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-rw-r--r--gsl-1.9/specfunc/log.c266
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diff --git a/gsl-1.9/specfunc/log.c b/gsl-1.9/specfunc/log.c
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+++ b/gsl-1.9/specfunc/log.c
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+/* specfunc/log.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_log.h>
+
+#include "error.h"
+
+#include "chebyshev.h"
+#include "cheb_eval.c"
+
+/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/
+
+/* Chebyshev expansion for log(1 + x(t))/x(t)
+ *
+ * x(t) = (4t-1)/(2(4-t))
+ * t(x) = (8x+1)/(2(x+2))
+ * -1/2 < x < 1/2
+ * -1 < t < 1
+ */
+static double lopx_data[21] = {
+ 2.16647910664395270521272590407,
+ -0.28565398551049742084877469679,
+ 0.01517767255690553732382488171,
+ -0.00200215904941415466274422081,
+ 0.00019211375164056698287947962,
+ -0.00002553258886105542567601400,
+ 2.9004512660400621301999384544e-06,
+ -3.8873813517057343800270917900e-07,
+ 4.7743678729400456026672697926e-08,
+ -6.4501969776090319441714445454e-09,
+ 8.2751976628812389601561347296e-10,
+ -1.1260499376492049411710290413e-10,
+ 1.4844576692270934446023686322e-11,
+ -2.0328515972462118942821556033e-12,
+ 2.7291231220549214896095654769e-13,
+ -3.7581977830387938294437434651e-14,
+ 5.1107345870861673561462339876e-15,
+ -7.0722150011433276578323272272e-16,
+ 9.7089758328248469219003866867e-17,
+ -1.3492637457521938883731579510e-17,
+ 1.8657327910677296608121390705e-18
+};
+static cheb_series lopx_cs = {
+ lopx_data,
+ 20,
+ -1, 1,
+ 10
+};
+
+/* Chebyshev expansion for (log(1 + x(t)) - x(t))/x(t)^2
+ *
+ * x(t) = (4t-1)/(2(4-t))
+ * t(x) = (8x+1)/(2(x+2))
+ * -1/2 < x < 1/2
+ * -1 < t < 1
+ */
+static double lopxmx_data[20] = {
+ -1.12100231323744103373737274541,
+ 0.19553462773379386241549597019,
+ -0.01467470453808083971825344956,
+ 0.00166678250474365477643629067,
+ -0.00018543356147700369785746902,
+ 0.00002280154021771635036301071,
+ -2.8031253116633521699214134172e-06,
+ 3.5936568872522162983669541401e-07,
+ -4.6241857041062060284381167925e-08,
+ 6.0822637459403991012451054971e-09,
+ -8.0339824424815790302621320732e-10,
+ 1.0751718277499375044851551587e-10,
+ -1.4445310914224613448759230882e-11,
+ 1.9573912180610336168921438426e-12,
+ -2.6614436796793061741564104510e-13,
+ 3.6402634315269586532158344584e-14,
+ -4.9937495922755006545809120531e-15,
+ 6.8802890218846809524646902703e-16,
+ -9.5034129794804273611403251480e-17,
+ 1.3170135013050997157326965813e-17
+};
+static cheb_series lopxmx_cs = {
+ lopxmx_data,
+ 19,
+ -1, 1,
+ 9
+};
+
+
+/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
+
+int
+gsl_sf_log_e(const double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(x <= 0.0) {
+ DOMAIN_ERROR(result);
+ }
+ else {
+ result->val = log(x);
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+
+int
+gsl_sf_log_abs_e(const double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(x == 0.0) {
+ DOMAIN_ERROR(result);
+ }
+ else {
+ result->val = log(fabs(x));
+ result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+int
+gsl_sf_complex_log_e(const double zr, const double zi, gsl_sf_result * lnr, gsl_sf_result * theta)
+{
+ /* CHECK_POINTER(lnr) */
+ /* CHECK_POINTER(theta) */
+
+ if(zr != 0.0 || zi != 0.0) {
+ const double ax = fabs(zr);
+ const double ay = fabs(zi);
+ const double min = GSL_MIN(ax, ay);
+ const double max = GSL_MAX(ax, ay);
+ lnr->val = log(max) + 0.5 * log(1.0 + (min/max)*(min/max));
+ lnr->err = 2.0 * GSL_DBL_EPSILON * fabs(lnr->val);
+ theta->val = atan2(zi, zr);
+ theta->err = GSL_DBL_EPSILON * fabs(lnr->val);
+ return GSL_SUCCESS;
+ }
+ else {
+ DOMAIN_ERROR_2(lnr, theta);
+ }
+}
+
+
+int
+gsl_sf_log_1plusx_e(const double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(x <= -1.0) {
+ DOMAIN_ERROR(result);
+ }
+ else if(fabs(x) < GSL_ROOT6_DBL_EPSILON) {
+ const double c1 = -0.5;
+ const double c2 = 1.0/3.0;
+ const double c3 = -1.0/4.0;
+ const double c4 = 1.0/5.0;
+ const double c5 = -1.0/6.0;
+ const double c6 = 1.0/7.0;
+ const double c7 = -1.0/8.0;
+ const double c8 = 1.0/9.0;
+ const double c9 = -1.0/10.0;
+ const double t = c5 + x*(c6 + x*(c7 + x*(c8 + x*c9)));
+ result->val = x * (1.0 + x*(c1 + x*(c2 + x*(c3 + x*(c4 + x*t)))));
+ result->err = GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(fabs(x) < 0.5) {
+ double t = 0.5*(8.0*x + 1.0)/(x+2.0);
+ gsl_sf_result c;
+ cheb_eval_e(&lopx_cs, t, &c);
+ result->val = x * c.val;
+ result->err = fabs(x * c.err);
+ return GSL_SUCCESS;
+ }
+ else {
+ result->val = log(1.0 + x);
+ result->err = GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+}
+
+
+int
+gsl_sf_log_1plusx_mx_e(const double x, gsl_sf_result * result)
+{
+ /* CHECK_POINTER(result) */
+
+ if(x <= -1.0) {
+ DOMAIN_ERROR(result);
+ }
+ else if(fabs(x) < GSL_ROOT5_DBL_EPSILON) {
+ const double c1 = -0.5;
+ const double c2 = 1.0/3.0;
+ const double c3 = -1.0/4.0;
+ const double c4 = 1.0/5.0;
+ const double c5 = -1.0/6.0;
+ const double c6 = 1.0/7.0;
+ const double c7 = -1.0/8.0;
+ const double c8 = 1.0/9.0;
+ const double c9 = -1.0/10.0;
+ const double t = c5 + x*(c6 + x*(c7 + x*(c8 + x*c9)));
+ result->val = x*x * (c1 + x*(c2 + x*(c3 + x*(c4 + x*t))));
+ result->err = GSL_DBL_EPSILON * fabs(result->val);
+ return GSL_SUCCESS;
+ }
+ else if(fabs(x) < 0.5) {
+ double t = 0.5*(8.0*x + 1.0)/(x+2.0);
+ gsl_sf_result c;
+ cheb_eval_e(&lopxmx_cs, t, &c);
+ result->val = x*x * c.val;
+ result->err = x*x * c.err;
+ return GSL_SUCCESS;
+ }
+ else {
+ const double lterm = log(1.0 + x);
+ result->val = lterm - x;
+ result->err = GSL_DBL_EPSILON * (fabs(lterm) + fabs(x));
+ return GSL_SUCCESS;
+ }
+}
+
+
+
+/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
+
+#include "eval.h"
+
+double gsl_sf_log(const double x)
+{
+ EVAL_RESULT(gsl_sf_log_e(x, &result));
+}
+
+double gsl_sf_log_abs(const double x)
+{
+ EVAL_RESULT(gsl_sf_log_abs_e(x, &result));
+}
+
+double gsl_sf_log_1plusx(const double x)
+{
+ EVAL_RESULT(gsl_sf_log_1plusx_e(x, &result));
+}
+
+double gsl_sf_log_1plusx_mx(const double x)
+{
+ EVAL_RESULT(gsl_sf_log_1plusx_mx_e(x, &result));
+}
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