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); }