CAMLprim value
ml_gsl_sf_legendre_Plm_array(value lmax, value m, value x, value result_array)
{
gsl_sf_legendre_Plm_array(Int_val(lmax),
Int_val(m),
Double_val(x),
Double_array_val(result_array));
return Val_unit;
}
static VALUE rb_gsl_sf_legendre_Plm_array(VALUE obj, VALUE lmax, VALUE m, VALUE x)
{
gsl_vector *v = NULL;
int size;
int ll, mm;
CHECK_FIXNUM(lmax);
CHECK_FIXNUM(m);
Need_Float(x);
ll = FIX2INT(lmax);
mm = FIX2INT(m);
size = gsl_sf_legendre_array_size(ll, mm);
v = gsl_vector_alloc(size);
gsl_sf_legendre_Plm_array(ll, mm, NUM2DBL(x), v->data);
return Data_Wrap_Struct(cgsl_vector, 0, gsl_vector_free, v);
}
//Computes the associated Legendre polynomials
void compute_P(double x, int L, int M, double * P_array)
{
if (M == 1){
gsl_sf_legendre_Pl_array (L - 1, x, P_array);
} else {
#if GSL_MAJOR_VERSION == 2
gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,L - 1, x, -1, P_array);
#else
int m;
for (m = 0; m < M; m++)
{
gsl_sf_legendre_Plm_array(L - 1, m, x, P_array);
P_array += L - m;
}
#endif
}
}
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;
}
int
gsl_sf_legendre_Plm_deriv_array(
const int lmax, const int m, const double x,
double * result_array,
double * result_deriv_array)
{
if(m < 0 || m > lmax)
{
GSL_ERROR("m < 0 or m > lmax", GSL_EDOM);
}
else if(m == 0)
{
/* It is better to do m=0 this way, so we can more easily
* trap the divergent case which can occur when m == 1.
*/
return gsl_sf_legendre_Pl_deriv_array(lmax, x, result_array, result_deriv_array);
}
else
{
int stat_array = gsl_sf_legendre_Plm_array(lmax, m, x, result_array);
if(stat_array == GSL_SUCCESS)
{
int ell;
if(m == 1 && (1.0 - fabs(x) < GSL_DBL_EPSILON))
{
/* This divergence is real and comes from the cusp-like
* behaviour for m = 1. For example, P[1,1] = - Sqrt[1-x^2].
*/
GSL_ERROR("divergence near |x| = 1.0 since m = 1", GSL_EOVRFLW);
}
else if(m == 2 && (1.0 - fabs(x) < GSL_DBL_EPSILON))
{
/* m = 2 gives a finite nonzero result for |x| near 1 */
if(fabs(x - 1.0) < GSL_DBL_EPSILON)
{
for(ell = m; ell <= lmax; ell++) result_deriv_array[ell-m] = -0.25 * x * (ell - 1.0)*ell*(ell+1.0)*(ell+2.0);
}
else if(fabs(x + 1.0) < GSL_DBL_EPSILON)
{
for(ell = m; ell <= lmax; ell++)
{
const double sgn = ( GSL_IS_ODD(ell) ? 1.0 : -1.0 );
result_deriv_array[ell-m] = -0.25 * sgn * x * (ell - 1.0)*ell*(ell+1.0)*(ell+2.0);
}
}
return GSL_SUCCESS;
}
else
{
/* m > 2 is easier to deal with since the endpoints always vanish */
if(1.0 - fabs(x) < GSL_DBL_EPSILON)
{
for(ell = m; ell <= lmax; ell++) result_deriv_array[ell-m] = 0.0;
return GSL_SUCCESS;
}
else
{
const double diff_a = 1.0 + x;
const double diff_b = 1.0 - x;
result_deriv_array[0] = - m * x / (diff_a * diff_b) * result_array[0];
if(lmax-m >= 1) result_deriv_array[1] = (2.0 * m + 1.0) * (x * result_deriv_array[0] + result_array[0]);
for(ell = m+2; ell <= lmax; ell++)
{
result_deriv_array[ell-m] = - (ell * x * result_array[ell-m] - (ell+m) * result_array[ell-1-m]) / (diff_a * diff_b);
}
return GSL_SUCCESS;
}
}
}
else
{
return stat_array;
}
}
}
