/* specfunc/coupling.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002 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 <stdlib.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_sf_gamma.h>

#include <gsl/gsl_sf_coupling.h>

#include <gsl/gsl_sf_exp.h>

#include "error.h"

inline

static

int locMax3(const int a, const int b, const int c)

{

  int d = GSL_MAX(a, b);

  return GSL_MAX(d, c);

}

inline

static

int locMin3(const int a, const int b, const int c)

{

  int d = GSL_MIN(a, b);

  return GSL_MIN(d, c);

}

inline

static

int locMin5(const int a, const int b, const int c, const int d, const int e)

{

  int f = GSL_MIN(a, b);

  int g = GSL_MIN(c, d);

  int h = GSL_MIN(f, g);

  return GSL_MIN(e, h);

}

/* See: [Thompson, Atlas for Computing Mathematical Functions] */

static

int

delta(int ta, int tb, int tc, gsl_sf_result * d)

{

  gsl_sf_result f1, f2, f3, f4;

  int status = 0;

  status += gsl_sf_fact_e((ta + tb - tc)/2, &f1;;

  status += gsl_sf_fact_e((ta + tc - tb)/2, &f2;;

  status += gsl_sf_fact_e((tb + tc - ta)/2, &f3;;

  status += gsl_sf_fact_e((ta + tb + tc)/2 + 1, &f4;;

  if(status != 0) {

    OVERFLOW_ERROR(d);

  }

  d->val = f1.val * f2.val * f3.val / f4.val;

  d->err = 4.0 * GSL_DBL_EPSILON * fabs(d->val);

  return GSL_SUCCESS;

}

static

int

triangle_selection_fails(int two_ja, int two_jb, int two_jc)

{

  /*

   * enough to check the triangle condition for one spin vs. the other two

   */

  return ( (two_jb < abs(two_ja - two_jc)) || (two_jb > two_ja + two_jc) ||

           GSL_IS_ODD(two_ja + two_jb + two_jc) );

}

static

int

m_selection_fails(int two_ja, int two_jb, int two_jc,

                  int two_ma, int two_mb, int two_mc)

{

  return (

         abs(two_ma) > two_ja 

      || abs(two_mb) > two_jb

      || abs(two_mc) > two_jc

      || GSL_IS_ODD(two_ja + two_ma)

      || GSL_IS_ODD(two_jb + two_mb)

      || GSL_IS_ODD(two_jc + two_mc)

      || (two_ma + two_mb + two_mc) != 0

          );

}

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

int

gsl_sf_coupling_3j_e (int two_ja, int two_jb, int two_jc,

                      int two_ma, int two_mb, int two_mc,

                      gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(two_ja < 0 || two_jb < 0 || two_jc < 0) {

    DOMAIN_ERROR(result);

  }

  else if (   triangle_selection_fails(two_ja, two_jb, two_jc)

           || m_selection_fails(two_ja, two_jb, two_jc, two_ma, two_mb, two_mc)

     ) {

    result->val = 0.0;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else if ( two_ma == 0 && two_mb == 0 && two_mc == 0

            && ((two_ja + two_jb + two_jc) % 4 == 2) ) {

    /* Special case for (ja jb jc; 0 0 0) = 0 when ja+jb+jc=odd */

    result->val = 0.0;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else {

    int jca  = (-two_ja + two_jb + two_jc) / 2,

        jcb  = ( two_ja - two_jb + two_jc) / 2,

        jcc  = ( two_ja + two_jb - two_jc) / 2,

        jmma = ( two_ja - two_ma) / 2,

        jmmb = ( two_jb - two_mb) / 2,

        jmmc = ( two_jc - two_mc) / 2,

        jpma = ( two_ja + two_ma) / 2,

        jpmb = ( two_jb + two_mb) / 2,

        jpmc = ( two_jc + two_mc) / 2,

        jsum = ( two_ja + two_jb + two_jc) / 2,

        kmin = locMax3 (0, jpmb - jmmc, jmma - jpmc),

        kmax = locMin3 (jcc, jmma, jpmb),

        k, sign = GSL_IS_ODD (kmin - jpma + jmmb) ? -1 : 1,

        status = 0;

    double sum_pos = 0.0, sum_neg = 0.0, sum_err = 0.0;

    gsl_sf_result bc1, bc2, bc3, bcn1, bcn2, bcd1, bcd2, bcd3, bcd4, term, lnorm;

    status += gsl_sf_lnchoose_e (two_ja, jcc , &bcn1);

    status += gsl_sf_lnchoose_e (two_jb, jcc , &bcn2);

    status += gsl_sf_lnchoose_e (jsum+1, jcc , &bcd1);

    status += gsl_sf_lnchoose_e (two_ja, jmma, &bcd2);

    status += gsl_sf_lnchoose_e (two_jb, jmmb, &bcd3);

    status += gsl_sf_lnchoose_e (two_jc, jpmc, &bcd4);

    lnorm.val = 0.5 * (bcn1.val + bcn2.val - bcd1.val - bcd2.val - bcd3.val

                       - bcd4.val - log(two_jc + 1.0));

    lnorm.err = 0.5 * (bcn1.err + bcn2.err + bcd1.err + bcd2.err + bcd3.err

                       + bcd4.err + GSL_DBL_EPSILON * log(two_jc + 1.0));

    for (k = kmin; k <= kmax; k++) {

      status += gsl_sf_lnchoose_e (jcc, k, &bc1;;

      status += gsl_sf_lnchoose_e (jcb, jmma - k, &bc2;;

      status += gsl_sf_lnchoose_e (jca, jpmb - k, &bc3;;

      status += gsl_sf_exp_err_e(bc1.val + bc2.val + bc3.val + lnorm.val,

                                 bc1.err + bc2.err + bc3.err + lnorm.err, 

                                 &term);

      if (status != 0) {

        OVERFLOW_ERROR (result);

      }

      if (sign < 0) {

        sum_neg += term.val;

      } else {

        sum_pos += term.val;

      }

      sum_err += term.err;

      sign = -sign;

    }

    result->val  = sum_pos - sum_neg;

    result->err  = sum_err;

    result->err += 2.0 * GSL_DBL_EPSILON * (sum_pos + sum_neg);

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

    return GSL_SUCCESS;

  }

}

#ifndef GSL_DISABLE_DEPRECATED

int

gsl_sf_coupling_6j_INCORRECT_e(int two_ja, int two_jb, int two_jc,

                               int two_jd, int two_je, int two_jf,

                               gsl_sf_result * result)

{

  return gsl_sf_coupling_6j_e(two_ja, two_jb, two_je, two_jd, two_jc, two_jf, result);

}

#endif

int

gsl_sf_coupling_6j_e(int two_ja, int two_jb, int two_jc,

                     int two_jd, int two_je, int two_jf,

                     gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(   two_ja < 0 || two_jb < 0 || two_jc < 0

     || two_jd < 0 || two_je < 0 || two_jf < 0

     ) {

    DOMAIN_ERROR(result);

  }

  else if(   triangle_selection_fails(two_ja, two_jb, two_jc)

          || triangle_selection_fails(two_ja, two_je, two_jf)

          || triangle_selection_fails(two_jb, two_jd, two_jf)

          || triangle_selection_fails(two_je, two_jd, two_jc)

     ) {

    result->val = 0.0;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else {

    gsl_sf_result n1;

    gsl_sf_result d1, d2, d3, d4, d5, d6;

    double norm;

    int tk, tkmin, tkmax;

    double phase;

    double sum_pos = 0.0;

    double sum_neg = 0.0;

    double sumsq_err = 0.0;

    int status = 0;

    status += delta(two_ja, two_jb, two_jc, &d1;;

    status += delta(two_ja, two_je, two_jf, &d2;;

    status += delta(two_jb, two_jd, two_jf, &d3;;

    status += delta(two_je, two_jd, two_jc, &d4;;

    if(status != GSL_SUCCESS) {

      OVERFLOW_ERROR(result);

    }

    norm = sqrt(d1.val) * sqrt(d2.val) * sqrt(d3.val) * sqrt(d4.val);

    tkmin = locMax3(0,

                   two_ja + two_jd - two_jc - two_jf,

                   two_jb + two_je - two_jc - two_jf);

    tkmax = locMin5(two_ja + two_jb + two_je + two_jd + 2,

                    two_ja + two_jb - two_jc,

                    two_je + two_jd - two_jc,

                    two_ja + two_je - two_jf,

                    two_jb + two_jd - two_jf);

    phase = GSL_IS_ODD((two_ja + two_jb + two_je + two_jd + tkmin)/2)

            ? -1.0

            :  1.0;

    for(tk=tkmin; tk<=tkmax; tk += 2) {

      double term;

      double term_err;

      gsl_sf_result den_1, den_2;

      gsl_sf_result d1_a, d1_b;

      status = 0;

      status += gsl_sf_fact_e((two_ja + two_jb + two_je + two_jd - tk)/2 + 1, &n1;;

      status += gsl_sf_fact_e(tk/2, &d1_a);

      status += gsl_sf_fact_e((two_jc + two_jf - two_ja - two_jd + tk)/2, &d1_b);

      status += gsl_sf_fact_e((two_jc + two_jf - two_jb - two_je + tk)/2, &d2;;

      status += gsl_sf_fact_e((two_ja + two_jb - two_jc - tk)/2, &d3;;

      status += gsl_sf_fact_e((two_je + two_jd - two_jc - tk)/2, &d4;;

      status += gsl_sf_fact_e((two_ja + two_je - two_jf - tk)/2, &d5;;

      status += gsl_sf_fact_e((two_jb + two_jd - two_jf - tk)/2, &d6;;

      if(status != GSL_SUCCESS) {

        OVERFLOW_ERROR(result);

      }

      d1.val = d1_a.val * d1_b.val;

      d1.err = d1_a.err * fabs(d1_b.val) + fabs(d1_a.val) * d1_b.err;

      den_1.val  = d1.val*d2.val*d3.val;

      den_1.err  = d1.err * fabs(d2.val*d3.val);

      den_1.err += d2.err * fabs(d1.val*d3.val);

      den_1.err += d3.err * fabs(d1.val*d2.val);

      den_2.val  = d4.val*d5.val*d6.val;

      den_2.err  = d4.err * fabs(d5.val*d6.val);

      den_2.err += d5.err * fabs(d4.val*d6.val);

      den_2.err += d6.err * fabs(d4.val*d5.val);

      term  = phase * n1.val / den_1.val / den_2.val;

      phase = -phase;

      term_err  = n1.err / fabs(den_1.val) / fabs(den_2.val);

      term_err += fabs(term / den_1.val) * den_1.err;

      term_err += fabs(term / den_2.val) * den_2.err;

      if(term >= 0.0) {

        sum_pos += norm*term;

      }

      else {

        sum_neg -= norm*term;

      }

      sumsq_err += norm*norm * term_err*term_err;

    }

    result->val  = sum_pos - sum_neg;

    result->err  = 2.0 * GSL_DBL_EPSILON * (sum_pos + sum_neg);

    result->err += sqrt(sumsq_err / (0.5*(tkmax-tkmin)+1.0));

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

    return GSL_SUCCESS;

  }

}

int

gsl_sf_coupling_RacahW_e(int two_ja, int two_jb, int two_jc,

                         int two_jd, int two_je, int two_jf,

                         gsl_sf_result * result)

{

  int status = gsl_sf_coupling_6j_e(two_ja, two_jb, two_je, two_jd, two_jc, two_jf, result);

  int phase_sum = (two_ja + two_jb + two_jc + two_jd)/2;

  result->val *= ( GSL_IS_ODD(phase_sum) ? -1.0 : 1.0 );

  return status;

}

int

gsl_sf_coupling_9j_e(int two_ja, int two_jb, int two_jc,

                     int two_jd, int two_je, int two_jf,

                     int two_jg, int two_jh, int two_ji,

                     gsl_sf_result * result)

{

  /* CHECK_POINTER(result) */

  if(   two_ja < 0 || two_jb < 0 || two_jc < 0

     || two_jd < 0 || two_je < 0 || two_jf < 0

     || two_jg < 0 || two_jh < 0 || two_ji < 0

     ) {

    DOMAIN_ERROR(result);

  }

  else if(   triangle_selection_fails(two_ja, two_jb, two_jc)

          || triangle_selection_fails(two_jd, two_je, two_jf)

          || triangle_selection_fails(two_jg, two_jh, two_ji)

          || triangle_selection_fails(two_ja, two_jd, two_jg)

          || triangle_selection_fails(two_jb, two_je, two_jh)

          || triangle_selection_fails(two_jc, two_jf, two_ji)

     ) {

    result->val = 0.0;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else {

    int tk;

    int tkmin = locMax3(abs(two_ja-two_ji), abs(two_jh-two_jd), abs(two_jb-two_jf));

    int tkmax = locMin3(two_ja + two_ji, two_jh + two_jd, two_jb + two_jf);

    double sum_pos = 0.0;

    double sum_neg = 0.0;

    double sumsq_err = 0.0;

    double phase;

    for(tk=tkmin; tk<=tkmax; tk += 2) {

      gsl_sf_result s1, s2, s3;

      double term;

      double term_err;

      int status = 0;

      status += gsl_sf_coupling_6j_e(two_ja, two_ji, tk,  two_jh, two_jd, two_jg,  &s1;;

      status += gsl_sf_coupling_6j_e(two_jb, two_jf, tk,  two_jd, two_jh, two_je,  &s2;;

      status += gsl_sf_coupling_6j_e(two_ja, two_ji, tk,  two_jf, two_jb, two_jc,  &s3;;

      if(status != GSL_SUCCESS) {

        OVERFLOW_ERROR(result);

      }

      term = s1.val * s2.val * s3.val;

      term_err  = s1.err * fabs(s2.val*s3.val);

      term_err += s2.err * fabs(s1.val*s3.val);

      term_err += s3.err * fabs(s1.val*s2.val);

      if(term >= 0.0) {

        sum_pos += (tk + 1) * term;

      }

      else {

        sum_neg -= (tk + 1) * term;

      }

      sumsq_err += ((tk+1) * term_err) * ((tk+1) * term_err);

    }

    phase = GSL_IS_ODD(tkmin) ? -1.0 : 1.0;

    result->val  = phase * (sum_pos - sum_neg);

    result->err  = 2.0 * GSL_DBL_EPSILON * (sum_pos + sum_neg);

    result->err += sqrt(sumsq_err / (0.5*(tkmax-tkmin)+1.0));

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

    return GSL_SUCCESS;

  }

}

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

#include "eval.h"

double gsl_sf_coupling_3j(int two_ja, int two_jb, int two_jc,

                          int two_ma, int two_mb, int two_mc)

{

  EVAL_RESULT(gsl_sf_coupling_3j_e(two_ja, two_jb, two_jc,

                                   two_ma, two_mb, two_mc,

                                   &result));

}

#ifndef GSL_DISABLE_DEPRECATED

double gsl_sf_coupling_6j_INCORRECT(int two_ja, int two_jb, int two_jc,

                                    int two_jd, int two_je, int two_jf)

{

  EVAL_RESULT(gsl_sf_coupling_6j_INCORRECT_e(two_ja, two_jb, two_jc,

                                             two_jd, two_je, two_jf,

                                             &result));

}

#endif

double gsl_sf_coupling_6j(int two_ja, int two_jb, int two_jc,

                          int two_jd, int two_je, int two_jf)

{

  EVAL_RESULT(gsl_sf_coupling_6j_e(two_ja, two_jb, two_jc,

                                   two_jd, two_je, two_jf,

                                   &result));

}

double gsl_sf_coupling_RacahW(int two_ja, int two_jb, int two_jc,

                          int two_jd, int two_je, int two_jf)

{

  EVAL_RESULT(gsl_sf_coupling_RacahW_e(two_ja, two_jb, two_jc,

                                      two_jd, two_je, two_jf,

                                      &result));

}

double gsl_sf_coupling_9j(int two_ja, int two_jb, int two_jc,

                          int two_jd, int two_je, int two_jf,

                          int two_jg, int two_jh, int two_ji)

{

  EVAL_RESULT(gsl_sf_coupling_9j_e(two_ja, two_jb, two_jc,

                                   two_jd, two_je, two_jf,

                                   two_jg, two_jh, two_ji,

                                   &result));

}