/* specfunc/synchrotron.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_exp.h>

#include <gsl/gsl_sf_pow_int.h>

#include <gsl/gsl_sf_synchrotron.h>

#include "error.h"

#include "chebyshev.h"

#include "cheb_eval.c"

static double synchrotron1_data[13] = {

  30.364682982501076273,

  17.079395277408394574,

   4.560132133545072889,

   0.549281246730419979,

   0.372976075069301172e-01,

   0.161362430201041242e-02,

   0.481916772120371e-04,

   0.10512425288938e-05,

   0.174638504670e-07,

   0.22815486544e-09,

   0.240443082e-11,

   0.2086588e-13,

   0.15167e-15

};

static cheb_series synchrotron1_cs = {

  synchrotron1_data,

  12,

  -1.0, 1.0,

  9

};

static double synchrotron2_data[12] = {

  0.4490721623532660844,

  0.898353677994187218e-01,

  0.81044573772151290e-02,

  0.4261716991089162e-03,

  0.147609631270746e-04,

  0.3628633615300e-06,

  0.66634807498e-08,

  0.949077166e-10,

  0.1079125e-11,

  0.10022e-13,

  0.77e-16,

  0.5e-18

};

static cheb_series synchrotron2_cs = {

  synchrotron2_data,

  11,

  -1.0, 1.0,

  7

};

static double synchrotron1a_data[23] = {

  2.1329305161355000985,

  0.741352864954200240e-01,

  0.86968099909964198e-02,

  0.11703826248775692e-02,

  0.1645105798619192e-03,

  0.240201021420640e-04,

  0.35827756389389e-05,

  0.5447747626984e-06,

  0.838802856196e-07,

  0.13069882684e-07,

  0.2053099071e-08,

  0.325187537e-09,

  0.517914041e-10,

  0.83002988e-11,

  0.13352728e-11,

  0.2159150e-12,

  0.349967e-13,

  0.56994e-14,

  0.9291e-15,

  0.152e-15,

  0.249e-16,

  0.41e-17,

  0.7e-18

};

static cheb_series synchrotron1a_cs = {

  synchrotron1a_data,

  22,

  -1.0, 1.0,

  11

};

static double synchrotron21_data[13] = {

  38.617839923843085480,

  23.037715594963734597,

  5.3802499868335705968,

  0.6156793806995710776,

  0.406688004668895584e-01,

  0.17296274552648414e-02,

  0.51061258836577e-04,

  0.110459595022e-05,

  0.18235530206e-07,

  0.2370769803e-09,

  0.24887296e-11,

  0.21529e-13,

  0.156e-15

};

static cheb_series synchrotron21_cs = {

  synchrotron21_data,

  12,

  -1.0, 1.0,

  9

};

static double synchrotron22_data[13] = {

   7.9063148270660804288,

   3.1353463612853425684,

   0.4854879477453714538,

   0.394816675827237234e-01,

   0.19661622334808802e-02,

   0.659078932293042e-04,

   0.15857561349856e-05,

   0.286865301123e-07,

   0.4041202360e-09,

   0.45568444e-11,

   0.420459e-13,

   0.3232e-15,

   0.21e-17

};

static cheb_series synchrotron22_cs = {

  synchrotron22_data,

  12,

  -1.0, 1.0,

  8

};

static double synchrotron2a_data[17] = {

  2.020337094170713600,

  0.10956237121807404e-01,

  0.8542384730114676e-03,

  0.723430242132822e-04,

  0.63124427962699e-05,

  0.5648193141174e-06,

  0.512832480138e-07,

  0.47196532914e-08,

  0.4380744214e-09,

  0.410268149e-10,

  0.38623072e-11,

  0.3661323e-12,

  0.348023e-13,

  0.33301e-14,

  0.319e-15,

  0.307e-16,

  0.3e-17

};

static cheb_series synchrotron2a_cs = {

  synchrotron2a_data,

  16,

  -1.0, 1.0,

  8

};

/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/

int gsl_sf_synchrotron_1_e(const double x, gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x < 2.0*M_SQRT2 * GSL_SQRT_DBL_EPSILON) {

    /* BJG: added first order correction term.  The taylor series

       is  S1(x) = ((4pi)/(sqrt(3)gamma(1/3))) * (x/2)^(1/3) 

       * (1 - (gamma(1/3)/2)*(x/2)^2/3 + (3/4) * (x/2)^2 ....) */

    double z = pow(x, 1.0/3.0);

    double cf = 1 - 8.43812762813205e-01 * z * z;

    result->val = 2.14952824153447863671 * z * cf;

    result->err = GSL_DBL_EPSILON * result->val;

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

    const double c0   = M_PI/M_SQRT3;

    const double px   = pow(x,1.0/3.0);

    const double px11 = gsl_sf_pow_int(px,11);

    const double t = x*x/8.0 - 1.0;

    gsl_sf_result result_c1;

    gsl_sf_result result_c2;

    cheb_eval_e(&synchrotron1_cs, t, &result_c1);

    cheb_eval_e(&synchrotron2_cs, t, &result_c2);

    result->val  = px * result_c1.val - px11 * result_c2.val - c0 * x;

    result->err  = px * result_c1.err + px11 * result_c2.err + c0 * x * GSL_DBL_EPSILON;

    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);

    return GSL_SUCCESS;

  }

  else if(x < -8.0*GSL_LOG_DBL_MIN/7.0) {

    const double c0 = 0.2257913526447274323630976; /* log(sqrt(pi/2)) */

    const double t = (12.0 - x) / (x + 4.0);

    gsl_sf_result result_c1;

    cheb_eval_e(&synchrotron1a_cs, t, &result_c1);

    result->val = sqrt(x) * result_c1.val * exp(c0 - x);

    result->err = 2.0 * GSL_DBL_EPSILON * result->val * (fabs(c0-x)+1.0);

    return GSL_SUCCESS;

  }

  else {

    UNDERFLOW_ERROR(result);

  }

}

int gsl_sf_synchrotron_2_e(const double x, gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x < 2.0*M_SQRT2*GSL_SQRT_DBL_EPSILON) {

    /* BJG: added first order correction term.  The taylor series

       is  S2(x) = ((2pi)/(sqrt(3)*gamma(1/3))) * (x/2)^(1/3) 

       * (1 - (gamma(1/3)/gamma(4/3))*(x/2)^(4/3) + (gamma(1/3)/gamma(4/3))*(x/2)^2...) */

    double z = pow(x, 1.0/3.0);

    double cf = 1 - 1.17767156510235e+00 * z * x;

    result->val = 1.07476412076723931836 * z * cf ;

    result->err = 2.0 * GSL_DBL_EPSILON * result->val;

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

    const double px  = pow(x, 1.0/3.0);

    const double px5 = gsl_sf_pow_int(px,5);

    const double t = x*x/8.0 - 1.0;

    gsl_sf_result cheb1;

    gsl_sf_result cheb2;

    cheb_eval_e(&synchrotron21_cs, t, &cheb1);

    cheb_eval_e(&synchrotron22_cs, t, &cheb2);

    result->val  = px * cheb1.val - px5 * cheb2.val;

    result->err  = px * cheb1.err + px5 * cheb2.err;

    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);

    return GSL_SUCCESS;

  }

  else if(x < -8.0*GSL_LOG_DBL_MIN/7.0) {

    const double c0 = 0.22579135264472743236;   /* log(sqrt(pi/2)) */

    const double t  = (10.0 - x) / (x + 2.0);

    gsl_sf_result cheb1;

    cheb_eval_e(&synchrotron2a_cs, t, &cheb1);

    result->val = sqrt(x) * exp(c0-x) * cheb1.val;

    result->err = GSL_DBL_EPSILON * result->val * (fabs(c0-x)+1.0);

    return GSL_SUCCESS;

  }

  else {

    UNDERFLOW_ERROR(result);

  }

}

/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/

#include "eval.h"

double gsl_sf_synchrotron_1(const double x)

{

  EVAL_RESULT(gsl_sf_synchrotron_1_e(x, &result));

}

double gsl_sf_synchrotron_2(const double x)

{

  EVAL_RESULT(gsl_sf_synchrotron_2_e(x, &result));

}