int gsl_sf_zetam1_int_e(const int n, gsl_sf_result * result)
{
if(n < 0) {
if(!GSL_IS_ODD(n)) {
result->val = -1.0; /* at even negative integers zetam1 == -1 since zeta is exactly zero */
result->err = 0.0;
return GSL_SUCCESS;
}
else if(n > -ZETA_NEG_TABLE_NMAX) {
result->val = zeta_neg_int_table[-(n+1)/2] - 1.0;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
/* could use gsl_sf_zetam1_e here but subtracting 1 makes no difference
for such large values, so go straight to the result */
return gsl_sf_zeta_e((double)n, result);
}
}
else if(n == 1){
DOMAIN_ERROR(result);
}
else if(n <= ZETA_POS_TABLE_NMAX){
result->val = zetam1_pos_int_table[n];
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
return gsl_sf_zetam1_e(n, result);
}
}
int gsl_sf_zeta_int_e(const int n, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(n < 0) {
if(!GSL_IS_ODD(n)) {
result->val = 0.0; /* exactly zero at even negative integers */
result->err = 0.0;
return GSL_SUCCESS;
}
else if(n > -ZETA_NEG_TABLE_NMAX) {
result->val = zeta_neg_int_table[-(n+1)/2];
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
return gsl_sf_zeta_e((double)n, result);
}
}
else if(n == 1){
DOMAIN_ERROR(result);
}
else if(n <= ZETA_POS_TABLE_NMAX){
result->val = 1.0 + zetam1_pos_int_table[n];
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
result->val = 1.0;
result->err = GSL_DBL_EPSILON;
return GSL_SUCCESS;
}
}
int gsl_sf_eta_e(const double s, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(s > 100.0) {
result->val = 1.0;
result->err = GSL_DBL_EPSILON;
return GSL_SUCCESS;
}
else if(fabs(s-1.0) < 10.0*GSL_ROOT5_DBL_EPSILON) {
double del = s-1.0;
double c0 = M_LN2;
double c1 = M_LN2 * (M_EULER - 0.5*M_LN2);
double c2 = -0.0326862962794492996;
double c3 = 0.0015689917054155150;
double c4 = 0.00074987242112047532;
result->val = c0 + del * (c1 + del * (c2 + del * (c3 + del * c4)));
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
gsl_sf_result z;
gsl_sf_result p;
int stat_z = gsl_sf_zeta_e(s, &z);
int stat_p = gsl_sf_exp_e((1.0-s)*M_LN2, &p);
int stat_m = gsl_sf_multiply_e(1.0-p.val, z.val, result);
result->err = fabs(p.err * (M_LN2*(1.0-s)) * z.val) + z.err * fabs(p.val);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_3(stat_m, stat_p, stat_z);
}
}
void zeta(double *s, int *len, double *val, double *err, int *status)
{
int i;
gsl_sf_result result;
gsl_set_error_handler_off();
for(i = 0; i< *len ; i++){
status[i] = gsl_sf_zeta_e(s[i], &result) ;
val[i] = result.val;
err[i] = result.err;
}
}
/// Riemann zeta function.
double
riemann_zeta(double x)
{
gsl_sf_result result;
int stat = gsl_sf_zeta_e(x, &result);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in riemann_zeta:");
msg << " x=" << x;
throw std::runtime_error(msg.str());
}
else
return result.val;
}
int gsl_sf_zetam1_e(const double s, gsl_sf_result * result)
{
if(s <= 5.0)
{
int stat = gsl_sf_zeta_e(s, result);
result->val = result->val - 1.0;
return stat;
}
else if(s < 15.0)
{
return riemann_zeta_minus_1_intermediate_s(s, result);
}
else
{
return riemann_zeta_minus1_large_s(s, result);
}
}
double gsl_sf_zeta(const double s)
{
EVAL_RESULT(gsl_sf_zeta_e(s, &result));
}
