r)' => 300.00333325926337415, 456 'gsl_sf_hazard_e(900.0,$r)' => 900.00111110836764382, 457 'gsl_sf_hazard_e(1001.0,$r)' => 1001.0009989990049990, 458 'gsl_sf_hazard_e(2000.0,$r)' => 2000.0004999997500003, 459 'gsl_sf_exp_e(-10.0,$r)' => exp(-10.0), 460 'gsl_sf_exp_e( 10.0,$r)' => exp( 10.0), 461 "gsl_sf_exp_err_e(-10.0, $TOL1,\$r)" => exp(-10.0), 462 "gsl_sf_exp_err_e( 10.0, $TOL1,\$r)" => exp( 10.0), 463 'gsl_sf_exp_mult_e(-10.0, 1.0e-06,$r)' => 1.0e-06*exp(-10.0), 464 'gsl_sf_exp_mult_e(-10.0, 2.0,$r)' => 2.0*exp(-10.0), 465 'gsl_sf_exp_mult_e(-10.0, -2.0,$r)' => -2.0*exp(-10.0), 466 'gsl_sf_exp_mult_e( 10.0, 1.0e-06,$r)' => 1.0e-06*exp( 10.0), 467 'gsl_sf_exp_mult_e( 10.0, -2.0,$r)' => -2.0*exp( 10.0), 468 "gsl_sf_exp_mult_e($w, 1.000001,\$r)" => 1.000001*exp($w), 469 "gsl_sf_exp_mult_e($w, 1.000000001,\$r)" => 1.000000001*exp($w), 470 "gsl_sf_exp_mult_e($w, 100.0,\$r)" => 100.0*exp($w), 471 "gsl_sf_exp_mult_e($w, 1.0e+20,\$r)" => 1.0e+20*exp($w), 472 "gsl_sf_exp_mult_e($w, exp(-$w)*exp($M_LN2),\$r)" => 2.0, 473 "gsl_sf_exp_mult_err_e(-10.0, $SQRT_TOL0, 2.0, $SQRT_TOL0,\$r)" => 2.0*exp(-10.0), 474 "gsl_sf_exp_mult_err_e($w, $SQRT_TOL0*$w, exp(-$w)*exp($M_LN2), $SQRT_TOL0*exp(-$w)*exp($M_LN2),\$r)" => 2.0, 475 'gsl_sf_expm1_e(-10.0,$r)' => exp(-10.0)-1.0, 476 'gsl_sf_expm1_e(-0.001,$r)' => -0.00099950016662500845, 477 'gsl_sf_expm1_e(-1.0e-8,$r)' => -1.0e-08 + 0.5e-16, 478 'gsl_sf_expm1_e( 1.0e-8,$r)' => 1.0e-08 + 0.5e-16, 479 'gsl_sf_expm1_e( 0.001,$r)' => 0.0010005001667083417, 480 'gsl_sf_expm1_e( 10.0,$r)' => exp(10.0)-1.0, 481 'gsl_sf_exprel_e(-10.0,$r)' => 0.0999954600070237515, 482 'gsl_sf_exprel_e(-0.001,$r)' => 0.9995001666250084, 483 'gsl_sf_exprel_e(-1.0e-8,$r)' => 1.0 - 0.5e-08, 484 'gsl_sf_exprel_e( 1.0e-8,$r)' => 1.0 + 0.5e-08, 485 'gsl_sf_exprel_e( 0.001,$r)' => 1.0005001667083417, 486 'gsl_sf_exprel_e( 10.0,$r)' => 2202.5465794806716517, 487 'gsl_sf_exprel_2_e(-10.0,$r)' => 0.18000090799859524970, 488 'gsl_sf_exprel_2_e(-0.001,$r)' => 0.9996667499833361107, 489 'gsl_sf_exprel_2_e(-1.0e-8,$r)' => 0.9999999966666666750, 490 'gsl_sf_exprel_2_e( 1.0e-8,$r)' => 1.0000000033333333417, 491 'gsl_sf_exprel_2_e( 0.001,$r)' => 1.0003334166833361115, 492 'gsl_sf_exprel_2_e( 10.0,$r)' => 440.3093158961343303, 493 'gsl_sf_exprel_n_e(3, -1000.0,$r)' => 0.00299400600000000000, 494 'gsl_sf_exprel_n_e(3, -100.0,$r)' => 0.02940600000000000000, 495 'gsl_sf_exprel_n_e(3, -10.0,$r)' => 0.24599972760042142509, 496 'gsl_sf_exprel_n_e(3, -3.0,$r)' => 0.5444917625849191238, 497 'gsl_sf_exprel_n_e(3, -0.001,$r)' => 0.9997500499916678570, 498 'gsl_sf_exprel_n_e(3, -1.0e-8,$r)' => 0.9999999975000000050, 499 'gsl_sf_exprel_n_e(3, 1.0e-8,$r)' => 1.0000000025000000050, 500 'gsl_sf_exprel_n_e(3, 0.001,$r)' => 1.0002500500083345240, 501 'gsl_sf_exprel_n_e(3, 3.0,$r)' => 2.5745637607083706091, 502 'gsl_sf_exprel_n_e(3, 3.1,$r)' => 2.6772417068460206247, 503 'gsl_sf_exprel_n_e(3, 10.0,$r)' => 131.79279476884029910, 504 'gsl_sf_exprel_n_e(3, 100.0,$r)' => 1.6128702850896812690e+38, 505 'gsl_sf_exprel_n_e(50, -1000.0,$r)' => 0.04766231609253975959, 506 'gsl_sf_exprel_n_e(50, -100.0,$r)' => 0.3348247572345889317, 507 'gsl_sf_exprel_n_e(50, -10.0,$r)' => 0.8356287051853286482, 508 'gsl_sf_exprel_n_e(50, -3.0,$r)' => 0.9443881609152163615, 509 'gsl_sf_exprel_n_e(50, -1.0,$r)' => 0.980762245565660617, 510 'gsl_sf_exprel_n_e(50, -1.0e-8,$r)' => 1.0 -1.0e-8/51.0, 511 'gsl_sf_exprel_n_e(50, 1.0e-8,$r)' => 1.0 +1.0e-8/51.0, 512 'gsl_sf_exprel_n_e(50, 1.0,$r)' => 1.01999216583666790, 513 'gsl_sf_exprel_n_e(50, 3.0,$r)' => 1.0624205757460368307, 514 'gsl_sf_exprel_n_e(50, 48.0,$r)' => 7.499573876877194416, 515 'gsl_sf_exprel_n_e(50, 50.1,$r)' => 9.311803306230992272, 516 'gsl_sf_exprel_n_e(50, 100.0,$r)' => 8.175664432485807634e+07, 517 'gsl_sf_exprel_n_e(50, 500.0,$r)' => 4.806352370663185330e+146, 518 'gsl_sf_exprel_n_e(500, -1000.0,$r)' => 0.3334815803127619256, 519 'gsl_sf_exprel_n_e(500, -100.0,$r)' => 0.8335646217536183909, 520 'gsl_sf_exprel_n_e(500, -10.0,$r)' => 0.9804297803131823066, 521 'gsl_sf_exprel_n_e(500, -3.0,$r)' => 0.9940475488850672997, 522 'gsl_sf_exprel_n_e(500, -1.0,$r)' => 0.9980079602383488808, 523 'gsl_sf_exprel_n_e(500, -1.0e-8,$r)' => 1.0 -1.0e-8/501.0, 524 'gsl_sf_exprel_n_e(500, 1.0e-8,$r)' => 1.0 +1.0e-8/501.0, 525 'gsl_sf_exprel_n_e(500, 1.0,$r)' => 1.0019999920160634252, 526 'gsl_sf_exprel_n_e(500, 3.0,$r)' => 1.0060240236632444934, 527 'gsl_sf_exprel_n_e(500, 48.0,$r)' => 1.1059355517981272174, 528 'gsl_sf_exprel_n_e(500, 100.0,$r)' => 1.2492221464878287204, 529 'gsl_sf_exprel_n_e(500, 500.0,$r)' => 28.363019877927630858, 530 'gsl_sf_exprel_n_e(500, 1000.0,$r)' => 2.4037563160335300322e+68, 531 'gsl_sf_exprel_n_e(500, 1600.0,$r)' => 7.899293535320607403e+226, 532 'gsl_sf_expint_E1_e(-1.0,$r)' => -1.8951178163559367555, 533 'gsl_sf_expint_E1_e(1.0e-10,$r)' => 22.448635265138923980, 534 'gsl_sf_expint_E1_e(1.0e-05,$r)' => 10.935719800043695615, 535 'gsl_sf_expint_E1_e(0.1,$r)' => 1.82292395841939066610, 536 'gsl_sf_expint_E1_e(1.0,$r)' => 0.21938393439552027368, 537 'gsl_sf_expint_E1_e(10.0,$r)' => 4.156968929685324277e-06, 538 'gsl_sf_expint_E1_e(50.0,$r)' => 3.783264029550459019e-24, 539 'gsl_sf_expint_E1_e(300.0,$r)' => 1.710384276804510115e-133, 540 'gsl_sf_expint_E2_e(-1.0,$r)' => 0.8231640121031084799, 541 'gsl_sf_expint_E2_e(0.0,$r)' => 1.0, 542 'gsl_sf_expint_E2_e(1.0/4294967296.0,$r)' => 0.9999999947372139168, 543 'gsl_sf_expint_E2_e(1.0/65536.0,$r)' => 0.9998243233207178845, 544 'gsl_sf_expint_E2_e(0.1,$r)' => 0.7225450221940205066, 545 'gsl_sf_expint_E2_e(1.0,$r)' => 0.14849550677592204792, 546 'gsl_sf_expint_E2_e(10.0,$r)' => 3.830240465631608762e-06, 547 'gsl_sf_expint_E2_e(50.0,$r)' => 3.711783318868827367e-24, 548 'gsl_sf_expint_E2_e(300.0,$r)' => 1.7047391998483433998e-133, 549 'gsl_sf_expint_En_e(1,-1.0,$r)' => -1.8951178163559367555, 550 'gsl_sf_expint_En_e(1,1.0e-10,$r)' => 22.448635265138923980, 551 'gsl_sf_expint_En_e(1,1.0e-05,$r)' => 10.935719800043695615, 552 'gsl_sf_expint_En_e(1,0.1,$r)' => 1.82292395841939066610, 553 'gsl_sf_expint_En_e(1,1.0,$r)' => 0.21938393439552027368, 554 'gsl_sf_expint_En_e(1,10.0,$r)' => 4.156968929685324277e-06, 555 'gsl_sf_expint_En_e(1,50.0,$r)' => 3.783264029550459019e-24, 556 'gsl_sf_expint_En_e(1,300.0,$r)' => 1.710384276804510115e-133, 557 'gsl_sf_expint_En_e(2,-1.0,$r)' => 0.8231640121031084799, 558 'gsl_sf_expint_En_e(2,0.0,$r)' => 1.0, 559 'gsl_sf_expint_En_e(2,1.0/4294967296.0,$r)' => 0.9999999947372139168, 560 'gsl_sf_expint_En_e(2,1.0/65536.0,$r)' => 0.9998243233207178845, 561 'gsl_sf_expint_En_e(2,0.1,$r)' => 0.7225450221940205066, 562 'gsl_sf_expint_En_e(2,1.0,$r)' => 0.14849550677592204792, 563 'gsl_sf_expint_En_e(2,10.0,$r)' => 3.830240465631608762e-06, 564 'gsl_sf_expint_En_e(2,50.0,$r)' => 3.711783318868827367e-24, 565 'gsl_sf_expint_En_e(2,300.0,$r)' => 1.7047391998483433998e-133, 566 'gsl_sf_expint_En_e(3,0.0,$r)' => 0.5, 567 'gsl_sf_expint_En_e(3,1.0/4294967296.0,$r)' => 0.499999999767169356972, 568 'gsl_sf_expint_En_e(3,1.0/65536.0,$r)' => 0.4999847426094515610, 569 'gsl_sf_expint_En_e(3,0.1,$r)' => 0.4162914579082787612543, 570 'gsl_sf_expint_En_e(3,1.0,$r)' => 0.10969196719776013683858, 571 'gsl_sf_expint_En_e(3,10.0,$r)' => .000003548762553084381959981, 572 'gsl_sf_expint_En_e(3,50.0,$r)' => 3.6429094264752049812e-24, 573 'gsl_sf_expint_En_e(10,0.0,$r)' => 0.111111111111111111, 574 'gsl_sf_expint_En_e(10,1.0/4294967296.0,$r)' => 0.111111111082007280658, 575 'gsl_sf_expint_En_e(10,1.0/65536.0,$r)' => 0.11110920377910896018606, 576 'gsl_sf_expint_En_e(10,0.1,$r)' => 0.099298432000896813567905, 577 'gsl_sf_expint_En_e(10,1.0,$r)' => 0.036393994031416401634164534, 578 'gsl_sf_expint_En_e(10,10.0,$r)' => 0.00000232530265702821081778968, 579 'gsl_sf_expint_En_e(10,50.0,$r)' => 3.223296586749110919572e-24, 580 'gsl_sf_expint_En_e(10,300.0,$r)' => 1.6608815083360041367294736e-133, 581 'gsl_sf_expint_Ei_e(-1.0,$r)' => -0.21938393439552027368, 582 'gsl_sf_expint_Ei_e(1.0/4294967296.0,$r)' => -21.603494112783886397, 583 'gsl_sf_expint_Ei_e(1.0,$r)' => 1.8951178163559367555, 584 'gsl_sf_expint_E1_scaled_e(-10000.0,$r)' => -0.00010001000200060024012, 585 'gsl_sf_expint_E1_scaled_e(-1000.0,$r)' => -0.0010010020060241207251, 586 'gsl_sf_expint_E1_scaled_e(-10.0,$r)' => -0.11314702047341077803, 587 'gsl_sf_expint_E1_scaled_e(-1.0,$r)' => -0.69717488323506606877, 588 'gsl_sf_expint_E1_scaled_e(1.0e-10,$r)' => 22.448635267383787506, 589 'gsl_sf_expint_E1_scaled_e(1.0e-05,$r)' => 10.935829157788483865, 590 'gsl_sf_expint_E1_scaled_e(0.1,$r)' => 2.0146425447084516791, 591 'gsl_sf_expint_E1_scaled_e(1.0,$r)' => 0.59634736232319407434, 592 'gsl_sf_expint_E1_scaled_e(10.0,$r)' => 0.091563333939788081876, 593 'gsl_sf_expint_E1_scaled_e(50.0,$r)' => 0.019615109930114870365, 594 'gsl_sf_expint_E1_scaled_e(300.0,$r)' => 0.0033222955652707070644, 595 'gsl_sf_expint_E1_scaled_e(1000.0,$r)' => 0.00099900199402388071500, 596 'gsl_sf_expint_E1_scaled_e(10000.0,$r)' => 0.000099990001999400239880, 597 'gsl_sf_expint_E2_scaled_e(-10000.0,$r)' => -0.00010002000600240120072, 598 'gsl_sf_expint_E2_scaled_e(-1000.0,$r)' => -0.0010020060241207250807, 599 'gsl_sf_expint_E2_scaled_e(-10.0,$r)' => -0.13147020473410778034, 600 'gsl_sf_expint_E2_scaled_e(-1.0,$r)' => 0.30282511676493393123, 601 'gsl_sf_expint_E2_scaled_e(0.0,$r)' => 1.0, 602 'gsl_sf_expint_E2_scaled_e(1.0/4294967296.0,$r)' => 0.99999999497004455927, 603 'gsl_sf_expint_E2_scaled_e(1.0/65536.0,$r)' => 0.99983957954556245453, 604 'gsl_sf_expint_E2_scaled_e(0.1,$r)' => 0.79853574552915483209, 605 'gsl_sf_expint_E2_scaled_e(1.0,$r)' => 0.40365263767680592566, 606 'gsl_sf_expint_E2_scaled_e(10.0,$r)' => 0.084366660602119181239, 607 'gsl_sf_expint_E2_scaled_e(50.0,$r)' => 0.019244503494256481735, 608 'gsl_sf_expint_E2_scaled_e(300.0,$r)' => 0.0033113304187878806691, 609 'gsl_sf_expint_E2_scaled_e(1000.0,$r)' => 0.00099800597611928500004, 610 'gsl_sf_expint_E2_scaled_e(10000.0,$r)' => 0.000099980005997601199281, 611 'gsl_sf_expint_En_scaled_e(1,-10000.0,$r)' => -0.00010001000200060024012, 612 'gsl_sf_expint_En_scaled_e(1,-1000.0,$r)' => -0.0010010020060241207251, 613 'gsl_sf_expint_En_scaled_e(1,-10.0,$r)' => -0.11314702047341077803, 614 'gsl_sf_expint_En_scaled_e(1,-1.0,$r)' => -0.69717488323506606877, 615 'gsl_sf_expint_En_scaled_e(1,1.0e-10,$r)' => 22.448635267383787506, 616 'gsl_sf_expint_En_scaled_e(1,1.0e-05,$r)' => 10.935829157788483865, 617 'gsl_sf_expint_En_scaled_e(1,0.1,$r)' => 2.0146425447084516791, 618 'gsl_sf_expint_En_scaled_e(1,1.0,$r)' => 0.59634736232319407434, 619 'gsl_sf_expint_En_scaled_e(1,10.0,$r)' => 0.091563333939788081876, 620 'gsl_sf_expint_En_scaled_e(1,50.0,$r)' => 0.019615109930114870365, 621 'gsl_sf_expint_En_scaled_e(1,300.0,$r)' => 0.0033222955652707070644, 622 'gsl_sf_expint_En_scaled_e(1,1000.0,$r)' => 0.00099900199402388071500, 623 'gsl_sf_expint_En_scaled_e(1,10000.0,$r)' => 0.000099990001999400239880, 624 'gsl_sf_expint_En_scaled_e(2,-10000.0,$r)' => -0.00010002000600240120072, 625 'gsl_sf_expint_En_scaled_e(2,-1000.0,$r)' => -0.0010020060241207250807, 626 'gsl_sf_expint_En_scaled_e(2,-10.0,$r)' => -0.13147020473410778034, 627 'gsl_sf_expint_En_scaled_e(2,-1.0,$r)' => 0.30282511676493393123, 628 'gsl_sf_expint_En_scaled_e(2,0.0,$r)' => 1.0, 629 'gsl_sf_expint_En_scaled_e(2,1.0/4294967296.0,$r)' => 0.99999999497004455927, 630 'gsl_sf_expint_En_scaled_e(2,1.0/65536.0,$r)' => 0.99983957954556245453, 631 'gsl_sf_expint_En_scaled_e(2,0.1,$r)' => 0.79853574552915483209, 632 'gsl_sf_expint_En_scaled_e(2,1.0,$r)' => 0.40365263767680592566, 633 'gsl_sf_expint_En_scaled_e(2,10.0,$r)' => 0.084366660602119181239, 634 'gsl_sf_expint_En_scaled_e(2,50.0,$r)' => 0.019244503494256481735, 635 'gsl_sf_expint_En_scaled_e(2,300.0,$r)' => 0.0033113304187878806691, 636 'gsl_sf_expint_En_scaled_e(2,1000.0,$r)' => 0.00099800597611928500004, 637 'gsl_sf_expint_En_scaled_e(2,10000.0,$r)' => 0.000099980005997601199281, 638 'gsl_sf_expint_En_scaled_e(3,0.0,$r)' => 0.5, 639 'gsl_sf_expint_En_scaled_e(3,1.0/4294967296.0,$r)' => 0.4999999998835846787586, 640 'gsl_sf_expint_En_scaled_e(3,1.0/65536.0,$r)' => 0.4999923718293796877864492, 641 'gsl_sf_expint_En_scaled_e(3,0.1,$r)' => 0.4600732127235422583955, 642 'gsl_sf_expint_En_scaled_e(3,1.0,$r)' => 0.298173681161597037170539, 643 'gsl_sf_expint_En_scaled_e(3,10.0,$r)' => 0.07816669698940409380349, 644 'gsl_sf_expint_En_scaled_e(3,50.0,$r)' => 0.0188874126435879566345, 645 'gsl_sf_expint_En_scaled_e(3,300.0,$r)' => 0.00330043718181789963028657675, 646 'gsl_sf_expint_En_scaled_e(10,0.0,$r)' => 0.111111111111111111, 647 'gsl_sf_expint_En_scaled_e(10,1.0/4294967296.0,$r)' => 0.11111111110787735217158, 648 'gsl_sf_expint_En_scaled_e(10,1.0/65536.0,$r)' => 0.1111108991839472074435, 649 'gsl_sf_expint_En_scaled_e(10,0.1,$r)' => 0.1097417392579033988025, 650 'gsl_sf_expint_En_scaled_e(10,1.0,$r)' => 0.09892913264064615521915, 651 'gsl_sf_expint_En_scaled_e(10,10.0,$r)' => 0.0512181994376050593314159875, 652 'gsl_sf_expint_En_scaled_e(10,50.0,$r)' => 0.0167118436335939556034579, 653 'gsl_sf_expint_En_scaled_e(10,300.0,$r)' => 0.0032261400811599644878615, 654 'gsl_sf_expint_Ei_scaled_e(-1000.0,$r)' => -0.00099900199402388071500, 655 'gsl_sf_expint_Ei_scaled_e(-1.0,$r)' => -0.59634736232319407434, 656 'gsl_sf_expint_Ei_scaled_e(1.0/4294967296.0,$r)' => -21.603494107753930958, 657 'gsl_sf_expint_Ei_scaled_e(1.0,$r)' => 0.69717488323506606877, 658 'gsl_sf_expint_Ei_scaled_e(1000.0,$r)' => 0.0010010020060241207251, 659 'gsl_sf_Shi_e(-1.0,$r)' => -1.0572508753757285146, 660 'gsl_sf_Shi_e(1.0/4294967296.0,$r)' => 2.3283064365386962891e-10, 661 'gsl_sf_Shi_e(1.0/65536.0,$r)' => 0.00001525878906269737298, 662 'gsl_sf_Shi_e(0.1,$r)' => 0.1000555722250569955, 663 'gsl_sf_Shi_e(1.0,$r)' => 1.0572508753757285146, 664 'gsl_sf_Shi_e(10.0,$r)' => 1246.1144901994233444, 665 'gsl_sf_Shi_e(50.0,$r)' => 5.292818448565845482e+19, 666 'gsl_sf_Shi_e(300.0,$r)' => 3.248241254044332895e+127, 667 'gsl_sf_Chi_e(-1.0,$r)' => 0.8378669409802082409, 668 'gsl_sf_Chi_e(1.0/4294967296.0,$r)' => -21.603494113016717041, 669 'gsl_sf_Chi_e(1.0/65536.0,$r)' => -10.513139223999384429, 670 'gsl_sf_Chi_e(1.0/8.0,$r)' => -1.4983170827635760646, 671 'gsl_sf_Chi_e(1.0,$r)' => 0.8378669409802082409, 672 'gsl_sf_Chi_e(10.0,$r)' => 1246.1144860424544147, 673 'gsl_sf_Chi_e(50.0,$r)' => 5.292818448565845482e+19, 674 'gsl_sf_Chi_e(300.0,$r)' => 3.248241254044332895e+127, 675 'gsl_sf_expint_3_e(1.0e-10,$r)' => 1.0e-10, 676 'gsl_sf_expint_3_e(1.0e-05,$r)' => 9.9999999999999975e-06, 677 'gsl_sf_expint_3_e(0.1,$r)' => 0.09997500714119079665122, 678 'gsl_sf_expint_3_e(0.5,$r)' => 0.48491714311363971332427, 679 'gsl_sf_expint_3_e(1.0,$r)' => 0.80751118213967145285833, 680 'gsl_sf_expint_3_e(2.0,$r)' => 0.89295351429387631138208, 681 'gsl_sf_expint_3_e(5.0,$r)' => 0.89297951156924921121856, 682 'gsl_sf_expint_3_e(10.0,$r)' => 0.89297951156924921121856, 683 'gsl_sf_expint_3_e(100.0,$r)' => 0.89297951156924921121856, 684 'gsl_sf_Si_e(-1.0,$r)' => -0.9460830703671830149, 685 'gsl_sf_Si_e(1.0e-10,$r)' => 1.0e-10, 686 'gsl_sf_Si_e(1.0e-05,$r)' => 9.999999999944444444e-06, 687 'gsl_sf_Si_e(0.1,$r)' => 0.09994446110827695016, 688 'gsl_sf_Si_e(1.0,$r)' => 0.9460830703671830149, 689 'gsl_sf_Si_e(10.0,$r)' => 1.6583475942188740493, 690 'gsl_sf_Si_e(50.0,$r)' => 1.5516170724859358947, 691 'gsl_sf_Si_e(300.0,$r)' => 1.5708810882137495193, 692 'gsl_sf_Si_e(1.0e+20,$r)' => 1.5707963267948966192, 693 'gsl_sf_Ci_e(1.0/4294967296.0,$r)' => -21.603494113016717041, 694 'gsl_sf_Ci_e(1.0/65536.0,$r)' => -10.513139224115799751, 695 'gsl_sf_Ci_e(1.0/8.0,$r)' => -1.5061295845296396649, 696 'gsl_sf_Ci_e(1.0,$r)' => 0.3374039229009681347, 697 'gsl_sf_Ci_e(10.0,$r)' => -0.04545643300445537263, 698 'gsl_sf_Ci_e(50.0,$r)' => -0.005628386324116305440, 699 'gsl_sf_Ci_e(300.0,$r)' => -0.003332199918592111780, 700 'gsl_sf_Ci_e(65536.0,$r)' => 0.000010560248837656279453, 701 'gsl_sf_Ci_e(4294967296.0,$r)' => -1.0756463261957757485e-10, 702 'gsl_sf_Ci_e(1099511627776.0,$r)' => -3.689865584710764214e-13, 703 'gsl_sf_atanint_e(1.0e-10,$r)' => 1.0e-10, 704 'gsl_sf_atanint_e(1.0e-05,$r)' => 9.99999999988888888889e-06, 705 'gsl_sf_atanint_e(0.1,$r)' => 0.09988928686033618404, 706 'gsl_sf_atanint_e(1.0,$r)' => 0.91596559417721901505, 707 'gsl_sf_atanint_e(2.0,$r)' => 1.57601540344632342236, 708 'gsl_sf_atanint_e(10.0,$r)' => 3.71678149306806859029, 709 'gsl_sf_atanint_e(50.0,$r)' => 6.16499047850274874222, 710 'gsl_sf_atanint_e(300.0,$r)' => 8.96281388924518959990, 711 'gsl_sf_atanint_e(1.0e+5,$r)' => 18.084471031038661920, 712 'gsl_sf_fermi_dirac_m1_e(-10.0,$r)' => 0.00004539786870243439450, 713 'gsl_sf_fermi_dirac_m1_e( -1.0,$r)' => 0.26894142136999512075, 714 'gsl_sf_fermi_dirac_m1_e( 1.0,$r)' => 0.7310585786300048793, 715 'gsl_sf_fermi_dirac_0_e(-10.0,$r)' => 0.00004539889921686464677, 716 'gsl_sf_fermi_dirac_0_e( -1.0,$r)' => 0.31326168751822283405, 717 'gsl_sf_fermi_dirac_0_e( 1.0,$r)' => 1.3132616875182228340, 718 'gsl_sf_fermi_dirac_0_e( 10.0,$r)' => 10.000045398899216865, 719 'gsl_sf_fermi_dirac_1_e(-10.0,$r)' => 0.00004539941448447633524, 720 'gsl_sf_fermi_dirac_1_e( -2.0,$r)' => 0.13101248471442377127, 721 'gsl_sf_fermi_dirac_1_e( -1.0,$r)' => 0.3386479964034521798, 722 'gsl_sf_fermi_dirac_1_e( -0.4,$r)' => 0.5825520806897909028, 723 'gsl_sf_fermi_dirac_1_e( 0.4,$r)' => 1.1423819861584355337, 724 'gsl_sf_fermi_dirac_1_e( 1.0,$r)' => 1.8062860704447742567, 725 'gsl_sf_fermi_dirac_1_e( 1.5,$r)' => 2.5581520872227806402, 726 'gsl_sf_fermi_dirac_1_e( 2.5,$r)' => 4.689474797599761667, 727 'gsl_sf_fermi_dirac_1_e( 10.0,$r)' => 51.64488866743374196, 728 'gsl_sf_fermi_dirac_1_e( 12.0,$r)' => 73.64492792264531092, 729 'gsl_sf_fermi_dirac_1_e( 20.0,$r)' => 201.64493406478707282, 730 'gsl_sf_fermi_dirac_1_e( 50.0,$r)' => 1251.6449340668482264, 731 'gsl_sf_fermi_dirac_2_e(-10.0,$r)' => 0.00004539967212174776662, 732 'gsl_sf_fermi_dirac_2_e( -2.0,$r)' => 0.13313272938565030508, 733 'gsl_sf_fermi_dirac_2_e( -1.0,$r)' => 0.3525648792978077590, 734 'gsl_sf_fermi_dirac_2_e( -0.4,$r)' => 0.6229402647001272120, 735 'gsl_sf_fermi_dirac_2_e( 0.4,$r)' => 1.2915805581060844533, 736 'gsl_sf_fermi_dirac_2_e( 1.0,$r)' => 2.1641656128127008622, 737 'gsl_sf_fermi_dirac_2_e( 1.5,$r)' => 3.247184513920792475, 738 'gsl_sf_fermi_dirac_2_e( 2.5,$r)' => 6.797764392735056317, 739 'gsl_sf_fermi_dirac_2_e( 10.0,$r)' => 183.11605273482105278, 740 'gsl_sf_fermi_dirac_2_e( 12.0,$r)' => 307.73921494638635166, 741 'gsl_sf_fermi_dirac_2_e( 20.0,$r)' => 1366.2320146723590157, 742 'gsl_sf_fermi_dirac_2_e( 50.0,$r)' => 20915.580036675744655, 743 'gsl_sf_fermi_dirac_2_e(200.0,$r)' => 1.3336623201467029786e+06, 744 'gsl_sf_fermi_dirac_mhalf_e(-10.0,$r)' => 0.00004539847236080549532, 745 'gsl_sf_fermi_dirac_mhalf_e( -2.0,$r)' => 0.12366562180120994266, 746 'gsl_sf_fermi_dirac_mhalf_e( -1.0,$r)' => 0.29402761761145122022, 747 'gsl_sf_fermi_dirac_mhalf_e( -0.4,$r)' => 0.4631755336886027800, 748 'gsl_sf_fermi_dirac_mhalf_e( 0.4,$r)' => 0.7654084737661656915, 749 'gsl_sf_fermi_dirac_mhalf_e( 1.0,$r)' => 1.0270571254743506890, 750 'gsl_sf_fermi_dirac_mhalf_e( 1.5,$r)' => 1.2493233478527122008, 751 'gsl_sf_fermi_dirac_mhalf_e( 2.5,$r)' => 1.6663128834358313625, 752 'gsl_sf_fermi_dirac_mhalf_e( 10.0,$r)' => 3.552779239536617160, 753 'gsl_sf_fermi_dirac_mhalf_e( 12.0,$r)' => 3.897268231925439359, 754 'gsl_sf_fermi_dirac_mhalf_e( 20.0,$r)' => 5.041018507535328603, 755 'gsl_sf_fermi_dirac_mhalf_e( 50.0,$r)' => 7.977530858581869960, 756 'gsl_sf_fermi_dirac_half_e(-10.0,$r)' => 0.00004539920105264132755, 757 'gsl_sf_fermi_dirac_half_e( -2.0,$r)' => 0.12929851332007559106, 758 'gsl_sf_fermi_dirac_half_e( -1.0,$r)' => 0.3277951592607115477, 759 'gsl_sf_fermi_dirac_half_e( -0.4,$r)' => 0.5522452153690688947, 760 'gsl_sf_fermi_dirac_half_e( 0.4,$r)' => 1.0386797503389389277, 761 'gsl_sf_fermi_dirac_half_e( 1.0,$r)' => 1.5756407761513002308, 762 'gsl_sf_fermi_dirac_half_e( 1.5,$r)' => 2.1448608775831140360, 763 'gsl_sf_fermi_dirac_half_e( 2.5,$r)' => 3.606975377950373251, 764 'gsl_sf_fermi_dirac_half_e( 10.0,$r)' => 24.084656964637653615, 765 'gsl_sf_fermi_dirac_half_e( 12.0,$r)' => 31.540203287044242593, 766 'gsl_sf_fermi_dirac_half_e( 20.0,$r)' => 67.49151222165892049, 767 'gsl_sf_fermi_dirac_half_e( 50.0,$r)' => 266.09281252136259343, 768 'gsl_sf_fermi_dirac_3half_e(-10.0,$r)' => 0.00004539956540456176333, 769 'gsl_sf_fermi_dirac_3half_e( -2.0,$r)' => 0.13224678225177236685, 770 'gsl_sf_fermi_dirac_3half_e( -1.0,$r)' => 0.3466747947990574170, 771 'gsl_sf_fermi_dirac_3half_e( -0.4,$r)' => 0.6056120213305040910, 772 'gsl_sf_fermi_dirac_3half_e( 0.4,$r)' => 1.2258236403963668282, 773 'gsl_sf_fermi_dirac_3half_e( 1.0,$r)' => 2.0022581487784644573, 774 'gsl_sf_fermi_dirac_3half_e( 1.5,$r)' => 2.9277494127932173068, 775 'gsl_sf_fermi_dirac_3half_e( 2.5,$r)' => 5.768879312210516582, 776 'gsl_sf_fermi_dirac_3half_e( 10.0,$r)' => 101.00510084332600020, 777 'gsl_sf_fermi_dirac_3half_e( 12.0,$r)' => 156.51518642795728036, 778 'gsl_sf_fermi_dirac_3half_e( 20.0,$r)' => 546.5630100657601959, 779 'gsl_sf_fermi_dirac_3half_e( 50.0,$r)' => 5332.353566687145552, 780 'gsl_sf_fermi_dirac_int_e(3, -2.0,$r)' => 0.1342199155038680215, 781 'gsl_sf_fermi_dirac_int_e(3, 0.0,$r)' => 0.9470328294972459176, 782 'gsl_sf_fermi_dirac_int_e(3, 0.1,$r)' => 1.0414170610956165759, 783 'gsl_sf_fermi_dirac_int_e(3, 1.0,$r)' => 2.3982260822489407070, 784 'gsl_sf_fermi_dirac_int_e(3, 3.0,$r)' => 12.621635313399690724, 785 'gsl_sf_fermi_dirac_int_e(3, 100.0,$r)' => 4.174893231066566793e+06, 786 'gsl_sf_fermi_dirac_int_e(3, 500.0,$r)' => 2.604372285319088354e+09, 787 'gsl_sf_fermi_dirac_int_e(5, -2.0,$r)' => 0.13505242246823676478, 788 'gsl_sf_fermi_dirac_int_e(5, 0.0,$r)' => 0.9855510912974351041, 789 'gsl_sf_fermi_dirac_int_e(5, 0.1,$r)' => 1.0876519750101492782, 790 'gsl_sf_fermi_dirac_int_e(5, 1.0,$r)' => 2.6222337848692390539, 791 'gsl_sf_fermi_dirac_int_e(5, 3.0,$r)' => 17.008801618012113022, 792 'gsl_sf_fermi_dirac_int_e(5, 100.0,$r)' => 1.3957522531334869874e+09, 793 'gsl_sf_fermi_dirac_int_e(5, 500.0,$r)' => 2.1705672808114817955e+13, 794 'gsl_sf_fermi_dirac_int_e(7, -2.0,$r)' => 0.1352641105671255851, 795 'gsl_sf_fermi_dirac_int_e(7, 0.0,$r)' => 0.9962330018526478992, 796 'gsl_sf_fermi_dirac_int_e(7, 0.1,$r)' => 1.1005861815180315485, 797 'gsl_sf_fermi_dirac_int_e(7, 1.0,$r)' => 2.6918878172003129203, 798 'gsl_sf_fermi_dirac_int_e(7, 3.0,$r)' => 19.033338976999367642, 799 'gsl_sf_fermi_dirac_int_e(7, 10.0,$r)' => 5654.530932873610014, 800 'gsl_sf_fermi_dirac_int_e(7, 50.0,$r)' => 1.005005069985066278e+09, 801 'gsl_sf_fermi_dirac_int_e(7, 500.0,$r)' => 9.691690268341569514e+16, 802 'gsl_sf_fermi_dirac_int_e(9, -2.0,$r)' => 0.1353174385330242691, 803 'gsl_sf_fermi_dirac_int_e(9, 0.0,$r)' => 0.9990395075982715656, 804 'gsl_sf_fermi_dirac_int_e(9, 0.1,$r)' => 1.1039997234712941212, 805 'gsl_sf_fermi_dirac_int_e(9, 1.0,$r)' => 2.7113648898129249947, 806 'gsl_sf_fermi_dirac_int_e(9, 3.0,$r)' => 19.768544008138602223, 807 'gsl_sf_fermi_dirac_int_e(9, 10.0,$r)' => 10388.990167312912478, 808 'gsl_sf_fermi_dirac_int_e(9, 50.0,$r)' => 2.85466960802601649e+10, 809 'gsl_sf_fermi_dirac_int_e(9, 500.0,$r)' => 2.69273849842695876e+20, 810 'gsl_sf_fermi_dirac_int_e(10, -2.0,$r)' => 0.13532635396712288092, 811 'gsl_sf_fermi_dirac_int_e(10, 0.0,$r)' => 0.9995171434980607541, 812 'gsl_sf_fermi_dirac_int_e(10, 0.1,$r)' => 1.1045818238852612296, 813 'gsl_sf_fermi_dirac_int_e(10, 1.0,$r)' => 2.7147765350346120647, 814 'gsl_sf_fermi_dirac_int_e(10, 3.0,$r)' => 19.917151938411675171, 815 'gsl_sf_fermi_dirac_int_e(10, 10.0,$r)' => 12790.918595516495955, 816 'gsl_sf_fermi_dirac_int_e(10, 50.0,$r)' => 1.3147703201869657654e+11, 817 'gsl_sf_fermi_dirac_int_e(10, 500.0,$r)' => 1.2241331244469204398e+22, 818 'gsl_sf_fermi_dirac_int_e(11, -2.0,$r)' => 0.1353308162894847149, 819 'gsl_sf_fermi_dirac_int_e(11, 0.0,$r)' => 0.9997576851438581909, 820 'gsl_sf_fermi_dirac_int_e(11, 0.1,$r)' => 1.1048751811565850418, 821 'gsl_sf_fermi_dirac_int_e(11, 1.0,$r)' => 2.7165128749007313436, 822 'gsl_sf_fermi_dirac_int_e(11, 3.0,$r)' => 19.997483022044603065, 823 'gsl_sf_fermi_dirac_int_e(11, 10.0,$r)' => 14987.996005901818036, 824 'gsl_sf_fermi_dirac_int_e(11, 50.0,$r)' => 5.558322924078990628e+11, 825 'gsl_sf_fermi_dirac_int_e(11, 500.0,$r)' => 5.101293089606198280e+23, 826 'gsl_sf_fermi_dirac_int_e(20, -2.0,$r)' => 0.13533527450327238373, 827 'gsl_sf_fermi_dirac_int_e(20, 0.0,$r)' => 0.9999995232582155428, 828 'gsl_sf_fermi_dirac_int_e(20, 0.1,$r)' => 1.1051703357941368203, 829 'gsl_sf_fermi_dirac_int_e(20, 1.0,$r)' => 2.7182783069905721654, 830 'gsl_sf_fermi_dirac_int_e(20, 3.0,$r)' => 20.085345296028242734, 831 'gsl_sf_fermi_dirac_int_e(20, 10.0,$r)' => 21898.072920149606475, 832 'gsl_sf_fermi_dirac_int_e(20, 50.0,$r)' => 1.236873256595717618e+16, 833 'gsl_sf_fermi_dirac_int_e(20, 500.0,$r)' => 9.358938204369557277e+36, 834 'gsl_sf_gegenpoly_1_e(-0.2, 1.0,$r)' => -0.4, 835 'gsl_sf_gegenpoly_1_e( 0.0, 1.0,$r)' => 2.0, 836 'gsl_sf_gegenpoly_1_e( 1.0, 1.0,$r)' => 2.0, 837 'gsl_sf_gegenpoly_1_e( 1.0, 0.5,$r)' => 1.0, 838 'gsl_sf_gegenpoly_1_e( 5.0, 1.0,$r)' => 10.0, 839 'gsl_sf_gegenpoly_1_e( 100.0, 0.5,$r)' => 100.0, 840 'gsl_sf_gegenpoly_2_e(-0.2, 0.5,$r)' => 0.12, 841 'gsl_sf_gegenpoly_2_e( 0.0, 1.0,$r)' => 1.00, 842 'gsl_sf_gegenpoly_2_e( 1.0, 1.0,$r)' => 3.00, 843 'gsl_sf_gegenpoly_2_e( 1.0, 0.1,$r)' => -0.96, 844 'gsl_sf_gegenpoly_2_e( 5.0, 1.0,$r)' => 55.0, 845 'gsl_sf_gegenpoly_2_e( 100.0, 0.5,$r)' => 4950.0, 846 'gsl_sf_gegenpoly_3_e(-0.2, 0.5,$r)' => 0.112, 847 'gsl_sf_gegenpoly_3_e( 0.0, 1.0,$r)' => -2.0/3.0, 848 'gsl_sf_gegenpoly_3_e( 1.0, 1.0,$r)' => 4.000, 849 'gsl_sf_gegenpoly_3_e( 1.0, 0.1,$r)' => -0.392, 850 'gsl_sf_gegenpoly_3_e( 5.0, 1.0,$r)' => 220.000, 851 'gsl_sf_gegenpoly_3_e( 100.0, 0.5,$r)' => 161600.000, 852 'gsl_sf_gegenpoly_n_e(1, 1.0, 1.0,$r)' => 2.000 , 853 'gsl_sf_gegenpoly_n_e(10, 1.0, 1.0,$r)' => 11.000 , 854 'gsl_sf_gegenpoly_n_e(10, 1.0, 0.1,$r)' => -0.4542309376 , 855 'gsl_sf_gegenpoly_n_e(10, 5.0, 1.0,$r)' => 9.23780e+4 , 856 'gsl_sf_gegenpoly_n_e(10, 100.0, 0.5,$r)' => 1.5729338392690000e+13, 857 'gsl_sf_gegenpoly_n_e(1000, 100.0, 1.0,$r)' => 3.3353666135627322e+232, 858 'gsl_sf_gegenpoly_n_e(100, 2000.0, 1.0,$r)' => 5.8753432034937579e+202, 859 'gsl_sf_gegenpoly_n_e(103, 207.0, 2.0,$r)' => 1.4210272202235983e+145, 860 'gsl_sf_gegenpoly_n_e(103, -0.4, 0.3,$r)' => -1.64527498094522e-04, 861 'gsl_sf_laguerre_1_e(0.5, -1.0,$r)' => 2.5, 862 'gsl_sf_laguerre_1_e(0.5, 1.0,$r)' => 0.5, 863 'gsl_sf_laguerre_1_e(1.0, 1.0,$r)' => 1.0, 864 'gsl_sf_laguerre_2_e( 0.5, -1.0,$r)' => 4.875, 865 'gsl_sf_laguerre_2_e( 0.5, 1.0,$r)' => -0.125, 866 'gsl_sf_laguerre_2_e( 1.0, 1.0,$r)' => 0.5, 867 'gsl_sf_laguerre_2_e(-1.0, 1.0,$r)' => -0.5, 868 'gsl_sf_laguerre_2_e(-2.0, 1.0,$r)' => 0.5, 869 'gsl_sf_laguerre_2_e(-3.0, 1.0,$r)' => 2.5, 870 'gsl_sf_laguerre_3_e(0.5, -1.0,$r)' => 8.479166666666666667, 871 'gsl_sf_laguerre_3_e(0.5, 1.0,$r)' => -0.6041666666666666667, 872 'gsl_sf_laguerre_3_e(1.0, 1.0,$r)' => -0.16666666666666666667, 873 'gsl_sf_laguerre_3_e( 2.0, 1.0,$r)' => 2.3333333333333333333, 874 'gsl_sf_laguerre_3_e(-2.0, 1.0,$r)' => 1.0/3.0, 875 'gsl_sf_laguerre_3_e(-3.0, 1.0,$r)' => -1.0/6.0, 876 'gsl_sf_laguerre_3_e(-4.0, 1.0,$r)' => -8.0/3.0, 877 'gsl_sf_laguerre_n_e(1, 0.5, 1.0,$r)' => 0.5, 878 'gsl_sf_laguerre_n_e(2, 1.0, 1.0,$r)' => 0.5, 879 'gsl_sf_laguerre_n_e(3, 2.0, 1.0,$r)' => 2.3333333333333333333, 880 'gsl_sf_laguerre_n_e(4, 2.0, 0.5,$r)' => 6.752604166666666667, 881 'gsl_sf_laguerre_n_e(90, 2.0, 0.5,$r)' => -48.79047157201507897, 882 'gsl_sf_laguerre_n_e(90, 2.0, -100.0,$r)' => 2.5295879275042410902e+63, 883 'gsl_sf_laguerre_n_e(90, 2.0, 100.0,$r)' => -2.0929042259546928670e+20, 884 'gsl_sf_laguerre_n_e(100, 2.0, 0.5,$r)' => -28.764832945909097418, 885 'gsl_sf_laguerre_n_e(1000, 2.0, -0.5,$r)' => 2.4399915170947549589e+21, 886 'gsl_sf_laguerre_n_e(1000, 2.0, 0.5,$r)' => -306.77440254315317525, 887 'gsl_sf_laguerre_n_e(100000, 2.0, 1.0,$r)' => 5107.73491348319, 888 'gsl_sf_laguerre_n_e(1e5, 2.5, 2.5,$r)' => -0.41491680394598644969113795e5, 889 'gsl_sf_laguerre_n_e(1e5+1, 2.5, 2.5,$r)' => -0.41629446949552321027514888e5, 890 'gsl_sf_laguerre_n_e(1e6+1, 2.5, 2.5,$r)' => -0.48017961545391273151977118e6, 891 'gsl_sf_laguerre_n_e(5e6+1, 2.5, 2.5,$r)' => -0.15174037401611122446089494e7, 892 'gsl_sf_laguerre_n_e(8e6+1, 2.5, 2.5,$r)' => 0.63251509472091810994286362e6, 893 'gsl_sf_laguerre_n_e(1e7+1, 2.5, 2.5,$r)' => 0.15299484685632983178033887e7, 894 'gsl_sf_laguerre_n_e(1e8+1, 2.5, 2.5,$r)' => 0.23645341644922756725290777e8, 895 'gsl_sf_laguerre_n_e(1e9+1, 2.5, 2.5,$r)' => -0.17731002248958790286185878e8, 896 'gsl_sf_laguerre_n_e(1, -2.0, 1.0,$r)' => -2.0, 897 'gsl_sf_laguerre_n_e(2, -2.0, 1.0,$r)' => 0.5, 898 'gsl_sf_laguerre_n_e(3, -2.0, 1.0,$r)' => 1.0/3.0, 899 'gsl_sf_laguerre_n_e(10, -2.0, 1.0,$r)' => -0.04654954805996472663, 900 'gsl_sf_laguerre_n_e(10, -5.0, 1.0,$r)' => -0.0031385030864197530864, 901 'gsl_sf_laguerre_n_e(10, -9.0, 1.0,$r)' => -2.480158730158730159e-06, 902 'gsl_sf_laguerre_n_e(10, -11.0, 1.0,$r)' => 2.7182818011463844797, 903 'gsl_sf_laguerre_n_e(10, -11.0, -1.0,$r)' => 0.3678794642857142857, 904 'gsl_sf_laguerre_n_e(100, -2.0, 1.0,$r)' => -0.0027339992019526273866, 905 'gsl_sf_laguerre_n_e(100, -2.0, -1.0,$r)' => 229923.09193402028290, 906 'gsl_sf_laguerre_n_e(100, -10.0, 1.0,$r)' => 3.25966665871244092e-11, 907 'gsl_sf_laguerre_n_e(100, -10.0, -1.0,$r)' => 0.00016484365618205810025, 908 'gsl_sf_laguerre_n_e(100, -20.0, 1.0,$r)' => 5.09567630343671251e-21, 909 'gsl_sf_laguerre_n_e(100, -30.0, 1.0,$r)' => 3.46063150272466192e-34, 910 'gsl_sf_laguerre_n_e(100, -50.0, 1.0,$r)' => 1.20981872933162889e-65, 911 'gsl_sf_laguerre_n_e(100, -50.0, -1.0,$r)' => 8.60763477742332922e-65, 912 'gsl_sf_laguerre_n_e(100, -50.5, 1.0,$r)' => 4.84021010426688393e-31, 913 'gsl_sf_laguerre_n_e(100, -50.5, -1.0,$r)' => 8.49861345212160618e-33, 914 'gsl_sf_laguerre_n_e(100, -101.0, 1.0,$r)' => 2.7182818284590452354, 915 'gsl_sf_laguerre_n_e(100, -101.0, -1.0,$r)' => 0.3678794411714423216, 916 'gsl_sf_laguerre_n_e(100, -102.0, 1.0,$r)' => 271.8281828459045235, 917 'gsl_sf_laguerre_n_e(100, -102.0, -1.0,$r)' => 37.52370299948711680, 918 'gsl_sf_laguerre_n_e(100, -110.0, 1.0,$r)' => 1.0666955248998831554e+13, 919 'gsl_sf_laguerre_n_e(100, -110.0, -1.0,$r)' => 1.7028306108058225871e+12, 920 'gsl_sf_laguerre_n_e(100, -200.0, 1.0,$r)' => 7.47851889721356628e+58, 921 'gsl_sf_laguerre_n_e(100, -200.0, -1.0,$r)' => 2.73740299754732273e+58, 922 'gsl_sf_laguerre_n_e(100, -50.0, 10.0,$r)' => 4.504712811317745591e-21, 923 'gsl_sf_laguerre_n_e(100, -50.0, -10.0,$r)' => 1.475165520610679937e-11, 924 'gsl_sf_laguerre_n_e(100, 0.0, 0.5,$r)' => 0.18682260367692278801, 925 'gsl_sf_laguerre_n_e(100, 0.0, 10.5,$r)' => 9.1796907354050059874, 926 'gsl_sf_laguerre_n_e(100, 0.0, -10.5,$r)' => 5.6329215744170606488e24, 927 'gsl_sf_laguerre_n_e(100, 0.0, 100.5,$r)' => -3.9844782875811907525e20, 928 'gsl_sf_laguerre_n_e(100, 0.0, 150,$r)' => -1.4463204337261709595e31, 929 'gsl_sf_lambert_W0_e(0.0,$r)' => 0.0, 930 'gsl_sf_lambert_W0_e(1.0,$r)' => 0.567143290409783872999969, 931 'gsl_sf_lambert_W0_e(2.0,$r)' => 0.852605502013725491346472, 932 'gsl_sf_lambert_W0_e(20.0,$r)' => 2.205003278024059970493066, 933 'gsl_sf_lambert_W0_e(1000.0,$r)' => 5.24960285240159622712606, 934 'gsl_sf_lambert_W0_e(1.0e+6,$r)' => 11.38335808614005262200016, 935 'gsl_sf_lambert_W0_e(1.0e+12,$r)' => 24.43500440493491313826305, 936 'gsl_sf_lambert_W0_e(1.0e+308,$r)' => 702.641362034106812081125, 937 'gsl_sf_lambert_W0_e(1.6849341956993852953416990,$r)' => 0.775706963944252869680440, 938 'gsl_sf_lambert_W0_e(-1.0/$M_E - $GSL_DBL_EPSILON,$r)' => -1.0, 939 'gsl_sf_lambert_W0_e(-1.0/$M_E + 1.0/(1024.0*1024.0*1024.0),$r)' => -0.999928845560308370714970, 940 'gsl_sf_lambert_W0_e(-1.0/$M_E + 1.0/(1024.0*1024.0),$r)' => -0.997724730359774141620354, 941 'gsl_sf_lambert_W0_e(-1.0/$M_E + 1.0/512.0,$r)' => -0.900335676696088773044678, 942 'gsl_sf_lambert_W0_e(-1.0/$M_E + 0.25,$r)' => -0.1349044682661213545487599, 943 'gsl_sf_lambert_Wm1_e(0.0,$r)' => 0.0, 944 'gsl_sf_lambert_Wm1_e(1.0,$r)' => 0.567143290409783872999969, 945 'gsl_sf_lambert_Wm1_e(2.0,$r)' => 0.852605502013725491346472, 946 'gsl_sf_lambert_Wm1_e(20.0,$r)' => 2.205003278024059970493066, 947 'gsl_sf_lambert_Wm1_e(-1.0/$M_E - $GSL_DBL_EPSILON,$r)' => -1.0, 948 'gsl_sf_lambert_Wm1_e(-1.0/$M_E + 1.0/(1024.0*1024.0*1024.0),$r)' => -1.000071157815154608049055, 949 'gsl_sf_lambert_Wm1_e(-1.0/$M_E + 1.0/(1024.0*1024.0),$r)' => -1.002278726118593023934693, 950 'gsl_sf_lambert_Wm1_e(-1.0/$M_E + 1.0/512.0,$r)' => -1.106761200865743124599130, 951 'gsl_sf_lambert_Wm1_e(-1.0/$M_E + 1.0/64.0,$r)' => -1.324240940341812125489772, 952 'gsl_sf_lambert_Wm1_e(-1.0/$M_E + 0.25,$r)' => -3.345798131120112, 953 'gsl_sf_log_e(0.1,$r)' => -2.3025850929940456840, 954 'gsl_sf_log_e(1.1,$r)' => 0.09531017980432486004, 955 'gsl_sf_log_e(1000.0,$r)' => 6.907755278982137052, 956 'gsl_sf_log_abs_e(-0.1,$r)' => -2.3025850929940456840, 957 'gsl_sf_log_abs_e(-1.1,$r)' => 0.09531017980432486004, 958 'gsl_sf_log_abs_e(-1000.0,$r)' => 6.907755278982137052, 959 'gsl_sf_log_abs_e(0.1,$r)' => -2.3025850929940456840, 960 'gsl_sf_log_abs_e(1.1,$r)' => 0.09531017980432486004, 961 'gsl_sf_log_abs_e(1000.0,$r)' => 6.907755278982137052, 962 'gsl_sf_log_1plusx_e(1.0e-10,$r)' => 9.999999999500000000e-11, 963 'gsl_sf_log_1plusx_e(1.0e-8,$r)' => 9.999999950000000333e-09, 964 'gsl_sf_log_1plusx_e(1.0e-4,$r)' => 0.00009999500033330833533, 965 'gsl_sf_log_1plusx_e(0.1,$r)' => 0.09531017980432486004, 966 'gsl_sf_log_1plusx_e(0.49,$r)' => 0.3987761199573677730, 967 'gsl_sf_log_1plusx_e(-0.49,$r)' => -0.6733445532637655964, 968 'gsl_sf_log_1plusx_e(1.0,$r)' => $M_LN2, 969 'gsl_sf_log_1plusx_e(-0.99,$r)' => -4.605170185988091368, 970 'gsl_sf_log_1plusx_mx_e(1.0e-10,$r)' => -4.999999999666666667e-21, 971 'gsl_sf_log_1plusx_mx_e(1.0e-8,$r)' => -4.999999966666666917e-17, 972 'gsl_sf_log_1plusx_mx_e(1.0e-4,$r)' => -4.999666691664666833e-09, 973 'gsl_sf_log_1plusx_mx_e(0.1,$r)' => -0.004689820195675139956, 974 'gsl_sf_log_1plusx_mx_e(0.49,$r)' => -0.09122388004263222704, 975 'gsl_sf_log_1plusx_mx_e(-0.49,$r)' => -0.18334455326376559639, 976 'gsl_sf_log_1plusx_mx_e(1.0,$r)' => $M_LN2-1.0, 977 'gsl_sf_log_1plusx_mx_e(-0.99,$r)' => -3.615170185988091368, 978 'gsl_sf_pow_int_e(2.0, 3,$r)' => 8.0, 979 'gsl_sf_pow_int_e(-2.0, 3,$r)' => -8.0, 980 'gsl_sf_pow_int_e(2.0, -3,$r)' => 1.0/8.0, 981 'gsl_sf_pow_int_e(-2.0, -3,$r)' => -1.0/8.0, 982 'gsl_sf_pow_int_e(10.0, 4,$r)' => 1.0e+4, 983 'gsl_sf_pow_int_e(10.0, -4,$r)' => 1.0e-4, 984 'gsl_sf_pow_int_e(-10.0, 4,$r)' => 1.0e+4, 985 'gsl_sf_pow_int_e(-10.0, -4,$r)' => 1.0e-4, 986 'gsl_sf_pow_int_e(10.0, 40,$r)' => 1.0e+40, 987 'gsl_sf_pow_int_e(8.0, -40,$r)' => 7.523163845262640051e-37, 988 'gsl_sf_pow_int_e(-10.0, 40,$r)' => 1.0e+40, 989 'gsl_sf_pow_int_e(-8.0, -40,$r)' => 7.523163845262640051e-37, 990 'gsl_sf_pow_int_e(10.0, 41,$r)' => 1.0e+41, 991 'gsl_sf_pow_int_e(8.0, -41,$r)' => 9.403954806578300064e-38, 992 'gsl_sf_pow_int_e(-10.0, 41,$r)' => -1.0e+41, 993 'gsl_sf_pow_int_e(-8.0, -41,$r)' => -9.403954806578300064e-38, 994 'gsl_sf_psi_int_e(1,$r)' => -0.57721566490153286060, 995 'gsl_sf_psi_int_e(2,$r)' => 0.42278433509846713939, 996 'gsl_sf_psi_int_e(3,$r)' => 0.92278433509846713939, 997 'gsl_sf_psi_int_e(4,$r)' => 1.2561176684318004727, 998 'gsl_sf_psi_int_e(5,$r)' => 1.5061176684318004727, 999 'gsl_sf_psi_int_e(100,$r)' => 4.600161852738087400, 1000 'gsl_sf_psi_int_e(110,$r)' => 4.695928024251535633, 1001 'gsl_sf_psi_int_e(5000,$r)' => 8.517093188082904107, 1002 'gsl_sf_psi_e(5000.0,$r)' => 8.517093188082904107, 1003 'gsl_sf_psi_e(5.0,$r)' => 1.5061176684318004727, 1004 'gsl_sf_psi_e(-10.5,$r)' => 2.3982391295357816134, 1005 'gsl_sf_psi_e(-100.5,$r)' => 4.615124601338064117, 1006 'gsl_sf_psi_e(-1.0e+5-0.5,$r)' => 11.512935464924395337, 1007 'gsl_sf_psi_e(-262144.0-0.5,$r)' => 12.476653064769611581, 1008 'gsl_sf_psi_1piy_e(0.8,$r)' => -0.07088340212750589223, 1009 'gsl_sf_psi_1piy_e(1.0,$r)' => 0.09465032062247697727, 1010 'gsl_sf_psi_1piy_e(5.0,$r)' => 1.6127848446157465854, 1011 'gsl_sf_psi_1piy_e(100.0,$r)' => 4.605178519404762003, 1012 'gsl_sf_psi_1piy_e(2000.0,$r)' => 7.600902480375416216, 1013 'gsl_sf_psi_1piy_e(-0.8,$r)' => -0.07088340212750589223, 1014 'gsl_sf_psi_1piy_e(-1.0,$r)' => 0.09465032062247697727, 1015 'gsl_sf_psi_1piy_e(-5.0,$r)' => 1.6127848446157465854, 1016 'gsl_sf_psi_1piy_e(-100.0,$r)' => 4.605178519404762003, 1017 'gsl_sf_psi_1piy_e(-2000.0,$r)' => 7.600902480375416216, 1018 'gsl_sf_psi_1_int_e(1,$r)' => 1.6449340668482264364, 1019 'gsl_sf_psi_1_int_e(2,$r)' => 0.64493406684822643647, 1020 'gsl_sf_psi_1_int_e(3,$r)' => 0.39493406684822643647, 1021 'gsl_sf_psi_1_int_e(4,$r)' => 0.28382295573711532536, 1022 'gsl_sf_psi_1_int_e(1,$r)' => 1.6449340668482264365, 1023 'gsl_sf_psi_1_int_e(5,$r)' => 0.22132295573711532536, 1024 'gsl_sf_psi_1_int_e(100,$r)' => 0.010050166663333571395, 1025 'gsl_sf_psi_1_int_e(110,$r)' => 0.009132356622022545705, 1026 'gsl_sf_psi_1_int_e(500,$r)' => 0.0020020013333322666697, 1027 'gsl_sf_psi_1_e(1.0/32.0,$r)' => 1025.5728544782377089, 1028 'gsl_sf_psi_1_e(1.0,$r)' => 1.6449340668482264365, 1029 'gsl_sf_psi_1_e(5.0,$r)' => 0.22132295573711532536, 1030 'gsl_sf_psi_1_e(100.0,$r)' => 0.010050166663333571395, 1031 'gsl_sf_psi_1_e(110.0,$r)' => 0.009132356622022545705, 1032 'gsl_sf_psi_1_e(500.0,$r)' => 0.0020020013333322666697, 1033 'gsl_sf_psi_1_e(-1.0 - 1.0/128.0,$r)' => 16386.648472598746587, 1034 'gsl_sf_psi_1_e(-1.50,$r)' => 9.3792466449891237539, 1035 'gsl_sf_psi_1_e(-10.5,$r)' => 9.7787577398148123845, 1036 'gsl_sf_psi_1_e(-15.5,$r)' => 9.8071247184113896201, 1037 'gsl_sf_psi_1_e(-50.5,$r)' => 9.8499971860824842274, 1038 'gsl_sf_psi_1_e(-1000.5,$r)' => 9.8686054001734414233, 1039 'gsl_sf_psi_n_e(1, 1,$r)' => 1.6449340668482264364, 1040 'gsl_sf_psi_n_e(1, 2,$r)' => 0.64493406684822643647, 1041 'gsl_sf_psi_n_e(1, 3,$r)' => 0.39493406684822643647, 1042 'gsl_sf_psi_n_e(1, 4,$r)' => 0.28382295573711532536, 1043 'gsl_sf_psi_n_e(1, 5,$r)' => 0.22132295573711532536, 1044 'gsl_sf_psi_n_e(1, 100,$r)' => 0.010050166663333571395, 1045 'gsl_sf_psi_n_e(1, 110,$r)' => 0.009132356622022545705, 1046 'gsl_sf_psi_n_e(1, 500,$r)' => 0.0020020013333322666697, 1047 'gsl_sf_psi_n_e(3, 5.0,$r)' => 0.021427828192755075022, 1048 'gsl_sf_psi_n_e(3, 500.0,$r)' => 1.6048063999872000683e-08, 1049 'gsl_sf_psi_n_e(10, 5.0,$r)' => -0.08675107579196581317, 1050 'gsl_sf_psi_n_e(10, 50.0,$r)' => -4.101091112731268288e-12, 1051 'gsl_sf_psi_n_e(0, -1.5,$r)' => 0.70315664064524318723, 1052 'gsl_sf_psi_n_e(1, -1.5,$r)' => 9.3792466449891237539, 1053 'gsl_sf_synchrotron_1_e(0.01,$r)' => 0.444972504114210632, 1054 'gsl_sf_synchrotron_1_e(1.0,$r)' => 0.651422815355364504, 1055 'gsl_sf_synchrotron_1_e(10.0,$r)' => 0.000192238264300868882, 1056 'gsl_sf_synchrotron_1_e(100.0,$r)' => 4.69759366592220221e-43, 1057 'gsl_sf_synchrotron_2_e(0.01,$r)' => 0.23098077342226277732, 1058 'gsl_sf_synchrotron_2_e(1.0,$r)' => 0.4944750621042082670, 1059 'gsl_sf_synchrotron_2_e(10.0,$r)' => 0.00018161187569530204281, 1060 'gsl_sf_synchrotron_2_e(256.0,$r)' => 1.3272635474353774058e-110, 1061 'gsl_sf_transport_2_e(1.0e-10,$r)' => 9.9999999999999999999e-11, 1062 'gsl_sf_transport_2_e(1.0,$r)' => 0.97303256135517012845, 1063 'gsl_sf_transport_2_e(3.0,$r)' => 2.41105004901695346199, 1064 'gsl_sf_transport_2_e(10.0,$r)' => 3.28432911449795173575, 1065 'gsl_sf_transport_2_e(100.0,$r)' => 3.28986813369645287294, 1066 'gsl_sf_transport_2_e(1.0e+05,$r)' => 3.28986813369645287294, 1067 'gsl_sf_transport_3_e(1.0e-10,$r)' => 4.999999999999999999997e-21, 1068 'gsl_sf_transport_3_e(1.0,$r)' => 0.479841006572417499939, 1069 'gsl_sf_transport_3_e(3.0,$r)' => 3.210604662942246772338, 1070 'gsl_sf_transport_3_e(5.0,$r)' => 5.614386613842273228585, 1071 'gsl_sf_transport_3_e(10.0,$r)' => 7.150322712008592975030, 1072 'gsl_sf_transport_3_e(30.0,$r)' => 7.212341416160946511930, 1073 'gsl_sf_transport_3_e(100.0,$r)' => 7.212341418957565712398, 1074 'gsl_sf_transport_3_e(1.0e+05,$r)' => 7.212341418957565712398, 1075 'gsl_sf_transport_4_e(1.0e-10,$r)' => 3.33333333333333333333e-31, 1076 'gsl_sf_transport_4_e(1.0e-07,$r)' => 3.33333333333333166666e-22, 1077 'gsl_sf_transport_4_e(1.0e-04,$r)' => 3.33333333166666666726e-13, 1078 'gsl_sf_transport_4_e(0.1,$r)' => 0.000333166726172109903824, 1079 'gsl_sf_transport_4_e(1.0,$r)' => 0.31724404523442648241, 1080 'gsl_sf_transport_4_e(3.0,$r)' => 5.96482239737147652446, 1081 'gsl_sf_transport_4_e(5.0,$r)' => 15.3597843168821829816, 1082 'gsl_sf_transport_4_e(10.0,$r)' => 25.2736676770304417334, 1083 'gsl_sf_transport_4_e(30.0,$r)' => 25.9757575220840937469, 1084 'gsl_sf_transport_4_e(100.0,$r)' => 25.9757576090673165963, 1085 'gsl_sf_transport_4_e(1.0e+05,$r)' => 25.9757576090673165963, 1086 'gsl_sf_transport_5_e(1.0e-10,$r)' => 2.49999999999999999999e-41, 1087 'gsl_sf_transport_5_e(1.0e-07,$r)' => 2.49999999999999861111e-29, 1088 'gsl_sf_transport_5_e(1.0e-04,$r)' => 2.49999999861111111163e-17, 1089 'gsl_sf_transport_5_e(0.1,$r)' => 0.000024986116317791487410, 1090 'gsl_sf_transport_5_e(1.0,$r)' => 0.236615879239094789259153, 1091 'gsl_sf_transport_5_e(3.0,$r)' => 12.77055769104415951115760, 1092 'gsl_sf_transport_5_e(5.0,$r)' => 50.26309221817518778543615, 1093 'gsl_sf_transport_5_e(10.0,$r)' => 116.3807454024207107698556, 1094 'gsl_sf_transport_5_e(30.0,$r)' => 124.4313279083858954839911, 1095 'gsl_sf_transport_5_e(100.0,$r)' => 124.4313306172043911597639, 1096 'gsl_sf_transport_5_e(1.0e+05,$r)' => 124.43133061720439115976, 1097 'gsl_sf_sin(-10.0)' => 0.5440211108893698134, 1098 'gsl_sf_sin(1.0)' => 0.8414709848078965067, 1099 'gsl_sf_sin(1000.0)' => 0.8268795405320025603, 1100 'gsl_sf_sin(1048576.75)' => 0.8851545351115651914, 1101 'gsl_sf_sin(62831853.75)' => 0.6273955953485000827, 1102 'gsl_sf_sin(1073741822.5)' => -0.8284043541754465988, 1103 'gsl_sf_sin(1073741824.0)' => -0.6173264150460421708, 1104 'gsl_sf_sin(1073741825.5)' => 0.7410684679436226926, 1105 'gsl_sf_sin(1099511627776.0)' => -0.4057050115328287198, 1106 'gsl_sf_cos(-10.0)' => -0.8390715290764524523, 1107 'gsl_sf_cos(1.0)' => 0.5403023058681397174, 1108 'gsl_sf_cos(1000.0)' => 0.5623790762907029911, 1109 'gsl_sf_cos(1048576.75)' => 0.4652971620066351799, 1110 'gsl_sf_cos(62831853.75)' => 0.7787006914966116436, 1111 'gsl_sf_cos(1073741822.5)' => -0.5601305436977716102, 1112 'gsl_sf_cos(1073741824.0)' => 0.7867071229411881196, 1113 'gsl_sf_cos(1099511627776.0)' => -0.9140040719915570023, 1114 'gsl_sf_sinc_e(1.0/1024.0,$r)' => 0.9999984312693665404, 1115 'gsl_sf_sinc_e(1.0/2.0 ,$r)' => 2.0/$M_PI, 1116 'gsl_sf_sinc_e(80.5 ,$r)' => 0.0039541600768172754, 1117 'gsl_sf_sinc_e(100.5 ,$r)' => 0.0031672625490924445, 1118 'gsl_sf_sinc_e(1.0e+06 + 0.5,$r)' => 3.18309727028927157e-07, 1119 'gsl_sf_lnsinh_e(0.1,$r)' => -2.3009189815304652235, 1120 'gsl_sf_lnsinh_e(1.0,$r)' => 0.16143936157119563361, 1121 'gsl_sf_lnsinh_e(5.0,$r)' => 4.306807418479684201, 1122 'gsl_sf_lnsinh_e(100.0,$r)' => 99.30685281944005469, 1123 'gsl_sf_lncosh_e(0.125,$r)' => 0.007792239318898252791, 1124 'gsl_sf_lncosh_e(1.0,$r)' => 0.4337808304830271870, 1125 'gsl_sf_lncosh_e(5.0,$r)' => 4.306898218339271555, 1126 'gsl_sf_lncosh_e(100.0,$r)' => 99.30685281944005469, 1127 'gsl_sf_angle_restrict_pos_err_e(2.0*$M_PI,$r)' => 2*$M_PI, 1128 'gsl_sf_angle_restrict_pos_err_e(-2.0*$M_PI,$r)' => 2*$DELTA, 1129 'gsl_sf_angle_restrict_pos_err_e(1e9,$r)' => 0.5773954235013851694, 1130 'gsl_sf_angle_restrict_pos_err_e(1e12,$r)' => 5.625560548042800009446, 1131 'gsl_sf_angle_restrict_pos_err_e(-1e9,$r)' => 5.7057898836782013075, 1132 'gsl_sf_angle_restrict_pos_err_e(-1e12,$r)' => 0.6576247591367864674792517289, 1133 'gsl_sf_angle_restrict_symm_err_e(1e9,$r)' => 0.5773954235013851694, 1134 'gsl_sf_angle_restrict_symm_err_e(1e12,$r)' => -0.6576247591367864674792517289, 1135 'gsl_sf_angle_restrict_symm_err_e(-1e9,$r)' => -0.5773954235013851694, 1136 'gsl_sf_angle_restrict_symm_err_e(-1e12,$r)' => 0.6576247591367864674792517289, 1137 'gsl_sf_zeta_int_e(-61.0,$r)' => -3.30660898765775767257e+34, 1138 'gsl_sf_zeta_int_e(-8,$r)' => 0.0, 1139 'gsl_sf_zeta_int_e(-6,$r)' => 0.0, 1140 'gsl_sf_zeta_int_e(-5.0,$r)' => -0.003968253968253968253968, 1141 'gsl_sf_zeta_int_e(-4,$r)' => 0.0, 1142 'gsl_sf_zeta_int_e(-3,$r)' => 1.0/120.0, 1143 'gsl_sf_zeta_int_e(-2,$r)' => 0.0, 1144 'gsl_sf_zeta_int_e(-1,$r)' => -1.0/12.0, 1145 'gsl_sf_zeta_int_e( 5.0,$r)' => 1.0369277551433699263313655, 1146 'gsl_sf_zeta_int_e(31.0,$r)' => 1.0000000004656629065033784, 1147 'gsl_sf_zetam1_int_e(-61.0,$r)' => -3.30660898765775767257e+34, 1148 'gsl_sf_zetam1_int_e(-5.0,$r)' => -1.003968253968253968253968, 1149 'gsl_sf_zetam1_int_e(-8,$r)' => -1.0, 1150 'gsl_sf_zetam1_int_e(-6,$r)' => -1.0, 1151 'gsl_sf_zetam1_int_e(-4,$r)' => -1.0, 1152 'gsl_sf_zetam1_int_e(-3,$r)' => -119.0/120.0, 1153 'gsl_sf_zetam1_int_e(-2,$r)' => -1.0, 1154 'gsl_sf_zetam1_int_e(-1,$r)' => -13.0/12.0, 1155 'gsl_sf_zetam1_int_e( 5.0,$r)' => 0.0369277551433699263313655, 1156 'gsl_sf_zetam1_int_e(31.0,$r)' => 0.0000000004656629065033784, 1157 'gsl_sf_zeta_e(-151,$r)' => 8.195215221831378294e+143, 1158 'gsl_sf_zeta_e(-51,$r)' => 9.68995788746359406565e+24, 1159 'gsl_sf_zeta_e(-5,$r)' => -0.003968253968253968253968, 1160 'gsl_sf_zeta_e(-8,$r)' => 0.0, 1161 'gsl_sf_zeta_e(-6,$r)' => 0.0, 1162 'gsl_sf_zeta_e(-4,$r)' => 0.0, 1163 'gsl_sf_zeta_e(-3,$r)' => 1.0/120.0, 1164 'gsl_sf_zeta_e(-2,$r)' => 0.0, 1165 'gsl_sf_zeta_e(-1,$r)' => -1.0/12.0, 1166 'gsl_sf_zeta_e(-0.5,$r)' => -0.207886224977354566017307, 1167 'gsl_sf_zeta_e(-1e-10,$r)' => -0.49999999990810614668948, 1168 'gsl_sf_zeta_e(0.0,$r)' => -0.5, 1169 'gsl_sf_zeta_e(1e-10,$r)' => -0.50000000009189385333058, 1170 'gsl_sf_zeta_e(0.5,$r)' => -1.460354508809586812889499, 1171 'gsl_sf_zeta_e(1.0-1.0/1024.0,$r)' => -1023.4228554489429787, 1172 'gsl_sf_zeta_e(1.0+1.0/1048576,$r)' => 1.0485765772157343441e+06, 1173 'gsl_sf_zeta_e(5.0,$r)' => 1.036927755143369926331365, 1174 'gsl_sf_zeta_e(25.5,$r)' => 1.000000021074106110269959, 1175 'gsl_sf_zetam1_e(-8,$r)' => -1.0, 1176 'gsl_sf_zetam1_e(-6,$r)' => -1.0, 1177 'gsl_sf_zetam1_e(-4,$r)' => -1.0, 1178 'gsl_sf_zetam1_e(-3,$r)' => -119.0/120.0, 1179 'gsl_sf_zetam1_e(-2,$r)' => -1.0, 1180 'gsl_sf_zetam1_e(-1,$r)' => -13.0/12.0, 1181 'gsl_sf_zetam1_e(-0.5,$r)' => -1.207886224977354566017307, 1182 'gsl_sf_zetam1_e(-1e-10,$r)' => -1.49999999990810614668948, 1183 'gsl_sf_zetam1_e(0.0,$r)' => -1.5, 1184 'gsl_sf_zetam1_e(1e-10,$r)' => -1.50000000009189385333058, 1185 'gsl_sf_zetam1_e(0.5,$r)' => -2.460354508809586812889499, 1186 'gsl_sf_zetam1_e(2.0,$r)' => 0.64493406684822643647, 1187 'gsl_sf_zetam1_e(3.0,$r)' => 0.20205690315959428540, 1188 'gsl_sf_zetam1_e(5.0,$r)' => 0.0369277551433699263314, 1189 'gsl_sf_zetam1_e(9.5,$r)' => 0.0014125906121736622712, 1190 'gsl_sf_zetam1_e(10.5,$r)' => 0.000700842641736155219500, 1191 'gsl_sf_zetam1_e(12.5,$r)' => 0.000173751733643178193390, 1192 'gsl_sf_zetam1_e(13.5,$r)' => 0.000086686727462338155188, 1193 'gsl_sf_zetam1_e(15.5,$r)' => 0.000021619904246069108133, 1194 'gsl_sf_zetam1_e(16.5,$r)' => 0.000010803124900178547671, 1195 'gsl_sf_zetam1_e(25.5,$r)' => 0.000000021074106110269959, 1196 'gsl_sf_hzeta_e(2, 1.0,$r)' => 1.6449340668482264365, 1197 'gsl_sf_hzeta_e(2, 10.0,$r)' => 0.1051663356816857461, 1198 'gsl_sf_hzeta_e(5, 1.0,$r)' => 1.0369277551433699263, 1199 'gsl_sf_hzeta_e(5, 10.0,$r)' => 0.000030413798676470276, 1200 'gsl_sf_hzeta_e(9, 0.1,$r)' => 1.0000000004253980e+09, 1201 'gsl_sf_hzeta_e(30, 0.5,$r)' => 1.0737418240000053e+09, 1202 'gsl_sf_hzeta_e(30, 0.9,$r)' => 2.3589824880264765e+01, 1203 'gsl_sf_hzeta_e(75, 0.25,$r)' => 1.4272476927059599e+45, 1204 'gsl_sf_eta_int_e(-91,$r)' => -4.945598888750002040e+94, 1205 'gsl_sf_eta_int_e(-51,$r)' => -4.363969073121683116e+40, 1206 'gsl_sf_eta_int_e(-5,$r)' => 0.25, 1207 'gsl_sf_eta_int_e(-1,$r)' => 0.25, 1208 'gsl_sf_eta_int_e( 0,$r)' => 0.5, 1209 'gsl_sf_eta_int_e( 5,$r)' => 0.9721197704469093059, 1210 'gsl_sf_eta_int_e( 6,$r)' => 0.9855510912974351041, 1211 'gsl_sf_eta_int_e( 20,$r)' => 0.9999990466115815221, 1212 'gsl_sf_eta_int_e( 1000,$r)' => 1.0, 1213 'gsl_sf_eta_e(-51.5, $r)' => -1.2524184036924703656e+41 , 1214 'gsl_sf_eta_e(-5, $r)' => 0.25, 1215 'gsl_sf_eta_e(0.5, $r)' => 0.6048986434216303702, 1216 'gsl_sf_eta_e(0.999, $r)' => 0.6929872789683383574, 1217 'gsl_sf_eta_e(1.0, $r)' => 0.6931471805599453094, 1218 'gsl_sf_eta_e(1.0+1.0e-10, $r)' => 0.6931471805759321998, 1219 'gsl_sf_eta_e( 5, $r)' => 0.9721197704469093059, 1220 'gsl_sf_eta_e( 5.2, $r)' => 0.9755278712546684682, 1221 'gsl_sf_eta_e( 6, $r)' => 0.9855510912974351041, 1222 'gsl_sf_eta_e( 20,$r)' => 0.9999990466115815221, 1223 }; 1224 1225 verify_results($results, 'Math::GSL::SF'); 1226} 1227 1228sub TEST_NAN_STRING : Tests(1) 1229{ 1230 my $self = shift; 1231 my $results = { 1232 'gsl_sf_gamma_e(-1,$r)' => $GSL_NAN, 1233 }; 1234 verify_results($results, 'Math::GSL::SF'); 1235} 1236 1237sub TEST_NAN : Tests(18) 1238{ 1239 my $results = { 1240 'gsl_sf_coupling_3j_e(-1, 1, 2, 1, -1, 0,$r)' => $GSL_NAN, 1241 'gsl_sf_coupling_3j_e(1, -1, 2, 1, -1, 0,$r)' => $GSL_NAN, 1242 'gsl_sf_coupling_3j_e(1, 1, -2, 1, -1, 0,$r)' => $GSL_NAN, 1243 'gsl_sf_coupling_6j_e(-2, 2, 4, 2, 2, 2,$r)' => $GSL_NAN, 1244 'gsl_sf_coupling_6j_e(2, -2, 4, 2, 2, 2,$r)' => $GSL_NAN, 1245 'gsl_sf_coupling_6j_e(2, 2, -4, 2, 2, 2,$r)' => $GSL_NAN, 1246 'gsl_sf_coupling_6j_e(2, 2, 4, -2, 2, 2,$r)' => $GSL_NAN, 1247 'gsl_sf_coupling_6j_e(2, 2, 4, 2, -2, 2,$r)' => $GSL_NAN, 1248 'gsl_sf_coupling_6j_e(2, 2, 4, 2, 2, -2,$r)' => $GSL_NAN, 1249 'gsl_sf_coupling_9j_e(-4, 2, 4, 3, 3, 2, 1, 1, 2,$r)' => $GSL_NAN, 1250 'gsl_sf_coupling_9j_e(4, -2, 4, 3, 3, 2, 1, 1, 2,$r)' => $GSL_NAN, 1251 'gsl_sf_coupling_9j_e(4, 2, -4, 3, 3, 2, 1, 1, 2,$r)' => $GSL_NAN, 1252 'gsl_sf_coupling_9j_e(4, 2, 4, -3, 3, 2, 1, 1, 2,$r)' => $GSL_NAN, 1253 'gsl_sf_coupling_9j_e(4, 2, 4, 3, -3, 2, 1, 1, 2,$r)' => $GSL_NAN, 1254 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, -2, 1, 1, 2,$r)' => $GSL_NAN, 1255 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 2, -1, 1, 2,$r)' => $GSL_NAN, 1256 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 2, 1, -1, 2,$r)' => $GSL_NAN, 1257 'gsl_sf_coupling_9j_e(4, 2, 4, 3, 3, 2, 1, 1, -2,$r)' => $GSL_NAN, 1258 }; 1259 verify_results($results, 'Math::GSL::SF'); 1260} 1261sub TEST_ZZZ_OLD_BUGS : Test(1) 1262{ 1263 my $r= Math::GSL::SF::gsl_sf_result_struct->new; 1264 ok_similar( [ gsl_sf_expint_En_e(3,300.0,$r) ] , [ 1.6608815083360041367294736e-133 ] ); 1265} 1266 1267sub TEST_J0_RESULT_STRUCT: Tests(2) { 1268 my $result = Math::GSL::SF::gsl_sf_result_struct->new; 1269 my ($status) = gsl_sf_bessel_J0_e(2.0,$result); 1270 ok( defined $result->{err}, '$result->{err}' ); 1271 ok( is_similar($result->{val}, gsl_sf_bessel_J0(2.0), $result->{err}) , '$result->{val}' ); 1272} 1273 1274sub TEST_MATHIEU : Tests { 1275 # https://github.com/ampl/gsl/blob/master/specfunc/test_mathieu.c 1276 my $version= gsl_version(); 1277 my ($major, $minor) = split /\./, $version; 1278 1279 diag("GSL version=$version"); 1280 1281 local $TODO = "these functions are not currently available"; 1282 return; 1283 1284 # these functions had _e added starting in 2.0 1285 my $suffix = $major >= 2 ? "_e" : ""; 1286 my $results = { 1287 "gsl_sf_mathieu_ce$suffix" . '(0,5.0,0,$r)' => 0.04480018165188902, 1288 "gsl_sf_mathieu_ce$suffix" . '(0,0,0,$r)' => sqrt(2)/2, 1289 "gsl_sf_mathieu_ce$suffix" . '(1,0,0,$r)' => 1.00, 1290 "gsl_sf_mathieu_ce$suffix" . '(0,0,$M_PI/2,$r)' => sqrt(2)/2, 1291 "gsl_sf_mathieu_se$suffix" . '(0,0,0,$r)' => 0, 1292 "gsl_sf_mathieu_se$suffix" . '(1,0,0,$r)' => 0, 1293 "gsl_sf_mathieu_se$suffix" . '(0,0,1,$r)' => 0, 1294 "gsl_sf_mathieu_se$suffix" . '(1,0,1,$r)' => sin(1), 1295 "gsl_sf_mathieu_se$suffix" . '(15,25,$M_PI/2,$r)' => -0.9467086958780897, 1296 }; 1297 verify_results($results, 'Math::GSL::SF'); 1298} 1299 1300sub TEST_ZBESSEL_ARRAYS : Tests { 1301 my $J = gsl_sf_bessel_Jn_array (0, 15, 0); 1302 ok_similar( $J, [ 1, (0) x 15 ], "gsl_sf_bessel_Jn_array(0,15,0)"); 1303 1304 $J = gsl_sf_bessel_Jn_array(0,1,1); 1305 # values from http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BesselJ 1306 ok_similar( $J, [ 0.765197686558, 0.440050585745 ], "gsl_sf_bessel_Jn_array(0,1,1)"); 1307 1308 my $K = gsl_sf_bessel_Kn_array(0,1,1); 1309 # values from http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BesselK 1310 ok_similar( $K, [ 0.421024438241, 0.601907230197], "gsl_sf_bessel_Kn_array(0,1,1)"); 1311 1312 $K = gsl_sf_bessel_Kn_scaled_array(0,1,1); 1313 ok_similar( $K, [ exp(1)*0.421024438241, exp(1)*0.601907230197], "gsl_sf_bessel_Kn_scaled_array(0,1,1)"); 1314 1315 my $j = gsl_sf_bessel_jl_array(1,1); 1316 ok_similar($j, [sin(1), sin(1) - cos(1)], "gsl_sf_bessel_jl_array(0,1,1)"); 1317 1318 $j = gsl_sf_bessel_jl_steed_array(1,1); 1319 ok_similar($j, [sin(1), sin(1) - cos(1)], "gsl_sf_bessel_jl_steed_array(0,1,1)"); 1320 1321 my $y = gsl_sf_bessel_yl_array(1,1); 1322 ok_similar($y, [-cos(1), -cos(1)-sin(1)], "gsl_sf_bessel_yl_array(0,1,1)"); 1323 1324 dies_ok( sub { 1325 my $K = gsl_sf_bessel_Kn_array(0,1,0); 1326 }, "gsl_sf_bessel_Kn_array(0,1,0) dies because it is not defined at 0"); 1327 1328 my $I = gsl_sf_bessel_In_array(0,1,1); 1329 # values from http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BesselI 1330 ok_similar( $I, [ 1.26606587775,0.565159103992 ], "gsl_sf_bessel_In_array(0,1,1)"); 1331 1332 my $Is = gsl_sf_bessel_In_scaled_array(0,1,1); 1333 1334 ok_similar( $Is, [ exp(-1)*1.26606587775,exp(-1)*0.565159103992 ], "gsl_sf_bessel_In_scaled_array(0,1,1)"); 1335 1336 my $Y = gsl_sf_bessel_Yn_array(0,1,1); 1337 # values from http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BesselY 1338 ok_similar( $Y, [ 0.0882569642157, -0.781212821300], "gsl_sf_bessel_Yn_array(0,1,1)"); 1339 1340 lives_ok(sub { my $il = gsl_sf_bessel_il_scaled_array(1,1) }, 'gsl_sf_bessel_il_scaled_array(1,1) lives '); 1341 1342 local $TODO = "gsl_sf_bessel_kl_scaled_array is missing"; 1343 lives_ok(sub { 1344 my $kl = gsl_sf_bessel_kl_scaled_array(1,1) 1345 }, 'gsl_sf_bessel_kl_scaled_array(1,1) lives '); 1346} 1347 1348Test::Class->runtests; 1349