/* specfunc/debye.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 */

/* augmented to n=5 and 6 2005-11-08 by R. J. Mathar, http://www.strw.leidenuniv.nl/~mathar */

#include <config.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_sf_debye.h>

#include "error.h"

#include "check.h"

#include "chebyshev.h"

#include "cheb_eval.c"

static double adeb1_data[17] = {

   2.4006597190381410194,

   0.1937213042189360089,

  -0.62329124554895770e-02,

   0.3511174770206480e-03,

  -0.228222466701231e-04,

   0.15805467875030e-05,

  -0.1135378197072e-06,

   0.83583361188e-08,

  -0.6264424787e-09,

   0.476033489e-10,

  -0.36574154e-11,

   0.2835431e-12,

  -0.221473e-13,

   0.17409e-14,

  -0.1376e-15,

   0.109e-16,

  -0.9e-18

};

static cheb_series adeb1_cs = {

  adeb1_data,

  16,

  -1.0, 1.0,

  9

};

static double adeb2_data[18] = {

   2.5943810232570770282,

   0.2863357204530719834,

  -0.102062656158046713e-01,

   0.6049109775346844e-03,

  -0.405257658950210e-04,

   0.28633826328811e-05,

  -0.2086394303065e-06,

   0.155237875826e-07,

  -0.11731280087e-08,

   0.897358589e-10,

  -0.69317614e-11,

   0.5398057e-12,

  -0.423241e-13,

   0.33378e-14,

  -0.2645e-15,

   0.211e-16,

  -0.17e-17,

   0.1e-18

};

static cheb_series adeb2_cs = {

  adeb2_data,

  17,

  -1.0, 1.0,

  10

};

static double adeb3_data[17] = {

   2.707737068327440945,

   0.340068135211091751,

  -0.12945150184440869e-01,

   0.7963755380173816e-03,

  -0.546360009590824e-04,

   0.39243019598805e-05,

  -0.2894032823539e-06,

   0.217317613962e-07,

  -0.16542099950e-08,

   0.1272796189e-09,

  -0.987963460e-11,

   0.7725074e-12,

  -0.607797e-13,

   0.48076e-14,

  -0.3820e-15,

   0.305e-16,

  -0.24e-17

};

static cheb_series adeb3_cs = {

  adeb3_data,

  16,

  -1.0, 1.0,

  10

};

static double adeb4_data[17] = {

   2.781869415020523460,

   0.374976783526892863,

  -0.14940907399031583e-01,

   0.945679811437042e-03,

  -0.66132916138933e-04,

   0.4815632982144e-05,

  -0.3588083958759e-06,

   0.271601187416e-07,

  -0.20807099122e-08,

   0.1609383869e-09,

  -0.125470979e-10,

   0.9847265e-12,

  -0.777237e-13,

   0.61648e-14,

  -0.4911e-15,

   0.393e-16,

  -0.32e-17

};

static cheb_series adeb4_cs = {

  adeb4_data,

  16,

  -1.0, 1.0,

  10

};

static double adeb5_data[17] = {

   2.8340269546834530149,

   0.3994098857106266445,

  -0.164566764773099646e-1,

   0.10652138340664541e-2,

  -0.756730374875418e-4,

   0.55745985240273e-5,

  -0.4190692330918e-6,

   0.319456143678e-7,

  -0.24613318171e-8,

   0.1912801633e-9,

  -0.149720049e-10,

   0.11790312e-11,

  -0.933329e-13,

   0.74218e-14,

  -0.5925e-15,

   0.475e-16,

  -0.39e-17

};

static cheb_series adeb5_cs = {

  adeb5_data,

  16,

  -1.0, 1.0,

  10

};

static double adeb6_data[17] = {

  2.8726727134130122113,

  0.4174375352339027746,

 -0.176453849354067873e-1,

  0.11629852733494556e-2,

 -0.837118027357117e-4,

  0.62283611596189e-5,

 -0.4718644465636e-6,

  0.361950397806e-7,

 -0.28030368010e-8,

  0.2187681983e-9,

 -0.171857387e-10,

  0.13575809e-11,

 -0.1077580e-12,

  0.85893e-14,

 -0.6872e-15,

  0.552e-16,

 -0.44e-17

};

static cheb_series adeb6_cs = {

  adeb6_data,

  16,

  -1.0, 1.0,

  10

};

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

int gsl_sf_debye_1_e(const double x, gsl_sf_result * result)

{

  const double val_infinity = 1.64493406684822644;

  const double xcut = -GSL_LOG_DBL_MIN;

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

  else if(x < 2.0*GSL_SQRT_DBL_EPSILON) {

    result->val = 1.0 - 0.25*x + x*x/36.0;

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

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

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

    gsl_sf_result c;

    cheb_eval_e(&adeb1_cs, t, &c);

    result->val = c.val - 0.25 * x;

    result->err = c.err + 0.25 * x * GSL_DBL_EPSILON;

    return GSL_SUCCESS;

  }

  else if(x < -(M_LN2 + GSL_LOG_DBL_EPSILON)) {

    const int nexp = floor(xcut/x);

    const double ex  = exp(-x);

    double sum = 0.0;

    double xk  = nexp * x;

    double rk  = nexp;

    int i;

    for(i=nexp; i>=1; i--) {

      sum *= ex;

      sum += (1.0 + 1.0/xk)/rk;

      rk -= 1.0;

      xk -= x;

    }

    result->val = val_infinity/x - sum*ex;

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

    return GSL_SUCCESS;

  }

  else if(x < xcut) {

    result->val = (val_infinity - exp(-x)*(x+1.0)) / x;

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

    return GSL_SUCCESS;

  }

  else {

    result->val = val_infinity/x;

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

    return GSL_SUCCESS;

  }

}

int gsl_sf_debye_2_e(const double x, gsl_sf_result * result)

{

  const double val_infinity = 4.80822761263837714;

  const double xcut = -GSL_LOG_DBL_MIN;

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

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

    result->val = 1.0 - x/3.0 + x*x/24.0;

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

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

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

    gsl_sf_result c;

    cheb_eval_e(&adeb2_cs, t, &c);

    result->val = c.val - x/3.0;

    result->err = c.err + GSL_DBL_EPSILON * x/3.0;

    return GSL_SUCCESS;

  }

  else if(x < -(M_LN2 + GSL_LOG_DBL_EPSILON)) {

    const int nexp = floor(xcut/x);

    const double ex  = exp(-x);

    double xk  = nexp * x;

    double rk  = nexp;

    double sum = 0.0;

    int i;

    for(i=nexp; i>=1; i--) {

      sum *= ex;

      sum += (1.0 + 2.0/xk + 2.0/(xk*xk)) / rk;

      rk -= 1.0;

      xk -= x;

    }

    result->val = val_infinity/(x*x) - 2.0 * sum * ex;

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

    return GSL_SUCCESS;

  }

  else if(x < xcut) {

    const double x2  = x*x;

    const double sum = 2.0 + 2.0*x + x2;

    result->val = (val_infinity - 2.0 * sum * exp(-x)) / x2;

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

    return GSL_SUCCESS;

  }

  else {

    result->val = (val_infinity/x)/x;

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

    CHECK_UNDERFLOW(result);

    return GSL_SUCCESS;

  }

}

int gsl_sf_debye_3_e(const double x, gsl_sf_result * result)

{

  const double val_infinity = 19.4818182068004875;

  const double xcut = -GSL_LOG_DBL_MIN;

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

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

    result->val = 1.0 - 3.0*x/8.0 + x*x/20.0;

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

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

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

    gsl_sf_result c;

    cheb_eval_e(&adeb3_cs, t, &c);

    result->val = c.val - 0.375*x;

    result->err = c.err + GSL_DBL_EPSILON * 0.375*x;

    return GSL_SUCCESS;

  }

  else if(x < -(M_LN2 + GSL_LOG_DBL_EPSILON)) {

    const int nexp = floor(xcut/x);

    const double ex  = exp(-x);

    double xk  = nexp * x;

    double rk  = nexp;

    double sum = 0.0;

    int i;

    for(i=nexp; i>=1; i--) {

      double xk_inv = 1.0/xk;

      sum *= ex;

      sum += (((6.0*xk_inv + 6.0)*xk_inv + 3.0)*xk_inv + 1.0) / rk;

      rk -= 1.0;

      xk -= x;

    }

    result->val = val_infinity/(x*x*x) - 3.0 * sum * ex;

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

    return GSL_SUCCESS;

  }

  else if(x < xcut) {

    const double x3 = x*x*x;

    const double sum = 6.0 + 6.0*x + 3.0*x*x + x3;

    result->val = (val_infinity - 3.0 * sum * exp(-x)) / x3;

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

    return GSL_SUCCESS;

  }

  else {

    result->val = ((val_infinity/x)/x)/x;

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

    CHECK_UNDERFLOW(result);

    return GSL_SUCCESS;

  }

}

int gsl_sf_debye_4_e(const double x, gsl_sf_result * result)

{

  const double val_infinity = 99.5450644937635129;

  const double xcut = -GSL_LOG_DBL_MIN;

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

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

    result->val = 1.0 - 2.0*x/5.0 + x*x/18.0;

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

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

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

    gsl_sf_result c;

    cheb_eval_e(&adeb4_cs, t, &c);

    result->val = c.val - 2.0*x/5.0;

    result->err = c.err + GSL_DBL_EPSILON * 2.0*x/5.0;

    return GSL_SUCCESS;

  }

  else if(x < -(M_LN2 + GSL_LOG_DBL_EPSILON)) {

    const int nexp = floor(xcut/x);

    const double ex  = exp(-x);

    double xk  = nexp * x;

    double rk  = nexp;

    double sum = 0.0;

    int i;

    for(i=nexp; i>=1; i--) {

      double xk_inv = 1.0/xk;

      sum *= ex;

      sum += ((((24.0*xk_inv + 24.0)*xk_inv + 12.0)*xk_inv + 4.0)*xk_inv + 1.0) / rk;

      rk -= 1.0;

      xk -= x;

    }

    result->val = val_infinity/(x*x*x*x) - 4.0 * sum * ex;

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

    return GSL_SUCCESS;

  }

  else if(x < xcut) {

    const double x2 = x*x;

    const double x4 = x2*x2;

    const double sum = 24.0 + 24.0*x + 12.0*x2 + 4.0*x2*x + x4;

    result->val = (val_infinity - 4.0 * sum * exp(-x)) / x4;

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

    return GSL_SUCCESS;

  }

  else {

    result->val = (((val_infinity/x)/x)/x)/x;

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

    CHECK_UNDERFLOW(result);

    return GSL_SUCCESS;

  }

}

int gsl_sf_debye_5_e(const double x, gsl_sf_result * result)

{

  const double val_infinity = 610.405837190669483828710757875 ;

  const double xcut = -GSL_LOG_DBL_MIN;

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

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

    result->val = 1.0 - 5.0*x/12.0 + 5.0*x*x/84.0;

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

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

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

    gsl_sf_result c;

    cheb_eval_e(&adeb5_cs, t, &c);

    result->val = c.val - 5.0*x/12.0;

    result->err = c.err + GSL_DBL_EPSILON * 5.0*x/12.0;

    return GSL_SUCCESS;

  }

  else if(x < -(M_LN2 + GSL_LOG_DBL_EPSILON)) {

    const int nexp = floor(xcut/x);

    const double ex  = exp(-x);

    double xk  = nexp * x;

    double rk  = nexp;

    double sum = 0.0;

    int i;

    for(i=nexp; i>=1; i--) {

      double xk_inv = 1.0/xk;

      sum *= ex;

      sum += (((((120.0*xk_inv + 120.0)*xk_inv + 60.0)*xk_inv + 20.0)*xk_inv + 5.0)*xk_inv+ 1.0) / rk;

      rk -= 1.0;

      xk -= x;

    }

    result->val = val_infinity/(x*x*x*x*x) - 5.0 * sum * ex;

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

    return GSL_SUCCESS;

  }

  else if(x < xcut) {

    const double x2 = x*x;

    const double x4 = x2*x2;

    const double x5 = x4*x;

    const double sum = 120.0 + 120.0*x + 60.0*x2 + 20.0*x2*x + 5.0*x4 + x5;

    result->val = (val_infinity - 5.0 * sum * exp(-x)) / x5;

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

    return GSL_SUCCESS;

  }

  else {

    result->val = ((((val_infinity/x)/x)/x)/x)/x;

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

    CHECK_UNDERFLOW(result);

    return GSL_SUCCESS;

  }

}

int gsl_sf_debye_6_e(const double x, gsl_sf_result * result)

{

  const double val_infinity = 4356.06887828990661194792541535 ;

  const double xcut = -GSL_LOG_DBL_MIN;

  /* CHECK_POINTER(result) */

  if(x < 0.0) {

    DOMAIN_ERROR(result);

  }

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

    result->val = 1.0 - 3.0*x/7.0 + x*x/16.0;

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

    return GSL_SUCCESS;

  }

  else if(x <= 4.0) {

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

    gsl_sf_result c;

    cheb_eval_e(&adeb6_cs, t, &c);

    result->val = c.val - 3.0*x/7.0;

    result->err = c.err + GSL_DBL_EPSILON * 3.0*x/7.0;

    return GSL_SUCCESS;

  }

  else if(x < -(M_LN2 + GSL_LOG_DBL_EPSILON)) {

    const int nexp = floor(xcut/x);

    const double ex  = exp(-x);

    double xk  = nexp * x;

    double rk  = nexp;

    double sum = 0.0;

    int i;

    for(i=nexp; i>=1; i--) {

      double xk_inv = 1.0/xk;

      sum *= ex;

      sum += ((((((720.0*xk_inv + 720.0)*xk_inv + 360.0)*xk_inv + 120.0)*xk_inv + 30.0)*xk_inv+ 6.0)*xk_inv+ 1.0) / rk;

      rk -= 1.0;

      xk -= x;

    }

    result->val = val_infinity/(x*x*x*x*x*x) - 6.0 * sum * ex;

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

    return GSL_SUCCESS;

  }

  else if(x < xcut) {

    const double x2 = x*x;

    const double x4 = x2*x2;

    const double x6 = x4*x2;

    const double sum = 720.0 + 720.0*x + 360.0*x2 + 120.0*x2*x + 30.0*x4 + 6.0*x4*x +x6 ;

    result->val = (val_infinity - 6.0 * sum * exp(-x)) / x6;

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

    return GSL_SUCCESS;

  }

  else {

    result->val = (((((val_infinity/x)/x)/x)/x)/x)/x ;

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

    CHECK_UNDERFLOW(result);

    return GSL_SUCCESS;

  }

}

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

#include "eval.h"

double gsl_sf_debye_1(const double x)

{

  EVAL_RESULT(gsl_sf_debye_1_e(x, &result));

}

double gsl_sf_debye_2(const double x)

{

  EVAL_RESULT(gsl_sf_debye_2_e(x, &result));

}

double gsl_sf_debye_3(const double x)

{

  EVAL_RESULT(gsl_sf_debye_3_e(x, &result));

}

double gsl_sf_debye_4(const double x)

{

  EVAL_RESULT(gsl_sf_debye_4_e(x, &result));

}

double gsl_sf_debye_5(const double x)

{

  EVAL_RESULT(gsl_sf_debye_5_e(x, &result));

}

double gsl_sf_debye_6(const double x)

{

  EVAL_RESULT(gsl_sf_debye_6_e(x, &result));

}