/* 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));

}