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-rw-r--r--gsl-1.9/specfunc/transport.c492
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diff --git a/gsl-1.9/specfunc/transport.c b/gsl-1.9/specfunc/transport.c
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+++ b/gsl-1.9/specfunc/transport.c
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+/* specfunc/transport.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 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_transport.h>
+
+#include "error.h"
+#include "check.h"
+
+#include "chebyshev.h"
+#include "cheb_eval.c"
+
+static double transport2_data[18] = {
+ 1.671760446434538503,
+ -0.147735359946794490,
+ 0.148213819946936338e-01,
+ -0.14195330326305613e-02,
+ 0.1306541324415708e-03,
+ -0.117155795867579e-04,
+ 0.10333498445756e-05,
+ -0.901911304223e-07,
+ 0.78177169833e-08,
+ -0.6744565684e-09,
+ 0.579946394e-10,
+ -0.49747619e-11,
+ 0.425961e-12,
+ -0.36422e-13,
+ 0.3111e-14,
+ -0.265e-15,
+ 0.23e-16,
+ -0.19e-17
+};
+static cheb_series transport2_cs = {
+ transport2_data,
+ 17,
+ -1, 1,
+ 9
+};
+
+static double transport3_data[18] = {
+ 0.762012543243872007,
+ -0.105674387705058533,
+ 0.119778084819657810e-01,
+ -0.12144015203698307e-02,
+ 0.1155099769392855e-03,
+ -0.105815992124423e-04,
+ 0.9474663385302e-06,
+ -0.836221212858e-07,
+ 0.73109099278e-08,
+ -0.6350594779e-09,
+ 0.549118282e-10,
+ -0.47321395e-11,
+ 0.4067695e-12,
+ -0.348971e-13,
+ 0.29892e-14,
+ -0.256e-15,
+ 0.219e-16,
+ -0.19e-17
+};
+static cheb_series transport3_cs = {
+ transport3_data,
+ 17,
+ -1, 1,
+ 9
+};
+
+
+static double transport4_data[18] = {
+ 0.4807570994615110579,
+ -0.8175378810321083956e-01,
+ 0.1002700665975162973e-01,
+ -0.10599339359820151e-02,
+ 0.1034506245030405e-03,
+ -0.96442705485899e-05,
+ 0.8745544408515e-06,
+ -0.779321207981e-07,
+ 0.68649886141e-08,
+ -0.5999571076e-09,
+ 0.521366241e-10,
+ -0.45118382e-11,
+ 0.3892159e-12,
+ -0.334936e-13,
+ 0.28767e-14,
+ -0.2467e-15,
+ 0.211e-16,
+ -0.18e-17
+};
+static cheb_series transport4_cs = {
+ transport4_data,
+ 17,
+ -1, 1,
+ 9
+};
+
+
+static double transport5_data[18] = {
+ 0.347777777133910789,
+ -0.66456988976050428e-01,
+ 0.8611072656883309e-02,
+ -0.9396682223755538e-03,
+ 0.936324806081513e-04,
+ -0.88571319340833e-05,
+ 0.811914989145e-06,
+ -0.72957654233e-07,
+ 0.646971455e-08,
+ -0.568490283e-09,
+ 0.49625598e-10,
+ -0.4310940e-11,
+ 0.373100e-12,
+ -0.32198e-13,
+ 0.2772e-14,
+ -0.238e-15,
+ 0.21e-16,
+ -0.18e-17
+};
+static cheb_series transport5_cs = {
+ transport5_data,
+ 17,
+ -1, 1,
+ 9
+};
+
+
+static
+double
+transport_sumexp(const int numexp, const int order, const double t, double x)
+{
+ double rk = (double)numexp;
+ double sumexp = 0.0;
+ int k;
+ for(k=1; k<=numexp; k++) {
+ double sum2 = 1.0;
+ double xk = 1.0/(rk*x);
+ double xk1 = 1.0;
+ int j;
+ for(j=1; j<=order; j++) {
+ sum2 = sum2*xk1*xk + 1.0;
+ xk1 += 1.0;
+ }
+ sumexp *= t;
+ sumexp += sum2;
+ rk -= 1.0;
+ }
+ return sumexp;
+}
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
+
+int
+gsl_sf_transport_2_e(const double x, gsl_sf_result * result)
+{
+ const double val_infinity = 3.289868133696452873;
+
+ /* CHECK_POINTER(result) */
+
+ if(x < 0.0) {
+ DOMAIN_ERROR(result);
+ }
+ else if(x < 3.0*GSL_SQRT_DBL_EPSILON) {
+ result->val = x;
+ result->err = GSL_DBL_EPSILON*fabs(x) + x*x/2.0;
+ return GSL_SUCCESS;
+ }
+ else if(x <= 4.0) {
+ double t = (x*x/8.0 - 0.5) - 0.5;
+ gsl_sf_result result_c;
+ cheb_eval_e(&transport2_cs, t, &result_c);
+ result->val = x * result_c.val;
+ result->err = x * result_c.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(x < -GSL_LOG_DBL_EPSILON) {
+ const int numexp = (int)((-GSL_LOG_DBL_EPSILON)/x) + 1;
+ const double sumexp = transport_sumexp(numexp, 2, exp(-x), x);
+ const double t = 2.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + fabs(t) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else if(x < 2.0/GSL_DBL_EPSILON) {
+ const int numexp = 1;
+ const double sumexp = transport_sumexp(numexp, 2, 1.0, x);
+ const double t = 2.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else {
+ const double t = 2.0 * log(x) - x;
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+}
+
+
+int
+gsl_sf_transport_3_e(const double x, gsl_sf_result * result)
+{
+ const double val_infinity = 7.212341418957565712;
+
+ /* CHECK_POINTER(result) */
+
+ if(x < 0.0) {
+ DOMAIN_ERROR(result);
+ }
+ else if(x == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(x < 3.0*GSL_SQRT_DBL_EPSILON) {
+ result->val = 0.5*x*x;
+ result->err = 2.0 * GSL_DBL_EPSILON * result->val;
+ CHECK_UNDERFLOW(result);
+ return GSL_SUCCESS;
+ }
+ else if(x <= 4.0) {
+ const double x2 = x*x;
+ const double t = (x2/8.0 - 0.5) - 0.5;
+ gsl_sf_result result_c;
+ cheb_eval_e(&transport3_cs, t, &result_c);
+ result->val = x2 * result_c.val;
+ result->err = x2 * result_c.err;
+ result->err += GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(x < -GSL_LOG_DBL_EPSILON) {
+ const int numexp = (int)((-GSL_LOG_DBL_EPSILON)/x) + 1;
+ const double sumexp = transport_sumexp(numexp, 3, exp(-x), x);
+ const double t = 3.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + fabs(t) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else if(x < 3.0/GSL_DBL_EPSILON) {
+ const int numexp = 1;
+ const double sumexp = transport_sumexp(numexp, 3, 1.0, x);
+ const double t = 3.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else {
+ const double t = 3.0 * log(x) - x;
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+}
+
+
+int
+gsl_sf_transport_4_e(const double x, gsl_sf_result * result)
+{
+ const double val_infinity = 25.97575760906731660;
+
+ /* CHECK_POINTER(result) */
+
+ if(x < 0.0) {
+ DOMAIN_ERROR(result);
+ }
+ else if(x == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(x < 3.0*GSL_SQRT_DBL_EPSILON) {
+ result->val = x*x*x/3.0;
+ result->err = 3.0 * GSL_DBL_EPSILON * result->val;
+ CHECK_UNDERFLOW(result);
+ return GSL_SUCCESS;
+ }
+ else if(x <= 4.0) {
+ const double x2 = x*x;
+ const double t = (x2/8.0 - 0.5) - 0.5;
+ gsl_sf_result result_c;
+ cheb_eval_e(&transport4_cs, t, &result_c);
+ result->val = x2*x * result_c.val;
+ result->err = x2*x * result_c.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(x < -GSL_LOG_DBL_EPSILON) {
+ const int numexp = (int)((-GSL_LOG_DBL_EPSILON)/x) + 1;
+ const double sumexp = transport_sumexp(numexp, 4, exp(-x), x);
+ const double t = 4.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else if(x < 3.0/GSL_DBL_EPSILON) {
+ const int numexp = 1;
+ const double sumexp = transport_sumexp(numexp, 4, 1.0, x);
+ const double t = 4.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else {
+ const double t = 4.0 * log(x) - x;
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+}
+
+
+int
+gsl_sf_transport_5_e(const double x, gsl_sf_result * result)
+{
+ const double val_infinity = 124.4313306172043912;
+
+ /* CHECK_POINTER(result) */
+
+ if(x < 0.0) {
+ DOMAIN_ERROR(result);
+ }
+ else if(x == 0.0) {
+ result->val = 0.0;
+ result->err = 0.0;
+ return GSL_SUCCESS;
+ }
+ else if(x < 3.0*GSL_SQRT_DBL_EPSILON) {
+ result->val = x*x*x*x/4.0;
+ result->err = 4.0 * GSL_DBL_EPSILON * result->val;
+ CHECK_UNDERFLOW(result);
+ return GSL_SUCCESS;
+ }
+ else if(x <= 4.0) {
+ const double x2 = x*x;
+ const double t = (x2/8.0 - 0.5) - 0.5;
+ gsl_sf_result result_c;
+ cheb_eval_e(&transport5_cs, t, &result_c);
+ result->val = x2*x2 * result_c.val;
+ result->err = x2*x2 * result_c.err;
+ result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(x < -GSL_LOG_DBL_EPSILON) {
+ const int numexp = (int)((-GSL_LOG_DBL_EPSILON)/x) + 1;
+ const double sumexp = transport_sumexp(numexp, 5, exp(-x), x);
+ const double t = 5.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else if(x < 3.0/GSL_DBL_EPSILON) {
+ const int numexp = 1;
+ const double sumexp = transport_sumexp(numexp, 5, 1.0, x);
+ const double t = 5.0 * log(x) - x + log(sumexp);
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+ else {
+ const double t = 5.0 * log(x) - x;
+ if(t < GSL_LOG_DBL_EPSILON) {
+ result->val = val_infinity;
+ result->err = 2.0 * GSL_DBL_EPSILON * val_infinity;
+ }
+ else {
+ const double et = exp(t);
+ result->val = val_infinity - et;
+ result->err = 2.0 * GSL_DBL_EPSILON * (val_infinity + (fabs(t)+1.0) * et);
+ }
+ return GSL_SUCCESS;
+ }
+}
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"
+
+double gsl_sf_transport_2(const double x)
+{
+ EVAL_RESULT(gsl_sf_transport_2_e(x, &result));
+}
+
+double gsl_sf_transport_3(const double x)
+{
+ EVAL_RESULT(gsl_sf_transport_3_e(x, &result));
+}
+
+double gsl_sf_transport_4(const double x)
+{
+ EVAL_RESULT(gsl_sf_transport_4_e(x, &result));
+}
+
+double gsl_sf_transport_5(const double x)
+{
+ EVAL_RESULT(gsl_sf_transport_5_e(x, &result));
+}
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