/* 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 3 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));
}