| /* specfunc/dilog.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU General Public License as published by |
| * the Free Software Foundation; either version 2 of the License, or (at |
| * your option) any later version. |
| * |
| * This program is distributed in the hope that it will be useful, but |
| * WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * General Public License for more details. |
| * |
| * You should have received a copy of the GNU General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. |
| */ |
| |
| /* Author: G. Jungman */ |
| |
| #include <config.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_errno.h> |
| #include <gsl/gsl_sf_clausen.h> |
| #include <gsl/gsl_sf_trig.h> |
| #include <gsl/gsl_sf_log.h> |
| #include <gsl/gsl_sf_dilog.h> |
| |
| |
| /* Evaluate series for real dilog(x) |
| * Sum[ x^k / k^2, {k,1,Infinity}] |
| * |
| * Converges rapidly for |x| < 1/2. |
| */ |
| static |
| int |
| dilog_series_1(const double x, gsl_sf_result * result) |
| { |
| const int kmax = 1000; |
| double sum = x; |
| double term = x; |
| int k; |
| for(k=2; k<kmax; k++) { |
| const double rk = (k-1.0)/k; |
| term *= x; |
| term *= rk*rk; |
| sum += term; |
| if(fabs(term/sum) < GSL_DBL_EPSILON) break; |
| } |
| |
| result->val = sum; |
| result->err = 2.0 * fabs(term); |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| |
| if(k == kmax) |
| GSL_ERROR ("error", GSL_EMAXITER); |
| else |
| return GSL_SUCCESS; |
| } |
| |
| |
| /* Compute the associated series |
| * |
| * sum_{k=1}{infty} r^k / (k^2 (k+1)) |
| * |
| * This is a series which appears in the one-step accelerated |
| * method, which splits out one elementary function from the |
| * full definition of Li_2(x). See below. |
| */ |
| static int |
| series_2(double r, gsl_sf_result * result) |
| { |
| static const int kmax = 100; |
| double rk = r; |
| double sum = 0.5 * r; |
| int k; |
| for(k=2; k<10; k++) |
| { |
| double ds; |
| rk *= r; |
| ds = rk/(k*k*(k+1.0)); |
| sum += ds; |
| } |
| for(; k<kmax; k++) |
| { |
| double ds; |
| rk *= r; |
| ds = rk/(k*k*(k+1.0)); |
| sum += ds; |
| if(fabs(ds/sum) < 0.5*GSL_DBL_EPSILON) break; |
| } |
| |
| result->val = sum; |
| result->err = 2.0 * kmax * GSL_DBL_EPSILON * fabs(sum); |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| /* Compute Li_2(x) using the accelerated series representation. |
| * |
| * Li_2(x) = 1 + (1-x)ln(1-x)/x + series_2(x) |
| * |
| * assumes: -1 < x < 1 |
| */ |
| static int |
| dilog_series_2(double x, gsl_sf_result * result) |
| { |
| const int stat_s3 = series_2(x, result); |
| double t; |
| if(x > 0.01) |
| t = (1.0 - x) * log(1.0-x) / x; |
| else |
| { |
| static const double c3 = 1.0/3.0; |
| static const double c4 = 1.0/4.0; |
| static const double c5 = 1.0/5.0; |
| static const double c6 = 1.0/6.0; |
| static const double c7 = 1.0/7.0; |
| static const double c8 = 1.0/8.0; |
| const double t68 = c6 + x*(c7 + x*c8); |
| const double t38 = c3 + x *(c4 + x *(c5 + x * t68)); |
| t = (x - 1.0) * (1.0 + x*(0.5 + x*t38)); |
| } |
| result->val += 1.0 + t; |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(t); |
| return stat_s3; |
| } |
| |
| |
| /* Calculates Li_2(x) for real x. Assumes x >= 0.0. |
| */ |
| static |
| int |
| dilog_xge0(const double x, gsl_sf_result * result) |
| { |
| if(x > 2.0) { |
| gsl_sf_result ser; |
| const int stat_ser = dilog_series_2(1.0/x, &ser); |
| const double log_x = log(x); |
| const double t1 = M_PI*M_PI/3.0; |
| const double t2 = ser.val; |
| const double t3 = 0.5*log_x*log_x; |
| result->val = t1 - t2 - t3; |
| result->err = GSL_DBL_EPSILON * fabs(log_x) + ser.err; |
| result->err += GSL_DBL_EPSILON * (fabs(t1) + fabs(t2) + fabs(t3)); |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| return stat_ser; |
| } |
| else if(x > 1.01) { |
| gsl_sf_result ser; |
| const int stat_ser = dilog_series_2(1.0 - 1.0/x, &ser); |
| const double log_x = log(x); |
| const double log_term = log_x * (log(1.0-1.0/x) + 0.5*log_x); |
| const double t1 = M_PI*M_PI/6.0; |
| const double t2 = ser.val; |
| const double t3 = log_term; |
| result->val = t1 + t2 - t3; |
| result->err = GSL_DBL_EPSILON * fabs(log_x) + ser.err; |
| result->err += GSL_DBL_EPSILON * (fabs(t1) + fabs(t2) + fabs(t3)); |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| return stat_ser; |
| } |
| else if(x > 1.0) { |
| /* series around x = 1.0 */ |
| const double eps = x - 1.0; |
| const double lne = log(eps); |
| const double c0 = M_PI*M_PI/6.0; |
| const double c1 = 1.0 - lne; |
| const double c2 = -(1.0 - 2.0*lne)/4.0; |
| const double c3 = (1.0 - 3.0*lne)/9.0; |
| const double c4 = -(1.0 - 4.0*lne)/16.0; |
| const double c5 = (1.0 - 5.0*lne)/25.0; |
| const double c6 = -(1.0 - 6.0*lne)/36.0; |
| const double c7 = (1.0 - 7.0*lne)/49.0; |
| const double c8 = -(1.0 - 8.0*lne)/64.0; |
| result->val = c0+eps*(c1+eps*(c2+eps*(c3+eps*(c4+eps*(c5+eps*(c6+eps*(c7+eps*c8))))))); |
| result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_SUCCESS; |
| } |
| else if(x == 1.0) { |
| result->val = M_PI*M_PI/6.0; |
| result->err = 2.0 * GSL_DBL_EPSILON * M_PI*M_PI/6.0; |
| return GSL_SUCCESS; |
| } |
| else if(x > 0.5) { |
| gsl_sf_result ser; |
| const int stat_ser = dilog_series_2(1.0-x, &ser); |
| const double log_x = log(x); |
| const double t1 = M_PI*M_PI/6.0; |
| const double t2 = ser.val; |
| const double t3 = log_x*log(1.0-x); |
| result->val = t1 - t2 - t3; |
| result->err = GSL_DBL_EPSILON * fabs(log_x) + ser.err; |
| result->err += GSL_DBL_EPSILON * (fabs(t1) + fabs(t2) + fabs(t3)); |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| return stat_ser; |
| } |
| else if(x > 0.25) { |
| return dilog_series_2(x, result); |
| } |
| else if(x > 0.0) { |
| return dilog_series_1(x, result); |
| } |
| else { |
| /* x == 0.0 */ |
| result->val = 0.0; |
| result->err = 0.0; |
| return GSL_SUCCESS; |
| } |
| } |
| |
| |
| /* Evaluate the series representation for Li2(z): |
| * |
| * Li2(z) = Sum[ |z|^k / k^2 Exp[i k arg(z)], {k,1,Infinity}] |
| * |z| = r |
| * arg(z) = theta |
| * |
| * Assumes 0 < r < 1. |
| * It is used only for small r. |
| */ |
| static |
| int |
| dilogc_series_1( |
| const double r, |
| const double x, |
| const double y, |
| gsl_sf_result * real_result, |
| gsl_sf_result * imag_result |
| ) |
| { |
| const double cos_theta = x/r; |
| const double sin_theta = y/r; |
| const double alpha = 1.0 - cos_theta; |
| const double beta = sin_theta; |
| double ck = cos_theta; |
| double sk = sin_theta; |
| double rk = r; |
| double real_sum = r*ck; |
| double imag_sum = r*sk; |
| const int kmax = 50 + (int)(22.0/(-log(r))); /* tuned for double-precision */ |
| int k; |
| for(k=2; k<kmax; k++) { |
| double dr, di; |
| double ck_tmp = ck; |
| ck = ck - (alpha*ck + beta*sk); |
| sk = sk - (alpha*sk - beta*ck_tmp); |
| rk *= r; |
| dr = rk/((double)k*k) * ck; |
| di = rk/((double)k*k) * sk; |
| real_sum += dr; |
| imag_sum += di; |
| if(fabs((dr*dr + di*di)/(real_sum*real_sum + imag_sum*imag_sum)) < GSL_DBL_EPSILON*GSL_DBL_EPSILON) break; |
| } |
| |
| real_result->val = real_sum; |
| real_result->err = 2.0 * kmax * GSL_DBL_EPSILON * fabs(real_sum); |
| imag_result->val = imag_sum; |
| imag_result->err = 2.0 * kmax * GSL_DBL_EPSILON * fabs(imag_sum); |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| /* Compute |
| * |
| * sum_{k=1}{infty} z^k / (k^2 (k+1)) |
| * |
| * This is a series which appears in the one-step accelerated |
| * method, which splits out one elementary function from the |
| * full definition of Li_2. |
| */ |
| static int |
| series_2_c( |
| double r, |
| double x, |
| double y, |
| gsl_sf_result * sum_re, |
| gsl_sf_result * sum_im |
| ) |
| { |
| const double cos_theta = x/r; |
| const double sin_theta = y/r; |
| const double alpha = 1.0 - cos_theta; |
| const double beta = sin_theta; |
| double ck = cos_theta; |
| double sk = sin_theta; |
| double rk = r; |
| double real_sum = 0.5 * r*ck; |
| double imag_sum = 0.5 * r*sk; |
| const int kmax = 30 + (int)(18.0/(-log(r))); /* tuned for double-precision */ |
| int k; |
| for(k=2; k<kmax; k++) |
| { |
| double dr, di; |
| const double ck_tmp = ck; |
| ck = ck - (alpha*ck + beta*sk); |
| sk = sk - (alpha*sk - beta*ck_tmp); |
| rk *= r; |
| dr = rk/((double)k*k*(k+1.0)) * ck; |
| di = rk/((double)k*k*(k+1.0)) * sk; |
| real_sum += dr; |
| imag_sum += di; |
| if(fabs((dr*dr + di*di)/(real_sum*real_sum + imag_sum*imag_sum)) < GSL_DBL_EPSILON*GSL_DBL_EPSILON) break; |
| } |
| |
| sum_re->val = real_sum; |
| sum_re->err = 2.0 * kmax * GSL_DBL_EPSILON * fabs(real_sum); |
| sum_im->val = imag_sum; |
| sum_im->err = 2.0 * kmax * GSL_DBL_EPSILON * fabs(imag_sum); |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| /* 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); |
| } |
| } |
| |
| |
| /* Evaluate a series for Li_2(z) when |z| is near 1. |
| * This is uniformly good away from z=1. |
| * |
| * Li_2(z) = Sum[ a^n/n! H_n(theta), {n, 0, Infinity}] |
| * |
| * where |
| * H_n(theta) = Sum[ e^(i m theta) m^n / m^2, {m, 1, Infinity}] |
| * a = ln(r) |
| * |
| * H_0(t) = Gl_2(t) + i Cl_2(t) |
| * H_1(t) = 1/2 ln(2(1-c)) + I atan2(-s, 1-c) |
| * H_2(t) = -1/2 + I/2 s/(1-c) |
| * H_3(t) = -1/2 /(1-c) |
| * H_4(t) = -I/2 s/(1-c)^2 |
| * H_5(t) = 1/2 (2 + c)/(1-c)^2 |
| * H_6(t) = I/2 s/(1-c)^5 (8(1-c) - s^2 (3 + c)) |
| */ |
| static |
| int |
| dilogc_series_3( |
| const double r, |
| const double x, |
| const double y, |
| gsl_sf_result * real_result, |
| gsl_sf_result * imag_result |
| ) |
| { |
| const double theta = atan2(y, x); |
| const double cos_theta = x/r; |
| const double sin_theta = y/r; |
| const double a = log(r); |
| const double omc = 1.0 - cos_theta; |
| const double omc2 = omc*omc; |
| double H_re[7]; |
| double H_im[7]; |
| double an, nfact; |
| double sum_re, sum_im; |
| gsl_sf_result Him0; |
| int n; |
| |
| H_re[0] = M_PI*M_PI/6.0 + 0.25*(theta*theta - 2.0*M_PI*fabs(theta)); |
| gsl_sf_clausen_e(theta, &Him0); |
| H_im[0] = Him0.val; |
| |
| H_re[1] = -0.5*log(2.0*omc); |
| H_im[1] = -atan2(-sin_theta, omc); |
| |
| H_re[2] = -0.5; |
| H_im[2] = 0.5 * sin_theta/omc; |
| |
| H_re[3] = -0.5/omc; |
| H_im[3] = 0.0; |
| |
| H_re[4] = 0.0; |
| H_im[4] = -0.5*sin_theta/omc2; |
| |
| H_re[5] = 0.5 * (2.0 + cos_theta)/omc2; |
| H_im[5] = 0.0; |
| |
| H_re[6] = 0.0; |
| H_im[6] = 0.5 * sin_theta/(omc2*omc2*omc) * (8.0*omc - sin_theta*sin_theta*(3.0 + cos_theta)); |
| |
| sum_re = H_re[0]; |
| sum_im = H_im[0]; |
| an = 1.0; |
| nfact = 1.0; |
| for(n=1; n<=6; n++) { |
| double t; |
| an *= a; |
| nfact *= n; |
| t = an/nfact; |
| sum_re += t * H_re[n]; |
| sum_im += t * H_im[n]; |
| } |
| |
| real_result->val = sum_re; |
| real_result->err = 2.0 * 6.0 * GSL_DBL_EPSILON * fabs(sum_re) + fabs(an/nfact); |
| imag_result->val = sum_im; |
| imag_result->err = 2.0 * 6.0 * GSL_DBL_EPSILON * fabs(sum_im) + Him0.err + fabs(an/nfact); |
| |
| return GSL_SUCCESS; |
| } |
| |
| |
| /* Calculate complex dilogarithm Li_2(z) in the fundamental region, |
| * which we take to be the intersection of the unit disk with the |
| * half-space x < MAGIC_SPLIT_VALUE. It turns out that 0.732 is a |
| * nice choice for MAGIC_SPLIT_VALUE since then points mapped out |
| * of the x > MAGIC_SPLIT_VALUE region and into another part of the |
| * unit disk are bounded in radius by MAGIC_SPLIT_VALUE itself. |
| * |
| * If |z| < 0.98 we use a direct series summation. Otherwise z is very |
| * near the unit circle, and the series_2 expansion is used; see above. |
| * Because the fundamental region is bounded away from z = 1, this |
| * works well. |
| */ |
| static |
| int |
| dilogc_fundamental(double r, double x, double y, gsl_sf_result * real_dl, gsl_sf_result * imag_dl) |
| { |
| if(r > 0.98) |
| return dilogc_series_3(r, x, y, real_dl, imag_dl); |
| else if(r > 0.25) |
| return dilogc_series_2(r, x, y, real_dl, imag_dl); |
| else |
| return dilogc_series_1(r, x, y, real_dl, imag_dl); |
| } |
| |
| |
| /* Compute Li_2(z) for z in the unit disk, |z| < 1. If z is outside |
| * the fundamental region, which means that it is too close to z = 1, |
| * then it is reflected into the fundamental region using the identity |
| * |
| * Li2(z) = -Li2(1-z) + zeta(2) - ln(z) ln(1-z). |
| */ |
| static |
| int |
| dilogc_unitdisk(double x, double y, gsl_sf_result * real_dl, gsl_sf_result * imag_dl) |
| { |
| static const double MAGIC_SPLIT_VALUE = 0.732; |
| static const double zeta2 = M_PI*M_PI/6.0; |
| const double r = hypot(x, y); |
| |
| if(x > MAGIC_SPLIT_VALUE) |
| { |
| /* Reflect away from z = 1 if we are too close. The magic value |
| * insures that the reflected value of the radius satisfies the |
| * related inequality r_tmp < MAGIC_SPLIT_VALUE. |
| */ |
| const double x_tmp = 1.0 - x; |
| const double y_tmp = - y; |
| const double r_tmp = hypot(x_tmp, y_tmp); |
| /* const double cos_theta_tmp = x_tmp/r_tmp; */ |
| /* const double sin_theta_tmp = y_tmp/r_tmp; */ |
| |
| gsl_sf_result result_re_tmp; |
| gsl_sf_result result_im_tmp; |
| |
| const int stat_dilog = dilogc_fundamental(r_tmp, x_tmp, y_tmp, &result_re_tmp, &result_im_tmp); |
| |
| const double lnz = log(r); /* log(|z|) */ |
| const double lnomz = log(r_tmp); /* log(|1-z|) */ |
| const double argz = atan2(y, x); /* arg(z) assuming principal branch */ |
| const double argomz = atan2(y_tmp, x_tmp); /* arg(1-z) */ |
| real_dl->val = -result_re_tmp.val + zeta2 - lnz*lnomz + argz*argomz; |
| real_dl->err = result_re_tmp.err; |
| real_dl->err += 2.0 * GSL_DBL_EPSILON * (zeta2 + fabs(lnz*lnomz) + fabs(argz*argomz)); |
| imag_dl->val = -result_im_tmp.val - argz*lnomz - argomz*lnz; |
| imag_dl->err = result_im_tmp.err; |
| imag_dl->err += 2.0 * GSL_DBL_EPSILON * (fabs(argz*lnomz) + fabs(argomz*lnz)); |
| |
| return stat_dilog; |
| } |
| else |
| { |
| return dilogc_fundamental(r, x, y, real_dl, imag_dl); |
| } |
| } |
| |
| |
| |
| /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ |
| |
| |
| int |
| gsl_sf_dilog_e(const double x, gsl_sf_result * result) |
| { |
| if(x >= 0.0) { |
| return dilog_xge0(x, result); |
| } |
| else { |
| gsl_sf_result d1, d2; |
| int stat_d1 = dilog_xge0( -x, &d1); |
| int stat_d2 = dilog_xge0(x*x, &d2); |
| result->val = -d1.val + 0.5 * d2.val; |
| result->err = d1.err + 0.5 * d2.err; |
| result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); |
| return GSL_ERROR_SELECT_2(stat_d1, stat_d2); |
| } |
| } |
| |
| |
| int |
| gsl_sf_complex_dilog_xy_e( |
| const double x, |
| const double y, |
| gsl_sf_result * real_dl, |
| gsl_sf_result * imag_dl |
| ) |
| { |
| const double zeta2 = M_PI*M_PI/6.0; |
| const double r2 = x*x + y*y; |
| |
| if(y == 0.0) |
| { |
| if(x >= 1.0) |
| { |
| imag_dl->val = -M_PI * log(x); |
| imag_dl->err = 2.0 * GSL_DBL_EPSILON * fabs(imag_dl->val); |
| } |
| else |
| { |
| imag_dl->val = 0.0; |
| imag_dl->err = 0.0; |
| } |
| return gsl_sf_dilog_e(x, real_dl); |
| } |
| else if(fabs(r2 - 1.0) < GSL_DBL_EPSILON) |
| { |
| /* Lewin A.2.4.1 and A.2.4.2 */ |
| |
| const double theta = atan2(y, x); |
| const double term1 = theta*theta/4.0; |
| const double term2 = M_PI*fabs(theta)/2.0; |
| real_dl->val = zeta2 + term1 - term2; |
| real_dl->err = 2.0 * GSL_DBL_EPSILON * (zeta2 + term1 + term2); |
| return gsl_sf_clausen_e(theta, imag_dl); |
| } |
| else if(r2 < 1.0) |
| { |
| return dilogc_unitdisk(x, y, real_dl, imag_dl); |
| } |
| else |
| { |
| /* Reduce argument to unit disk. */ |
| const double r = sqrt(r2); |
| const double x_tmp = x/r2; |
| const double y_tmp = -y/r2; |
| /* const double r_tmp = 1.0/r; */ |
| gsl_sf_result result_re_tmp, result_im_tmp; |
| |
| const int stat_dilog = |
| dilogc_unitdisk(x_tmp, y_tmp, &result_re_tmp, &result_im_tmp); |
| |
| /* Unwind the inversion. |
| * |
| * Li_2(z) + Li_2(1/z) = -zeta(2) - 1/2 ln(-z)^2 |
| */ |
| const double theta = atan2(y, x); |
| const double theta_abs = fabs(theta); |
| const double theta_sgn = ( theta < 0.0 ? -1.0 : 1.0 ); |
| const double ln_minusz_re = log(r); |
| const double ln_minusz_im = theta_sgn * (theta_abs - M_PI); |
| const double lmz2_re = ln_minusz_re*ln_minusz_re - ln_minusz_im*ln_minusz_im; |
| const double lmz2_im = 2.0*ln_minusz_re*ln_minusz_im; |
| real_dl->val = -result_re_tmp.val - 0.5 * lmz2_re - zeta2; |
| real_dl->err = result_re_tmp.err + 2.0*GSL_DBL_EPSILON*(0.5 * fabs(lmz2_re) + zeta2); |
| imag_dl->val = -result_im_tmp.val - 0.5 * lmz2_im; |
| imag_dl->err = result_im_tmp.err + 2.0*GSL_DBL_EPSILON*fabs(lmz2_im); |
| return stat_dilog; |
| } |
| } |
| |
| |
| int |
| gsl_sf_complex_dilog_e( |
| const double r, |
| const double theta, |
| gsl_sf_result * real_dl, |
| gsl_sf_result * imag_dl |
| ) |
| { |
| const double cos_theta = cos(theta); |
| const double sin_theta = sin(theta); |
| const double x = r * cos_theta; |
| const double y = r * sin_theta; |
| return gsl_sf_complex_dilog_xy_e(x, y, real_dl, imag_dl); |
| } |
| |
| |
| int |
| gsl_sf_complex_spence_xy_e( |
| const double x, |
| const double y, |
| gsl_sf_result * real_sp, |
| gsl_sf_result * imag_sp |
| ) |
| { |
| const double oms_x = 1.0 - x; |
| const double oms_y = - y; |
| return gsl_sf_complex_dilog_xy_e(oms_x, oms_y, real_sp, imag_sp); |
| } |
| |
| |
| |
| /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ |
| |
| #include "eval.h" |
| |
| double gsl_sf_dilog(const double x) |
| { |
| EVAL_RESULT(gsl_sf_dilog_e(x, &result)); |
| } |