int gsl_sf_expint_Ei_e(const double x, gsl_sf_result * result) { /* CHECK_POINTER(result) */ { int status = gsl_sf_expint_E1_e(-x, result); result->val = -result->val; return status; } }
/// Exponential integral E_1. double expint_E1(double x) { gsl_sf_result result; int stat = gsl_sf_expint_E1_e(x, &result); if (stat != GSL_SUCCESS) { std::ostringstream msg("Error in expint_E1:"); msg << " x=" << x; throw std::runtime_error(msg.str()); } else return result.val; }
int gsl_sf_expint_E2_e(const double x, gsl_sf_result * result) { const double xmaxt = -GSL_LOG_DBL_MIN; const double xmax = xmaxt - log(xmaxt); /* CHECK_POINTER(result) */ if(x < -xmax) { OVERFLOW_ERROR(result); } else if(x < 100.0) { const double ex = exp(-x); gsl_sf_result result_E1; int stat_E1 = gsl_sf_expint_E1_e(x, &result_E1); result->val = ex - x*result_E1.val; result->err = fabs(x) * (GSL_DBL_EPSILON*ex + result_E1.err); result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); return stat_E1; } else if(x < xmax) { const double c1 = -2.0; const double c2 = 6.0; const double c3 = -24.0; const double c4 = 120.0; const double c5 = -720.0; const double c6 = 5040.0; const double c7 = -40320.0; const double c8 = 362880.0; const double c9 = -3628800.0; const double c10 = 39916800.0; const double c11 = -479001600.0; const double c12 = 6227020800.0; const double c13 = -87178291200.0; const double y = 1.0/x; const double sum6 = c6+y*(c7+y*(c8+y*(c9+y*(c10+y*(c11+y*(c12+y*c13)))))); const double sum = y*(c1+y*(c2+y*(c3+y*(c4+y*(c5+y*sum6))))); result->val = exp(-x) * (1.0 + sum)/x; result->err = 2.0 * (x + 1.0) * GSL_DBL_EPSILON * result->val; return GSL_SUCCESS; } else { UNDERFLOW_ERROR(result); } }
int gsl_sf_Chi_e(const double x, gsl_sf_result * result) { gsl_sf_result result_Ei; gsl_sf_result result_E1; int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei); int status_E1 = gsl_sf_expint_E1_e(x, &result_E1); if(status_Ei == GSL_EDOM || status_E1 == GSL_EDOM) { DOMAIN_ERROR(result); } else if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) { UNDERFLOW_ERROR(result); } else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) { OVERFLOW_ERROR(result); } else { result->val = 0.5 * (result_Ei.val - result_E1.val); result->err = 0.5 * (result_Ei.err + result_E1.err); result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); return GSL_SUCCESS; } }
int gsl_sf_Shi_e(const double x, gsl_sf_result * result) { const double xsml = GSL_SQRT_DBL_EPSILON; /* sqrt (r1mach(3)) */ const double ax = fabs(x); if(ax < xsml) { result->val = x; result->err = 0.0; return GSL_SUCCESS; } else if(ax <= 0.375) { gsl_sf_result result_c; cheb_eval_e(&shi_cs, 128.0*x*x/9.0-1.0, &result_c); result->val = x * (1.0 + result_c.val); result->err = x * result_c.err; result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); return GSL_SUCCESS; } else { gsl_sf_result result_Ei; gsl_sf_result result_E1; int status_Ei = gsl_sf_expint_Ei_e(x, &result_Ei); int status_E1 = gsl_sf_expint_E1_e(x, &result_E1); result->val = 0.5*(result_Ei.val + result_E1.val); result->err = 0.5*(result_Ei.err + result_E1.err); result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); if(status_Ei == GSL_EUNDRFLW && status_E1 == GSL_EUNDRFLW) { GSL_ERROR ("underflow", GSL_EUNDRFLW); } else if(status_Ei == GSL_EOVRFLW || status_E1 == GSL_EOVRFLW) { GSL_ERROR ("overflow", GSL_EOVRFLW); } else { return GSL_SUCCESS; } } }
double gsl_sf_expint_E1(const double x) { EVAL_RESULT(gsl_sf_expint_E1_e(x, &result)); }