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diff --git a/gsl-1.9/specfunc/erfc.c b/gsl-1.9/specfunc/erfc.c
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+/* specfunc/erfc.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003 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: J. Theiler (modifications by G. Jungman) */
+
+/*
+ * See Hart et al, Computer Approximations, John Wiley and Sons, New York (1968)
+ * (This applies only to the erfc8 stuff, which is the part
+ * of the original code that survives. I have replaced much of
+ * the other stuff with Chebyshev fits. These are simpler and
+ * more precise than the original approximations. [GJ])
+ */
+#include <config.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_sf_exp.h>
+#include <gsl/gsl_sf_erf.h>
+
+#include "check.h"
+
+#include "chebyshev.h"
+#include "cheb_eval.c"
+
+#define LogRootPi_ 0.57236494292470008706
+
+
+static double erfc8_sum(double x)
+{
+ /* estimates erfc(x) valid for 8 < x < 100 */
+ /* This is based on index 5725 in Hart et al */
+
+ static double P[] = {
+ 2.97886562639399288862,
+ 7.409740605964741794425,
+ 6.1602098531096305440906,
+ 5.019049726784267463450058,
+ 1.275366644729965952479585264,
+ 0.5641895835477550741253201704
+ };
+ static double Q[] = {
+ 3.3690752069827527677,
+ 9.608965327192787870698,
+ 17.08144074746600431571095,
+ 12.0489519278551290360340491,
+ 9.396034016235054150430579648,
+ 2.260528520767326969591866945,
+ 1.0
+ };
+ double num=0.0, den=0.0;
+ int i;
+
+ num = P[5];
+ for (i=4; i>=0; --i) {
+ num = x*num + P[i];
+ }
+ den = Q[6];
+ for (i=5; i>=0; --i) {
+ den = x*den + Q[i];
+ }
+
+ return num/den;
+}
+
+inline
+static double erfc8(double x)
+{
+ double e;
+ e = erfc8_sum(x);
+ e *= exp(-x*x);
+ return e;
+}
+
+inline
+static double log_erfc8(double x)
+{
+ double e;
+ e = erfc8_sum(x);
+ e = log(e) - x*x;
+ return e;
+}
+
+#if 0
+/* Abramowitz+Stegun, 7.2.14 */
+static double erfcasympsum(double x)
+{
+ int i;
+ double e = 1.;
+ double coef = 1.;
+ for (i=1; i<5; ++i) {
+ /* coef *= -(2*i-1)/(2*x*x); ??? [GJ] */
+ coef *= -(2*i+1)/(i*(4*x*x*x*x));
+ e += coef;
+ /*
+ if (fabs(coef) < 1.0e-15) break;
+ if (fabs(coef) > 1.0e10) break;
+
+ [GJ]: These tests are not useful. This function is only
+ used below. Took them out; they gum up the pipeline.
+ */
+ }
+ return e;
+}
+#endif /* 0 */
+
+
+/* Abramowitz+Stegun, 7.1.5 */
+static int erfseries(double x, gsl_sf_result * result)
+{
+ double coef = x;
+ double e = coef;
+ double del;
+ int k;
+ for (k=1; k<30; ++k) {
+ coef *= -x*x/k;
+ del = coef/(2.0*k+1.0);
+ e += del;
+ }
+ result->val = 2.0 / M_SQRTPI * e;
+ result->err = 2.0 / M_SQRTPI * (fabs(del) + GSL_DBL_EPSILON);
+ return GSL_SUCCESS;
+}
+
+
+/* Chebyshev fit for erfc((t+1)/2), -1 < t < 1
+ */
+static double erfc_xlt1_data[20] = {
+ 1.06073416421769980345174155056,
+ -0.42582445804381043569204735291,
+ 0.04955262679620434040357683080,
+ 0.00449293488768382749558001242,
+ -0.00129194104658496953494224761,
+ -0.00001836389292149396270416979,
+ 0.00002211114704099526291538556,
+ -5.23337485234257134673693179020e-7,
+ -2.78184788833537885382530989578e-7,
+ 1.41158092748813114560316684249e-8,
+ 2.72571296330561699984539141865e-9,
+ -2.06343904872070629406401492476e-10,
+ -2.14273991996785367924201401812e-11,
+ 2.22990255539358204580285098119e-12,
+ 1.36250074650698280575807934155e-13,
+ -1.95144010922293091898995913038e-14,
+ -6.85627169231704599442806370690e-16,
+ 1.44506492869699938239521607493e-16,
+ 2.45935306460536488037576200030e-18,
+ -9.29599561220523396007359328540e-19
+};
+static cheb_series erfc_xlt1_cs = {
+ erfc_xlt1_data,
+ 19,
+ -1, 1,
+ 12
+};
+
+/* Chebyshev fit for erfc(x) exp(x^2), 1 < x < 5, x = 2t + 3, -1 < t < 1
+ */
+static double erfc_x15_data[25] = {
+ 0.44045832024338111077637466616,
+ -0.143958836762168335790826895326,
+ 0.044786499817939267247056666937,
+ -0.013343124200271211203618353102,
+ 0.003824682739750469767692372556,
+ -0.001058699227195126547306482530,
+ 0.000283859419210073742736310108,
+ -0.000073906170662206760483959432,
+ 0.000018725312521489179015872934,
+ -4.62530981164919445131297264430e-6,
+ 1.11558657244432857487884006422e-6,
+ -2.63098662650834130067808832725e-7,
+ 6.07462122724551777372119408710e-8,
+ -1.37460865539865444777251011793e-8,
+ 3.05157051905475145520096717210e-9,
+ -6.65174789720310713757307724790e-10,
+ 1.42483346273207784489792999706e-10,
+ -3.00141127395323902092018744545e-11,
+ 6.22171792645348091472914001250e-12,
+ -1.26994639225668496876152836555e-12,
+ 2.55385883033257575402681845385e-13,
+ -5.06258237507038698392265499770e-14,
+ 9.89705409478327321641264227110e-15,
+ -1.90685978789192181051961024995e-15,
+ 3.50826648032737849245113757340e-16
+};
+static cheb_series erfc_x15_cs = {
+ erfc_x15_data,
+ 24,
+ -1, 1,
+ 16
+};
+
+/* Chebyshev fit for erfc(x) x exp(x^2), 5 < x < 10, x = (5t + 15)/2, -1 < t < 1
+ */
+static double erfc_x510_data[20] = {
+ 1.11684990123545698684297865808,
+ 0.003736240359381998520654927536,
+ -0.000916623948045470238763619870,
+ 0.000199094325044940833965078819,
+ -0.000040276384918650072591781859,
+ 7.76515264697061049477127605790e-6,
+ -1.44464794206689070402099225301e-6,
+ 2.61311930343463958393485241947e-7,
+ -4.61833026634844152345304095560e-8,
+ 8.00253111512943601598732144340e-9,
+ -1.36291114862793031395712122089e-9,
+ 2.28570483090160869607683087722e-10,
+ -3.78022521563251805044056974560e-11,
+ 6.17253683874528285729910462130e-12,
+ -9.96019290955316888445830597430e-13,
+ 1.58953143706980770269506726000e-13,
+ -2.51045971047162509999527428316e-14,
+ 3.92607828989125810013581287560e-15,
+ -6.07970619384160374392535453420e-16,
+ 9.12600607264794717315507477670e-17
+};
+static cheb_series erfc_x510_cs = {
+ erfc_x510_data,
+ 19,
+ -1, 1,
+ 12
+};
+
+#if 0
+inline
+static double
+erfc_asymptotic(double x)
+{
+ return exp(-x*x)/x * erfcasympsum(x) / M_SQRTPI;
+}
+inline
+static double
+log_erfc_asymptotic(double x)
+{
+ return log(erfcasympsum(x)/x) - x*x - LogRootPi_;
+}
+#endif /* 0 */
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
+
+int gsl_sf_erfc_e(double x, gsl_sf_result * result)
+{
+ const double ax = fabs(x);
+ double e_val, e_err;
+
+ /* CHECK_POINTER(result) */
+
+ if(ax <= 1.0) {
+ double t = 2.0*ax - 1.0;
+ gsl_sf_result c;
+ cheb_eval_e(&erfc_xlt1_cs, t, &c);
+ e_val = c.val;
+ e_err = c.err;
+ }
+ else if(ax <= 5.0) {
+ double ex2 = exp(-x*x);
+ double t = 0.5*(ax-3.0);
+ gsl_sf_result c;
+ cheb_eval_e(&erfc_x15_cs, t, &c);
+ e_val = ex2 * c.val;
+ e_err = ex2 * (c.err + 2.0*fabs(x)*GSL_DBL_EPSILON);
+ }
+ else if(ax < 10.0) {
+ double exterm = exp(-x*x) / ax;
+ double t = (2.0*ax - 15.0)/5.0;
+ gsl_sf_result c;
+ cheb_eval_e(&erfc_x510_cs, t, &c);
+ e_val = exterm * c.val;
+ e_err = exterm * (c.err + 2.0*fabs(x)*GSL_DBL_EPSILON + GSL_DBL_EPSILON);
+ }
+ else {
+ e_val = erfc8(ax);
+ e_err = (x*x + 1.0) * GSL_DBL_EPSILON * fabs(e_val);
+ }
+
+ if(x < 0.0) {
+ result->val = 2.0 - e_val;
+ result->err = e_err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ }
+ else {
+ result->val = e_val;
+ result->err = e_err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ }
+
+ return GSL_SUCCESS;
+}
+
+
+int gsl_sf_log_erfc_e(double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(x*x < 10.0*GSL_ROOT6_DBL_EPSILON) {
+ const double y = x / M_SQRTPI;
+ /* series for -1/2 Log[Erfc[Sqrt[Pi] y]] */
+ const double c3 = (4.0 - M_PI)/3.0;
+ const double c4 = 2.0*(1.0 - M_PI/3.0);
+ const double c5 = -0.001829764677455021; /* (96.0 - 40.0*M_PI + 3.0*M_PI*M_PI)/30.0 */
+ const double c6 = 0.02629651521057465; /* 2.0*(120.0 - 60.0*M_PI + 7.0*M_PI*M_PI)/45.0 */
+ const double c7 = -0.01621575378835404;
+ const double c8 = 0.00125993961762116;
+ const double c9 = 0.00556964649138;
+ const double c10 = -0.0045563339802;
+ const double c11 = 0.0009461589032;
+ const double c12 = 0.0013200243174;
+ const double c13 = -0.00142906;
+ const double c14 = 0.00048204;
+ double series = c8 + y*(c9 + y*(c10 + y*(c11 + y*(c12 + y*(c13 + c14*y)))));
+ series = y*(1.0 + y*(1.0 + y*(c3 + y*(c4 + y*(c5 + y*(c6 + y*(c7 + y*series)))))));
+ result->val = -2.0 * series;
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ /*
+ don't like use of log1p(); added above series stuff for small x instead, should be ok [GJ]
+ else if (fabs(x) < 1.0) {
+ gsl_sf_result result_erf;
+ gsl_sf_erf_e(x, &result_erf);
+ result->val = log1p(-result_erf.val);
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ */
+ else if(x > 8.0) {
+ result->val = log_erfc8(x);
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ gsl_sf_result result_erfc;
+ gsl_sf_erfc_e(x, &result_erfc);
+ result->val = log(result_erfc.val);
+ result->err = fabs(result_erfc.err / result_erfc.val);
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+
+int gsl_sf_erf_e(double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(fabs(x) < 1.0) {
+ return erfseries(x, result);
+ }
+ else {
+ gsl_sf_result result_erfc;
+ gsl_sf_erfc_e(x, &result_erfc);
+ result->val = 1.0 - result_erfc.val;
+ result->err = result_erfc.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+
+int gsl_sf_erf_Z_e(double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ {
+ const double ex2 = exp(-x*x/2.0);
+ result->val = ex2 / (M_SQRT2 * M_SQRTPI);
+ result->err = fabs(x * result->val) * GSL_DBL_EPSILON;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ CHECK_UNDERFLOW(result);
+ return GSL_SUCCESS;
+ }
+}
+
+
+int gsl_sf_erf_Q_e(double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ {
+ gsl_sf_result result_erfc;
+ int stat = gsl_sf_erfc_e(x/M_SQRT2, &result_erfc);
+ result->val = 0.5 * result_erfc.val;
+ result->err = 0.5 * result_erfc.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return stat;
+ }
+}
+
+
+int gsl_sf_hazard_e(double x, gsl_sf_result * result)
+{
+ if(x < 25.0)
+ {
+ gsl_sf_result result_ln_erfc;
+ const int stat_l = gsl_sf_log_erfc_e(x/M_SQRT2, &result_ln_erfc);
+ const double lnc = -0.22579135264472743236; /* ln(sqrt(2/pi)) */
+ const double arg = lnc - 0.5*x*x - result_ln_erfc.val;
+ const int stat_e = gsl_sf_exp_e(arg, result);
+ result->err += 3.0 * (1.0 + fabs(x)) * GSL_DBL_EPSILON * fabs(result->val);
+ result->err += fabs(result_ln_erfc.err * result->val);
+ return GSL_ERROR_SELECT_2(stat_l, stat_e);
+ }
+ else
+ {
+ const double ix2 = 1.0/(x*x);
+ const double corrB = 1.0 - 9.0*ix2 * (1.0 - 11.0*ix2);
+ const double corrM = 1.0 - 5.0*ix2 * (1.0 - 7.0*ix2 * corrB);
+ const double corrT = 1.0 - ix2 * (1.0 - 3.0*ix2*corrM);
+ result->val = x / corrT;
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"
+
+double gsl_sf_erfc(double x)
+{
+ EVAL_RESULT(gsl_sf_erfc_e(x, &result));
+}
+
+double gsl_sf_log_erfc(double x)
+{
+ EVAL_RESULT(gsl_sf_log_erfc_e(x, &result));
+}
+
+double gsl_sf_erf(double x)
+{
+ EVAL_RESULT(gsl_sf_erf_e(x, &result));
+}
+
+double gsl_sf_erf_Z(double x)
+{
+ EVAL_RESULT(gsl_sf_erf_Z_e(x, &result));
+}
+
+double gsl_sf_erf_Q(double x)
+{
+ EVAL_RESULT(gsl_sf_erf_Q_e(x, &result));
+}
+
+double gsl_sf_hazard(double x)
+{
+ EVAL_RESULT(gsl_sf_hazard_e(x, &result));
+}
+
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