int
test_hermite(void)
{
gsl_sf_result r;
int s = 0;
int m, n, sa;
double res[256];
double x;
const double aizero1 = -2.3381074104597670384891972524467; /* first zero of the Airy function Ai */
/* test some known identities */
test_hermite_id1(10, 0.75, 0.33);
test_hermite_id1(8, -0.75, 1.20);
test_hermite_id1(7, 2.88, -3.2);
x = 0.75;
TEST_SF(s, gsl_sf_hermite_prob_e, (0, 0.75, &r), 1., TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hermite_prob_e, (1, 0.75, &r), x, TEST_TOL0, GSL_SUCCESS);
n = 25;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, 0., &r), 0., TEST_TOL0, GSL_SUCCESS);
n = 28;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, 0., &r), 213458046676875, TEST_TOL0, GSL_SUCCESS);
n = 25;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, 0.75, &r), -1.08128685847680748265939328423e12, TEST_TOL0, GSL_SUCCESS);
n = 28;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, 0.75, &r), -1.60620252094658918105511125135e14, TEST_TOL0, GSL_SUCCESS);
#if 0
n = 10025;
x = ((sqrt(2*n+1.)+aizero1/pow(8.*n,1/6.))/2)*M_SQRT2;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, x, &r), -3.3090527852387782540121569578e18961, TEST_TOL0, GSL_SUCCESS);
n = 10028;
x = ((sqrt(2*n+1.)+aizero1/pow(8.*n,1/6.))/2)*M_SQRT2;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, x, &r), -7.515478445930242044360704363e18967, TEST_TOL0, GSL_SUCCESS);
n = 10025;
x = (sqrt(2*n+1.)-(aizero1/pow(8.*n,1/6.))/2)*M_SQRT2;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, x, &r), 4.1369269649092456235914193753e22243, TEST_TOL0, GSL_SUCCESS);
n = 10028;
x = (sqrt(2*n+1.)-(aizero1/pow(8.*n,1/6.))/2)*M_SQRT2;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, x, &r), 8.363694992558646923734666303e22250, TEST_TOL0, GSL_SUCCESS);
n = 10025;
x = (sqrt(2*n+1.)-2*(aizero1/pow(8.*n,1/6.)))*M_SQRT2;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, x, &r), 7.398863979737363164340057757e22273, TEST_TOL0, GSL_SUCCESS);
n = 10028;
x = (sqrt(2*n+1.)-2*(aizero1/pow(8.*n,1/6.)))*M_SQRT2;
TEST_SF(s, gsl_sf_hermite_prob_e, (n, x, &r), 1.507131397474022356488976968e22281, TEST_TOL0, GSL_SUCCESS);
#endif
x = 0.75;
n = 128;
m = 225;
TEST_SF(s, gsl_sf_hermite_prob_der_e, (m, n, x, &r), 0., TEST_TOL0, GSL_SUCCESS);
n = 128;
m = 5;
TEST_SF(s, gsl_sf_hermite_prob_der_e, (m, n, x, &r), -3.0288278964712702882066404e112, TEST_TOL1, GSL_SUCCESS);
sa = 0;
gsl_sf_hermite_prob_array(0, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_prob_array(0, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_prob_array(1, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
TEST_SF_VAL(sa, res[1], +0.0, x, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_prob_array(1, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_prob_array(100, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 823.810509681701660156250, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 1.03749254986255755872498e78, TEST_TOL1);
gsl_test(sa, "gsl_sf_hermite_prob_array(100, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_prob_array_der(0, 100, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 823.810509681701660156250, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 1.03749254986255755872498e78, TEST_TOL1);
gsl_test(sa, "gsl_sf_hermite_prob_array_der(0, 100, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_prob_array_der(1000, 100, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 0.0, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 0.0, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 0.0, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_prob_array_der(1000, 100, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_prob_array_der(23, 100, x, res);
TEST_SF_VAL(sa, res[10], +0.0, 0.0, TEST_TOL0);
TEST_SF_VAL(sa, res[37], +0.0, 2.3592417210568968566591219172e37, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 2.6503570965896336273549197e100, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_prob_array(23, 37, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_prob_der_array(100, 50, x, res);
TEST_SF_VAL(sa, res[0], +0.0, -3.88338863813139372375411561e31, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 7.9614368698398116765703194e38, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 0.0, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_prob_der_array(100, 50, 0.75)");
s += sa;
n = 128;
res[0] = 1.;
for(m=1; m<=n; m++){
res[m] = res[m-1]/2.;
}
TEST_SF(s, gsl_sf_hermite_prob_series_e, (n, x, res, &r), -4.0451066556993485405907339548e68, TEST_TOL0, GSL_SUCCESS);
/* phys */
x = 0.75;
TEST_SF(s, gsl_sf_hermite_phys_e, (0, 0.75, &r), 1., TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hermite_phys_e, (1, 0.75, &r), 2.*x, TEST_TOL0, GSL_SUCCESS);
n = 25;
TEST_SF(s, gsl_sf_hermite_phys_e, (n, 0., &r), 0., TEST_TOL0, GSL_SUCCESS);
n = 28;
TEST_SF(s, gsl_sf_hermite_phys_e, (n, 0., &r), 3497296636753920000, TEST_TOL0, GSL_SUCCESS);
n = 25;
TEST_SF(s, gsl_sf_hermite_phys_e, (n, 0.75, &r), -9.7029819451106077507781088352e15, TEST_TOL0, GSL_SUCCESS);
n = 28;
TEST_SF(s, gsl_sf_hermite_phys_e, (n, 0.75, &r), 3.7538457078067672096408339776e18, TEST_TOL0, GSL_SUCCESS);
#if 0
n = 10025;
x = ((sqrt(2*n+1.)+aizero1/pow(8.*n,1/6.))/2);
TEST_SF(s, gsl_sf_hermite_phys_e, (n, x, &r), -2.7074282783315424535693575770e20470, TEST_TOL0, GSL_SUCCESS);
n = 10028;
x = ((sqrt(2*n+1.)+aizero1/pow(8.*n,1/6.))/2);
TEST_SF(s, gsl_sf_hermite_phys_e, (n, x, &r), -1.7392214893577690864150561850e20477, TEST_TOL0, GSL_SUCCESS);
n = 10025;
x = (sqrt(2*n+1.)-(aizero1/pow(8.*n,1/6.))/2);
TEST_SF(s, gsl_sf_hermite_phys_e, (n, x, &r), 3.3847852473526979744366379542e23752, TEST_TOL0, GSL_SUCCESS);
n = 10028;
x = (sqrt(2*n+1.)-(aizero1/pow(8.*n,1/6.))/2);
TEST_SF(s, gsl_sf_hermite_phys_e, (n, x, &r), 1.9355145738418079256435712027e23760, TEST_TOL0, GSL_SUCCESS);
n = 10025;
x = (sqrt(2*n+1.)-2*(aizero1/pow(8.*n,1/6.)));
TEST_SF(s, gsl_sf_hermite_phys_e, (n, x, &r), 6.053663953512337293393128307e23782, TEST_TOL0, GSL_SUCCESS);
n = 10028;
x = (sqrt(2*n+1.)-2*(aizero1/pow(8.*n,1/6.)));
TEST_SF(s, gsl_sf_hermite_phys_e, (n, x, &r), 3.487782358276961096026268141e23790, TEST_TOL0, GSL_SUCCESS);
#endif
x = 0.75;
n = 128;
m = 225;
TEST_SF(s, gsl_sf_hermite_phys_der_e, (m, n, x, &r), 0., TEST_TOL0, GSL_SUCCESS);
n = 128;
m = 5;
TEST_SF(s, gsl_sf_hermite_phys_der_e, (m, n, x, &r), 2.89461215568095657569833e132, TEST_TOL0, GSL_SUCCESS);
sa = 0;
gsl_sf_hermite_phys_array(0, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_phys_array(0, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_phys_array(1, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
TEST_SF_VAL(sa, res[1], +0.0, 2.*x, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_phys_array(1, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_phys_array(100, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 38740.4384765625, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, -1.4611185395125104593177790757e93, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_phys_array(100, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_phys_array_der(0, 100, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 1.0, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 38740.4384765625, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, -1.4611185395125104593177790757e93, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_phys_array_der(0, 100, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_phys_array_der(1000, 100, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 0.0, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 0.0, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 0.0, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_phys_array_der(1000, 100, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_phys_array_der(23, 100, x, res);
TEST_SF_VAL(sa, res[10], +0.0, 0.0, TEST_TOL0);
TEST_SF_VAL(sa, res[37], +0.0, 1.930387357696033719818118732e46, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 2.957966000491202678467161e118, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_phys_array(23, 37, 0.75)");
s += sa;
sa = 0;
gsl_sf_hermite_phys_der_array(100, 50, x, res);
TEST_SF_VAL(sa, res[0], +0.0, -8.2663221830586310072686183e38, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 1.52281030265187793605875604e49, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, 0.0, TEST_TOL0);
gsl_test(sa, "gsl_sf_hermite_phys_der_array(100, 50, 0.75)");
s += sa;
n = 128;
/* arbitrary weights */
res[0] = 1.;
for(m=1; m<=n; m++){
res[m] = res[m-1]/2.;
}
TEST_SF(s, gsl_sf_hermite_phys_series_e, (n, x, res, &r), 1.07772223811696567390619566842e88, TEST_TOL0, GSL_SUCCESS);
x = 0.75;
n = 28;
TEST_SF(s, gsl_sf_hermite_func_e, (n, 0, &r), 0.290371943657199641200016132937, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), 0.23526280808621240649319140441, TEST_TOL0, GSL_SUCCESS);
n = 100028;
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), -0.02903467369856961147236598086, TEST_TOL4, GSL_SUCCESS);
n = 10025;
x = ((sqrt(2*n+1.)+aizero1/pow(8.*n,1/6.))/2.5);
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), -0.05301278920004176459797680403, TEST_TOL4, GSL_SUCCESS);
n = 10028;
x = ((sqrt(2*n+1.)+aizero1/pow(8.*n,1/6.))/2.5);
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), 0.06992968509693993526829596970, TEST_TOL3, GSL_SUCCESS);
n = 10025;
x = (sqrt(2*n+1.)-(aizero1/pow(8.*n,1/6.))/2.5);
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), 0.08049000991742150521366671021, TEST_TOL4, GSL_SUCCESS);
n = 10028;
x = (sqrt(2*n+1.)-(aizero1/pow(8.*n,1/6.))/2.5);
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), 0.08048800667512084252723933250, TEST_TOL4, GSL_SUCCESS);
n = 10025;
x = (sqrt(2*n+1.)-2.5*(aizero1/pow(8.*n,1/6.)));
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), 7.97206830806663013555068100e-6, TEST_TOL4, GSL_SUCCESS);
n = 10028;
x = (sqrt(2*n+1.)-2.5*(aizero1/pow(8.*n,1/6.)));
TEST_SF(s, gsl_sf_hermite_func_e, (n, x, &r), 7.97188517397786729928465829e-6, TEST_TOL4, GSL_SUCCESS);
x = 0.75;
sa = 0;
gsl_sf_hermite_func_array(100, x, res);
TEST_SF_VAL(sa, res[0], +0.0, 0.566979307027693616978839335983, TEST_TOL0);
TEST_SF_VAL(sa, res[10], +0.0, 0.360329854170806945032958735574, TEST_TOL0);
TEST_SF_VAL(sa, res[100], +0.0, -0.07616422890563462489003733382, TEST_TOL1);
gsl_test(sa, "gsl_sf_hermite_func_array(100, 0.75)");
s += sa;
n = 128;
/* arbitrary weights */
res[0] = 1.;
for(m=1; m<=n; m++){
res[m] = res[m-1]/2.;
}
TEST_SF(s, gsl_sf_hermite_func_series_e, (n, x, res, &r), 0.81717103529960997134154552556, TEST_TOL0, GSL_SUCCESS);
m = 5;
n = 28;
TEST_SF(s, gsl_sf_hermite_func_der_e, (0, n, x, &r), 0.235262808086212406493191404, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_hermite_func_der_e, (m, n, x, &r), 4035.32788513029308540826835, TEST_TOL1, GSL_SUCCESS);
{
/* positive zeros of the probabilists' Hermite polynomial of order 17 */
double He17z[8] = { 0.751842600703896170737870774614, 1.50988330779674075905491513417, 2.28101944025298889535537879396,
3.07379717532819355851658337833, 3.90006571719800990903311840097, 4.77853158962998382710540812497,
5.74446007865940618125547815768,6.88912243989533223256205432938 };
n = 17;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_prob_zero_e, (n, m, &r), He17z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
{
/* positive zeros of the probabilists' Hermite polynomial of order 18 */
double He18z[9] = { 0.365245755507697595916901619097, 1.09839551809150122773848360538, 1.83977992150864548966395498992,
2.59583368891124032910545091458, 3.37473653577809099529779309480, 4.18802023162940370448450911428,
5.05407268544273984538327527397, 6.00774591135959752029303858752, 7.13946484914647887560975631213 };
n = 18;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_prob_zero_e, (n, m, &r), He18z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
{
/* positive zeros of the probabilists' Hermite polynomial of order 23 */
double He23z[11] = { 0.648471153534495816722576841197, 1.29987646830397886997876116860, 1.95732755293342410739100839243,
2.62432363405918177067330340783, 3.30504002175296456723204112903, 4.00477532173330406712238633738,
4.73072419745147329426707133987, 5.49347398647179412855289367747, 6.31034985444839982842886078177,
7.21465943505186138595859194492, 8.29338602741735258945596770157 };
n = 23;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_prob_zero_e, (n, m, &r), He23z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
{
/* positive zeros of the probabilists' Hermite polynomial of order 24 */
double He24z[12] = { 0.317370096629452319318170455994, 0.953421922932109084904629632351, 1.59348042981642010695074168129,
2.24046785169175236246653790858, 2.89772864322331368932008199475, 3.56930676407356024709649151613,
4.26038360501990548884317727406, 4.97804137463912033462166468006, 5.73274717525120114834341822330,
6.54167500509863444148277523364, 7.43789066602166310850331715501, 8.50780351919525720508386233432 };
n = 24;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_prob_zero_e, (n, m, &r), He24z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
{
/* positive zeros of the physicists' Hermite polynomial of order 17 */
double H17z[8] = { 0.531633001342654731349086553718, 1.06764872574345055363045773799, 1.61292431422123133311288254454,
2.17350282666662081927537907149, 2.75776291570388873092640349574, 3.37893209114149408338327069289,
4.06194667587547430689245559698, 4.87134519367440308834927655662 };
n = 17;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_phys_zero_e, (n, m, &r), H17z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
{
/* positive zeros of the physicists' Hermite polynomial of order 18 */
double H18z[9] = { 0.258267750519096759258116098711, 0.776682919267411661316659462284, 1.30092085838961736566626555439,
1.83553160426162889225383944409, 2.38629908916668600026459301424, 2.96137750553160684477863254906,
3.57376906848626607950067599377, 4.24811787356812646302342016090, 5.04836400887446676837203757885 };
n = 18;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_phys_zero_e, (n, m, &r), H18z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
{
/* positive zeros of the physicists' Hermite polynomial of order 23 */
double H23z[11] = { 0.458538350068104797757887329284, 0.919151465442563765431719239593, 1.38403958568249523732634717118,
1.85567703767137106251504753718, 2.33701621147445578644623502174, 2.83180378712615690144806140734,
3.34512715994122457247439814585, 3.88447270810610186607248760288, 4.46209117374000667673186157071,
5.10153461047667712968749766165, 5.86430949898457256538748413474 };
n = 23;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_phys_zero_e, (n, m, &r), H23z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
{
/* positive zeros of the physicists' Hermite polynomial of order 24 */
double H24z[12] = { 0.224414547472515585151136715527, 0.674171107037212236000245923730, 1.12676081761124507213306126773,
1.58425001096169414850563336202, 2.04900357366169891178708399532, 2.52388101701142697419907602333,
3.01254613756556482565453858421, 3.52000681303452471128987227609, 4.05366440244814950394766297923,
4.62566275642378726504864923776, 5.25938292766804436743072304398, 6.01592556142573971734857350899 };
n = 24;
for (m=1; m<=n/2; m++) {
TEST_SF(s, gsl_sf_hermite_phys_zero_e, (n, m, &r), H24z[m-1], TEST_TOL0, GSL_SUCCESS);
}
}
n = 2121;
x = -1.*n;
res[0] = (double) n;
sa = 0;
for (m=1; m<=n/2; m++) {
gsl_sf_hermite_prob_zero_e(n, m, &r);
if (x>=r.val) {
sa += TEST_SF_INCONS;
printf("sanity check failed! (gsl_sf_hermite_prob_zero)\n");
}
res[0] = GSL_MIN(res[0],fabs(x-r.val));
x = r.val;
}
gsl_test(sa, "gsl_sf_hermite_prob_zero(n, m, r)");
n = 2121;
x = -1.*n;
res[0] = (double) n;
sa = 0;
for (m=1; m<=n/2; m++) {
gsl_sf_hermite_phys_zero_e(n, m, &r);
if (x>=r.val) {
sa += TEST_SF_INCONS;
printf("sanity check failed! (gsl_sf_hermite_phys_zero)\n");
}
res[0] = GSL_MIN(res[0],fabs(x-r.val));
x = r.val;
}
gsl_test(sa, "gsl_sf_hermite_phys_zero(n, m, r)");
return s;
}
int test_legendre(void)
{
gsl_sf_result r;
double L[256], DL[256];
int s = 0;
int sa;
TEST_SF(s, gsl_sf_legendre_P1_e, (-0.5, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P1_e, ( 0.5, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P2_e, (0.0, &r), -0.5 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P2_e, (0.5, &r), -0.125, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P2_e, (1.0, &r), 1.0 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P2_e, (100.0, &r), 14999.5 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P3_e, ( -0.5, &r), 0.4375, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P3_e, ( 0.5, &r), -0.4375, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P3_e, ( 1.0, &r), 1.0 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_P3_e, (100.0, &r), 2.49985e+06, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1, -0.5, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1, 1.0e-8, &r), 1.0e-08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1, 0.5, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (10, -0.5, &r), -0.1882286071777345, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (10, 1.0e-8, &r), -0.24609374999999864648, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (10, 0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (10, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (99, -0.5, &r), 0.08300778172138770477, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 1.0e-8, &r), -7.958923738716563193e-08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 0.5, &r), -0.08300778172138770477, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 0.999, &r), -0.3317727359254778874, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, -0.5, &r), -0.019168251091650277878, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, 1.0e-8, &r), 0.0252250181770982897470252620, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, 0.5, &r), -0.019168251091650277878, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (4000, -0.5, &r), -0.009585404456573080972, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (4000, 0.5, &r), -0.009585404456573080972, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Pl_e, (4000, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
sa = 0;
gsl_sf_legendre_Pl_array(100, 0.5, L);
TEST_SF_VAL(sa, L[0], +0.0, 1.0, TEST_TOL1);
TEST_SF_VAL(sa, L[10], +0.0, -0.18822860717773437500, TEST_TOL1);
TEST_SF_VAL(sa, L[100], +0.0, -0.06051802596186118687, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_Pl_array(100, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_Pl_deriv_array(100, 0.5, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, -2.3171234130859375000, TEST_TOL1);
TEST_SF_VAL(sa, DL[100], +0.0, -7.0331691653942815112, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(100, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_Pl_deriv_array(10, 1.0, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, 55.0, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, 1.0)");
s += sa;
gsl_sf_legendre_Pl_deriv_array(10, 1.0 - 1.0e-11, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, 54.999999985150000001, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, 1.0 - 1.0e-11)");
s += sa;
gsl_sf_legendre_Pl_deriv_array(10, -1.0, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, -55.0, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, -1.0)");
s += sa;
gsl_sf_legendre_Pl_deriv_array(10, -1.0 + 1.0e-11, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, -54.999999985150000001, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, -1.0 + 1.0e-11)");
s += sa;
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, -0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 1.0e-08, &r), -0.24609374999999864648, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, -0.5, &r), -2.0066877394361256516, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, 1.0e-08, &r), -2.7070312499999951725e-07, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, 0.5, &r), 2.0066877394361256516, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, -0.5, &r), -30086.169706116174977, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 1.0e-08, &r), -0.0025337812499999964949, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 0.5, &r), 30086.169706116174977, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 0.999, &r), -0.5036411489013270406, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, -0.5, &r), -6.617107444248382171e+08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 1.0e-08, &r), 817.8987598063712851, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.5, &r), 6.617107444248382171e+08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.999, &r), -1.9831610803806212189e+09, TEST_TOL2, GSL_SUCCESS);
sa = 0;
gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0/1125899906842624.0, L, DL);
TEST_SF_VAL(sa, L[0], +0.0, 5.3290705182007490275e-15, TEST_TOL1);
TEST_SF_VAL(sa, L[1], +0.0, -2.6645352591003721471e-14, TEST_TOL1);
TEST_SF_VAL(sa, L[98], +0.0, 2.2646284847349109694e-08, TEST_TOL2);
gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 2^(-50)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0/1125899906842624.0, L, DL);
TEST_SF_VAL(sa, L[0], +0.0, 5.3290705182007490275e-15, TEST_TOL1);
TEST_SF_VAL(sa, L[1], +0.0, 2.6645352591003721471e-14, TEST_TOL1);
TEST_SF_VAL(sa, L[10], +0.0, 5.3343995887188313290e-12, TEST_TOL1);
TEST_SF_VAL(sa, L[98], +0.0, 2.2646284847349109694e-08, TEST_TOL2);
gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 2^(-50)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_array(100, 5, 0.5, L);
TEST_SF_VAL(sa, L[0], +0.0, -460.3466286991656682, TEST_TOL1);
TEST_SF_VAL(sa, L[10], +0.0, 38852.51334152290535, TEST_TOL1 );
TEST_SF_VAL(sa, L[95], +0.0, 6.617107444248382171e+08, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_array(100, 5, 0.999, L);
TEST_SF_VAL(sa, L[0], +0.0, -0.00016883550990916552255, TEST_TOL2);
TEST_SF_VAL(sa, L[10], +0.0, -30.651334850159821525, TEST_TOL2 );
TEST_SF_VAL(sa, L[95], +0.0, -1.9831610803806212189e+09, TEST_TOL2);
gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, 0.999)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_array(100, 5, -0.999, L);
TEST_SF_VAL(sa, L[0], +0.0, -0.00016883550990916552255, TEST_TOL2);
TEST_SF_VAL(sa, L[10], +0.0, -30.651334850159821525, TEST_TOL2 );
TEST_SF_VAL(sa, L[95], +0.0, 1.9831610803806212189e+09, TEST_TOL2);
gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, -0.999)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_deriv_array(100, 2, 0.999, L, DL);
TEST_SF_VAL(sa, L[0], +0.0, 0.00599700000000000000, TEST_TOL1);
TEST_SF_VAL(sa, L[1], +0.0, 0.02995501500000000000, TEST_TOL1 );
TEST_SF_VAL(sa, DL[0], +0.0, -5.9940000000000000000, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, -29.910045000000000000, TEST_TOL1 );
TEST_SF_VAL(sa, DL[2], +0.0, -89.490629790000000000, TEST_TOL1 );
TEST_SF_VAL(sa, DL[10], +0.0, -5703.9461633355291972, TEST_TOL1 );
TEST_SF_VAL(sa, DL[95], +0.0, 6.4518473603456858414E+06, TEST_TOL3);
gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 0.999)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0e-15, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, -5.9999999999999940000, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, -29.999999999999910000, TEST_TOL1 );
TEST_SF_VAL(sa, DL[2], +0.0, -89.999999999999490000, TEST_TOL1 );
TEST_SF_VAL(sa, DL[10], +0.0, -6005.9999999996936940, TEST_TOL1 );
TEST_SF_VAL(sa, DL[95], +0.0, -2.2586255999928454270e+07, TEST_TOL3);
gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0e-15)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0e-15, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 5.9999999999999940000, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, -29.999999999999910000, TEST_TOL1 );
TEST_SF_VAL(sa, DL[95], +0.0, -2.2586255999928454270e+07, TEST_TOL3);
gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0e-15)");
s += sa;
sa = 0;
gsl_sf_legendre_Plm_deriv_array(100, 5, 0.999, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.42187762481054616565, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 4.6341560284340909936, TEST_TOL1 );
TEST_SF_VAL(sa, DL[2], +0.0, 27.759505566959219127, TEST_TOL1 );
TEST_SF_VAL(sa, DL[10], +0.0, 76051.795860179545484, TEST_TOL1 );
TEST_SF_VAL(sa, DL[95], +0.0, 3.0344503083851936814e+12, TEST_TOL3);
gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 5, 0.999)");
s += sa;
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, -0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.999, &r), 1.2225754122797385990, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, -0.5, &r), -0.3725739049803293972, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 1.0e-08, &r), -3.1377233589376792243e-08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.5, &r), 0.3725739049803293972, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.999, &r), -6.236870674727370094e-06, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, -0.5, &r), 0.12876871185785724117, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.5, &r), 0.12876871185785724117, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.999, &r), 1.7320802307583118647e-14, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, -0.5, &r), 0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.5, &r), -0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.999, &r), -1.4069792055546256912, TEST_TOL2, GSL_SUCCESS);
/* Test case from [email protected] */
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (3, 1, 0.0, &r), 0.323180184114150653007, TEST_TOL2, GSL_SUCCESS);
/* Other test cases */
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, -0.5, &r), 0.3302975570099492931418227583, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (140,135,1,&r), 0.0, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_sphPlm_e, (140,135,0.99998689456491752,&r), -6.54265253269093276310395668335e-305, TEST_TOL6, GSL_SUCCESS);
sa = 0;
gsl_sf_legendre_sphPlm_array(100, 5, 0.5, L);
TEST_SF_VAL(sa, L[0], +0.0, -0.22609703187800460722, TEST_TOL1);
TEST_SF_VAL(sa, L[10], +0.0, 0.07452710323813558940, TEST_TOL1);
TEST_SF_VAL(sa, L[95], +0.0, 0.25865355990880161717, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 5, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_array(100, 2, 1.0 - 1.0/1125899906842624.0, L);
TEST_SF_VAL(sa, L[0], +0.0, 6.8616082064776657177e-16, TEST_TOL2);
TEST_SF_VAL(sa, L[10], +0.0, 4.8543150313086787324e-14, TEST_TOL2);
TEST_SF_VAL(sa, L[95], +0.0, 8.3138984963650838973e-12, TEST_TOL2);
gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 2, 1.0 - 2^(-50))");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_array(100, 2, -1.0 + 1.0/1125899906842624.0, L);
TEST_SF_VAL(sa, L[0], +0.0, 6.8616082064776657177e-16, TEST_TOL2);
TEST_SF_VAL(sa, L[95], +0.0, -8.3138984963650838973e-12, TEST_TOL2);
gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 2, -1.0 + 2^(-50))");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_deriv_array(100, 0, 0.5, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, -2.9953934850252897591, TEST_TOL1);
TEST_SF_VAL(sa, DL[95], +0.0, -36.411811015111761007, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 0, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_deriv_array(100, 1, 0.5, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.19947114020071633897, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, -0.44603102903819277863, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, 1.3658895325030216565, TEST_TOL1);
TEST_SF_VAL(sa, DL[99], +0.0, -27.925571865639037118, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 1, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_deriv_array(100, 1, 1.0 - 1.0/1125899906842624.0, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 8.1973898803378530946e+06, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 1.8329921010504257405e+07, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, 1.8439572562895384115e+08, TEST_TOL1);
TEST_SF_VAL(sa, DL[99], +0.0, 4.7682463136232210552e+09, TEST_TOL3);
gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 1, 1.0 - 2^(-50))");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_deriv_array(100, 2, 0.5, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, -0.38627420202318958034, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 0.25549636910832059085, TEST_TOL1);
TEST_SF_VAL(sa, DL[2], +0.0, 1.5053547230039006279, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, 0.73576559668648243477, TEST_TOL1);
TEST_SF_VAL(sa, DL[98], +0.0, 28.444589950264378407, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 2, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_deriv_array(100, 5, 0.5, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 0.75365677292668202407, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 0.54346962777757450534, TEST_TOL1);
TEST_SF_VAL(sa, DL[2], +0.0, -0.98309969029001383773, TEST_TOL1);
TEST_SF_VAL(sa, DL[3], +0.0, -2.7728270988954534293, TEST_TOL1);
TEST_SF_VAL(sa, DL[10], +0.0, -5.7407133315443482193, TEST_TOL1);
TEST_SF_VAL(sa, DL[95], +0.0, -25.893934624747394561, TEST_TOL1);
gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, 0.5)");
s += sa;
sa = 0;
gsl_sf_legendre_sphPlm_deriv_array(100, 5, 1.0 - 1.0/1125899906842624.0, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, 1.7374288379067753301e-22, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 6.2643887625426827113e-22, TEST_TOL1);
TEST_SF_VAL(sa, DL[2], +0.0, 1.6482697200734667281e-21, TEST_TOL1);
TEST_SF_VAL(sa, DL[95], +0.0, 3.9890549466071349506e-15, TEST_TOL2);
gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, 1.0 - 2^(-50))");
s += sa;
gsl_sf_legendre_sphPlm_deriv_array(100, 5, -1.0 + 1.0/1125899906842624.0, L, DL);
TEST_SF_VAL(sa, DL[0], +0.0, -1.7374288379067753301e-22, TEST_TOL1);
TEST_SF_VAL(sa, DL[1], +0.0, 6.2643887625426827113e-22, TEST_TOL1);
TEST_SF_VAL(sa, DL[2], +0.0, -1.6482697200734667281e-21, TEST_TOL1);
TEST_SF_VAL(sa, DL[95], +0.0, 3.9890549466071349506e-15, TEST_TOL3);
gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, -1.0 + 2^(-50))");
s += sa;
TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, -0.5, &r), 0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, 0.5, &r), 0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, 2.0, &r), 0.6062611623284649811, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, 100.0, &r), 0.07979045091636735635, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, -0.5, &r), 5.345484922591867188e+08, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, 0.5, &r), 15137.910380385258370, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, 2.0, &r), 0.4992680691891618544, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, 100.0, &r), -0.07272008163718195685, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, -1.0e-3, &r), 1.3347639529084185010e+136, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 1.0e-8, &r), 1.0928098010940058507e+136, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 0.5, &r), 3.895546021611205442e+90, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 10.0, &r), -0.04308567180833581268, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 100.0, &r), -0.04694669186576399194, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 1000.0, &r), 0.023698140704121273277, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 1.0e+8, &r), -0.00006790983312124277891, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8, 1.1, &r), 1.1599311133054742944, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8, 100.0, &r), 0.07971967557381557875, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, -0.5, &r), 1.7956982494514644808, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, 0.5, &r), 0.8978491247257322404, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, 2.0, &r), 0.7984204253272901551, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, 100.0, &r), 0.4227531369388072584, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, -0.5, &r), 5.345484922591867181e+07, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, 0.5, &r), 1513.7910356104985334, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, 2.0, &r), 0.03439243987215615642, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, 100.0, &r), 0.003283756665952609624, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, -0.5, &r), 1.7699538115312304280e+179, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 1.0e-8, &r), 5.464049005470029253e+133, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 0.5, &r), 1.9477730108056027211e+88, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 10.0, &r), 0.0012462575917716355362, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 100.0, &r), -0.0003225881344802625149, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 1000.0, &r), -0.00004330652890886567623, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 1.0e+8, &r), 2.0943091278037078483e-07, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (1.0e+8, 1.1, &r), 2.092320445620989618e-09, 16.0*TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_mhalf_e, (1.0e+8, 100.0, &r), -3.359967833599016923e-11, 256.0*TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, -0.5, &r), 1.3728805006183501647, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, 0.5, &r), 1.0731820071493643751, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, 2.0, &r), 0.9012862993604472987, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, 100.0, &r), 0.30091748588199264556, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, -0.5, &r), 1.6795592815421804669e+08, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, 0.5, &r), 4826.034132009618240, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, 2.0, &r), 0.18798468917758716146, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, 100.0, &r), -0.008622130749987962529, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (200.0, -0.5, &r), 2.502194818646823e+180, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (1000.0, 100.0, &r), 0.0017908817653497715844, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (1000.0, 1000.0, &r), -0.0006566893804926284301, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_0_e, (1000.0, 1.0e+8, &r), 2.3167213561756390068e-06, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, -0.5, &r), 0.4939371126656998499, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, 0.5, &r), 0.14933621085538265636, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, 2.0, &r), -0.13666874968871549533, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, 100.0, &r), -0.10544528203156629098, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, -0.5, &r), 1.7253802958788312520e+09, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, 0.5, &r), 46781.02294059967988, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, 2.0, &r), 0.26613342643657444400, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, 100.0, &r), -0.23281959695501029796, TEST_TOL2, GSL_SUCCESS);
/* FIXME: Mathematica gets some brain-damaged numbers for
* these x < 0 points. I have checked what I am doing in detail,
* and it must be right because you can do it by summing
* manifestly positive definite quantities.
*/
TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, -0.999, &r), 2.71635193199341135e+270, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, -0.9, &r), 4.2952493176812905e+234, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, -0.5, &r), 5.01159205956053439e+182, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, 0.999, &r), 195733.0396081538, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, 10.0, &r), -2.9272610662414349553, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (1000.0, 100.0, &r), -1.7783258105862399857, TEST_TOL6, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (1000.0, 1000.0, &r), 0.4535161075156427179, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_1_e, (1000.0, 1.0e+8, &r), 0.0009983414549874888478, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (2, 1.0, -0.5, &r), 1.6406279287008789526, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (10, 1.0, -0.5, &r), 0.000029315266725049129448, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (20, 1.0, -0.5, &r), 7.335769429462034431e-15, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (30, 1.0, -0.5, &r), 1.3235612394267378871e-26, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (10, 1.0, 0.5, &r), 2.7016087199857873954e-10, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (20, 1.0, 0.5, &r), 1.1782569701435933399e-24, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (30, 1.0, 0.5, &r), 3.636240588303797919e-41, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (10, 1.0, 2.0, &r), 2.4934929626284934483e-10, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (20, 1.0, 2.0, &r), 1.1284762488012616191e-24, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (30, 100.0, 100.0, &r), -1.6757772087159526048e-64, TEST_TOL6, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (2, 1.0, -0.5, &r), 2.2048510472375258708, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (10, 1.0, -0.5, &r), 0.00007335034531618655690, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (20, 1.0, -0.5, &r), 2.5419860619212164696e-14, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (30, 1.0, -0.5, &r), 5.579714972260536827e-26, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (10, 1.0, 0.5, &r), 1.1674078819646475282e-09, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (20, 1.0, 0.5, &r), 7.066408031229072207e-24, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (30, 1.0, 0.5, &r), 2.6541973286862588488e-40, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (10, 1.0, 2.0, &r), 1.0736109751890863051e-09, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (20, 1.0, 2.0, &r), 6.760965304863386741e-24, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (30, 100.0, 100.0, &r), -4.268753482520651007e-63, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0e-06, 1.0e-06, &r), 0.9999999999998333333 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 0.0, &r), 1.0 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 1.0, &r), 0.7160229153604338713 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 100.0, &r), -3.767437313149604566e-44 , TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 500.0, &r), -6.665351935878582205e-218, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (100.0, 1.0, &r), -0.004308757035378200029 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (100.0, 10.0, &r), 7.508054627912986427e-07 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1000.0, 1.0, &r), 0.0007036067909088818319 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0e+08, 1.0, &r), 7.927485371429105968e-09 , TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0e+08, 100.0, &r), -3.627118904186918957e-52 , 32.0*TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e-06, 1.0e-06, &r), 3.333333333334222222e-07, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 1.0e-10, &r), 4.714045207910316829e-11, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 1.0, &r), 0.3397013994799344639, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 100.0, &r), -7.200624449531811272e-44, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 500.0, &r), 4.192260336821728677e-218, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (100.0, 0.01, &r), 0.30117664944267412324 , TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (100.0, 1.0, &r), -0.007393833425336299309 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (100.0, 10.0, &r), -5.031062029821254982e-07 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1000.0, 0.001, &r), 0.30116875865090396421 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1000.0, 1.0, &r), -0.0004776144516074971885 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e+08, 1.0e-08, &r), 0.30116867893975679722 , TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e+08, 1.0, &r), 3.0921097047369081582e-09, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e+08, 100.0, &r), -6.496142701296286936e-52 , 32.0*TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0e-06, 1.0e-06, &r), 1.1544011544013627977e-32, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 1.0e-10, &r), 2.0224912016958766992e-52, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 1.0, &r), 0.011498635037491577728, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 5.0, &r), 0.0020696945662545205776, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 7.0, &r), -0.0017555303787488993676, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 10.0, &r), 0.00008999979724504887101, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 100.0, &r), -4.185397793298567945e-44, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 500.0, &r), 1.4235113901091961263e-217, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 0.001, &r), 9.642762597222417946e-10, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 0.002, &r), 3.0821201254308036109e-08, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 0.01, &r), 0.00009281069019005840532, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 1.0, &r), -0.008043100696178624653, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 10.0, &r), -3.927678432813974207e-07, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1000.0, 0.001, &r), 0.00009256365284253254503, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1000.0, 0.01, &r), -0.05553733815473079983, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0e+08, 1.0e-08, &r), 0.00009256115861125841299, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0e+08, 100.0, &r), -6.496143209092860765e-52 , 128.0*TEST_SQRT_TOL0, GSL_SUCCESS);
#if 0
sa = 0;
gsl_sf_legendre_H3d_array(100, 1.0, 3.0, L);
TEST_SF_VAL(sa, L[0], +0.0, gsl_sf_legendre_H3d(0, 1.0, 3.0), 1.0e-12);
TEST_SF_VAL(sa, L[1], +0.0, gsl_sf_legendre_H3d(1, 1.0, 3.0), 1.0e-12);
TEST_SF_VAL(sa, L[10], +0.0, gsl_sf_legendre_H3d(10, 1.0, 3.0), 1.0e-12);
TEST_SF_VAL(sa, L[100], +0.0, gsl_sf_legendre_H3d(100, 1.0, 3.0), 1.0e-12);
gsl_test(sa, " gsl_sf_legendre_H3d_array(100, 1.0, 3.0)");
s += sa;
#endif
/* x = -1 + 2^-16 */
TEST_SF(s, gsl_sf_legendre_Q0_e, (-0.9999847412109375, &r), -5.8917472200477175158028143531855, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, (-0.5, &r), -0.5493061443340548457, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, (-1e-10, &r), -1.000000000000000000e-10, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, (1e-10, &r), 1.000000000000000000e-10, TEST_TOL0, GSL_SUCCESS);
/* x = 1 - 2^-16 */
TEST_SF(s, gsl_sf_legendre_Q0_e, (0.9999847412109375, &r), 5.8917472200477175158028143531855, TEST_TOL4, GSL_SUCCESS);
/* x = 1 + 2^-16 */
TEST_SF(s, gsl_sf_legendre_Q0_e, ( 1.0000152587890625, &r), 5.8917548494422489138325509750429, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, ( 1.5, &r), 0.8047189562170501873, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, ( 9.99, &r), 0.1004364599660005447, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, ( 10.0, &r), 0.1003353477310755806, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, ( 10.01, &r), 0.1002344395571710243, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, ( 100, &r), 0.010000333353334762015, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q0_e, ( 1e10, &r), 1.000000000000000000e-10, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (-0.9999847412109375, &r), 4.8916573191196772369, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (-0.5, &r), -0.7253469278329725772, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (-0.01, &r), -0.9998999966664666524, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (-1e-10, &r), -0.999999999999999999, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (0.0, &r), -1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (1e-10, &r), -0.999999999999999999, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (0.0001, &r), -0.9999999899999999667, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (0.01, &r), -0.9998999966664666524, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (0.5, &r), -0.7253469278329725772, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (0.9999847412109375, &r), 4.8916573191196772369, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, (1.0000152587890625, &r), 4.8918447504867045145, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, ( 1.5, &r), 0.20707843432557528095, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, ( 9.99, &r), 3.360235060345441639e-3, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, ( 10.0, &r), 3.353477310755806357e-3, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, ( 10.01, &r), 3.346739967281953346e-3, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, ( 100.0, &r), 3.333533347620158821e-5, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Q1_e, ( 1e10, &r), 3.333333333333333333e-21, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (10, -0.5, &r), -0.29165813966586752393, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (10, 0.5, &r), 0.29165813966586752393, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (10, 1.5, &r), 0.000014714232718207477406, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (100, -0.5, &r), -0.09492507395207282096, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (100, 0.5, &r), 0.09492507395207282096, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (100, 1.5, &r), 1.1628163435044121988e-43, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (1000, -0.5, &r), -0.030105074974005303500, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (1000, 0.5, &r), 0.030105074974005303500, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_legendre_Ql_e, (1000, 1.1, &r), 1.0757258447825356443e-194, TEST_TOL3, GSL_SUCCESS);
return s;
}