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debye.c

/* 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 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 */
/* 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));
}

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