int
gsl_sf_complex_logsin_e(const double zr, const double zi,
gsl_sf_result * lszr, gsl_sf_result * lszi)
{
/* CHECK_POINTER(lszr) */
/* CHECK_POINTER(lszi) */
if(zi > 60.0) {
lszr->val = -M_LN2 + zi;
lszi->val = 0.5*M_PI - zr;
lszr->err = 2.0 * GSL_DBL_EPSILON * fabs(lszr->val);
lszi->err = 2.0 * GSL_DBL_EPSILON * fabs(lszi->val);
}
else if(zi < -60.0) {
lszr->val = -M_LN2 - zi;
lszi->val = -0.5*M_PI + zr;
lszr->err = 2.0 * GSL_DBL_EPSILON * fabs(lszr->val);
lszi->err = 2.0 * GSL_DBL_EPSILON * fabs(lszi->val);
}
else {
gsl_sf_result sin_r, sin_i;
int status;
gsl_sf_complex_sin_e(zr, zi, &sin_r, &sin_i); /* ok by construction */
status = gsl_sf_complex_log_e(sin_r.val, sin_i.val, lszr, lszi);
if(status == GSL_EDOM) {
DOMAIN_ERROR_2(lszr, lszi);
}
}
return gsl_sf_angle_restrict_symm_e(&(lszi->val));
}
/* Compute Li_2(z) using the one-step accelerated series.
*
* Li_2(z) = 1 + (1-z)ln(1-z)/z + series_2_c(z)
*
* z = r exp(i theta)
* assumes: r < 1
* assumes: r > epsilon, so that we take no special care with log(1-z)
*/
static
int
dilogc_series_2(
const double r,
const double x,
const double y,
gsl_sf_result * real_dl,
gsl_sf_result * imag_dl
)
{
if(r == 0.0)
{
real_dl->val = 0.0;
imag_dl->val = 0.0;
real_dl->err = 0.0;
imag_dl->err = 0.0;
return GSL_SUCCESS;
}
else
{
gsl_sf_result sum_re;
gsl_sf_result sum_im;
const int stat_s3 = series_2_c(r, x, y, &sum_re, &sum_im);
/* t = ln(1-z)/z */
gsl_sf_result ln_omz_r;
gsl_sf_result ln_omz_theta;
const int stat_log = gsl_sf_complex_log_e(1.0-x, -y, &ln_omz_r, &ln_omz_theta);
const double t_x = ( ln_omz_r.val * x + ln_omz_theta.val * y)/(r*r);
const double t_y = (-ln_omz_r.val * y + ln_omz_theta.val * x)/(r*r);
/* r = (1-z) ln(1-z)/z */
const double r_x = (1.0 - x) * t_x + y * t_y;
const double r_y = (1.0 - x) * t_y - y * t_x;
real_dl->val = sum_re.val + r_x + 1.0;
imag_dl->val = sum_im.val + r_y;
real_dl->err = sum_re.err + 2.0*GSL_DBL_EPSILON*(fabs(real_dl->val) + fabs(r_x));
imag_dl->err = sum_im.err + 2.0*GSL_DBL_EPSILON*(fabs(imag_dl->val) + fabs(r_y));
return GSL_ERROR_SELECT_2(stat_s3, stat_log);
}
}
CAMLprim value ml_gsl_sf_complex_log_e(value zr, value zi)
{
gsl_sf_result lnr, theta;
gsl_sf_complex_log_e(Double_val(zr), Double_val(zi), &lnr, &theta);
return val_of_result_pair (&lnr, &theta);
}