static VALUE rb_gsl_sf_pow_int_e(VALUE obj, VALUE x, VALUE n)
{
gsl_sf_result *rslt = NULL;
VALUE v;
int status;
Need_Float(x);
CHECK_FIXNUM(n);
v = Data_Make_Struct(cgsl_sf_result, gsl_sf_result, 0, free, rslt);
status = gsl_sf_pow_int_e(NUM2DBL(x), FIX2INT(n), rslt);
return v;
}
double gsl_sf_pow_int(const double x, const int n)
{
EVAL_RESULT(gsl_sf_pow_int_e(x, n, &result));
}
int
gsl_sf_bessel_zero_Jnu_e(double nu, unsigned int s, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(nu <= -1.0) {
DOMAIN_ERROR(result);
}
else if(s == 0) {
result->val = 0.0;
result->err = 0.0;
if (nu == 0.0) {
GSL_ERROR ("no zero-th root for nu = 0.0", GSL_EINVAL);
}
return GSL_SUCCESS;
}
else if(nu < 0.0) {
/* This can be done, I'm just lazy now. */
result->val = 0.0;
result->err = 0.0;
GSL_ERROR("unimplemented", GSL_EUNIMPL);
}
else if(s == 1) {
/* Chebyshev fits for the first positive zero.
* For some reason Nemeth made this different from the others.
*/
if(nu < 2.0) {
const double * c = coef_jnu_a[s];
const size_t L = size_jnu_a[s];
const double arg = nu/2.0;
const double chb = clenshaw(c, L-1, arg);
result->val = chb;
result->err = 2.0e-15 * result->val;
}
else {
const double * c = coef_jnu_b[s];
const size_t L = size_jnu_b[s];
const double arg = pow(2.0/nu, 2.0/3.0);
const double chb = clenshaw(c, L-1, arg);
result->val = nu * chb;
result->err = 2.0e-15 * result->val;
}
return GSL_SUCCESS;
}
else if(s <= 10) {
/* Chebyshev fits for the first 10 positive zeros. */
if(nu < s) {
const double * c = coef_jnu_a[s];
const size_t L = size_jnu_a[s];
const double arg = nu/s;
const double chb = clenshaw(c, L-1, arg);
result->val = chb;
result->err = 2.0e-15 * result->val;
}
else {
const double * c = coef_jnu_b[s];
const size_t L = size_jnu_b[s];
const double arg = pow(s/nu, 2.0/3.0);
const double chb = clenshaw(c, L-1, arg);
result->val = nu * chb;
result->err = 2.0e-15 * result->val;
/* FIXME: truth in advertising for the screwed up
* s = 5 fit. Need to fix that.
*/
if(s == 5) {
result->err *= 5.0e+06;
}
}
return GSL_SUCCESS;
}
else if(s > 0.5*nu && s <= 20) {
/* Chebyshev fits for 10 < s <= 20. */
const double * c = coef_jnu_a[s];
const size_t L = size_jnu_a[s];
const double arg = nu/(2.0*s);
const double chb = clenshaw(c, L-1, arg);
result->val = chb;
result->err = 4.0e-15 * chb;
return GSL_SUCCESS;
}
else if(s > 2.0 * nu) {
/* McMahon expansion if s is large compared to nu. */
const double beta = (s + 0.5*nu - 0.25) * M_PI;
const double mc = mcmahon_correction(4.0*nu*nu, beta);
gsl_sf_result rat12;
gsl_sf_pow_int_e(nu/beta, 14, &rat12);
result->val = beta * mc;
result->err = 4.0 * fabs(beta) * rat12.val;
result->err += 4.0 * fabs(GSL_DBL_EPSILON * result->val);
return GSL_SUCCESS;
}
else {
/* Olver uniform asymptotic. */
gsl_sf_result as;
const int stat_as = gsl_sf_airy_zero_Ai_e(s, &as);
const double minus_zeta = -pow(nu,-2.0/3.0) * as.val;
const double z = gsl_sf_bessel_Olver_zofmzeta(minus_zeta);
const double f1 = olver_f1(z, minus_zeta);
result->val = nu * (z + f1/(nu*nu));
result->err = 0.001/(nu*nu*nu);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return stat_as;
}
}