| /* 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)); |
| } |