/* mpfr_gamma -- gamma function

Copyright 2001 Free Software Foundation.

This file is part of the MPFR Library, and was contributed by Mathieu Dutour.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The MPFR Library 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"

int mpfr_gamma _PROTO ((mpfr_ptr, mpfr_srcptr, mp_rnd_t));

/* We use the reflection formula 
  Gamma(1+x)Gamma(1-x)=\pi x/(sin(\pi x))
  in order to treat the case x<=1  */

#define CST   0.38  /* CST=ln(2)/(ln(2*pi)) */
#define zCST  0.26  /* zCST=1/(2*ln(2*pi)) */
#define ecCST  1.84  /* {1+sup_{x\in [0,1]} x*ln((1-x)/x)}/ln(2)  */

int
#if __STDC__
mpfr_gamma (mpfr_ptr gamma, mpfr_srcptr x, mp_rnd_t rnd_mode)
#else
mpfr_gamma (gamma, x, rnd_mode)
     mpfr_ptr gamma;
     mpfr_srcptr x; 
     mp_rnd_t rnd_mode;
#endif
{
  mpfr_t xp;
  mpfr_t product;
  mpfr_t the_pi;
  mpfr_t Csin;
  mpfr_t GammaTrial;
  mpfr_t tmp, tmp2;

  int Prec;
  int prec_gamma;
  int prec_nec;
  int good = 0;
  double C;
  long A, N, estimated_cancel;
  int realprec;
  int compared;
  int k;
  int sign;
  /* Trivial cases */
  if (MPFR_IS_NAN(x))
    {
      MPFR_SET_NAN(gamma);
      return 1;
    }
  if (!MPFR_NOTZERO(x))
    {
      MPFR_SET_INF(gamma);
      return 1;
    }
  if (MPFR_IS_INF(x))
    {
      MPFR_SET_INF(gamma);
      return 1;
    }
  /* Set x_p=x if x> 1 else set x_p=2-x */
  prec_gamma = MPFR_PREC(gamma);
  compared = mpfr_cmp_ui(x, 1);
  if (compared == 0)
    {
      mpfr_set_ui(gamma, 1, rnd_mode);
      return 1;
    }
  realprec = prec_gamma+10;

  while (!good){
    /* Precision stuff */
    if (compared == -1)
      {
	prec_nec = 2+realprec; /* We will use the reflexion formula! */
      }
    else
      {
	prec_nec = realprec;
      }
    C = (double)(((double) prec_nec)*CST-0.5);
    A = (int)C;
    N = A-1;
#ifdef DEBUG
    printf("C=%u", (int)C);
    printf(" A=%u", (int)A);
    printf(" N=%u", (int)N);
    printf("\n");
#endif

    /* estimated_cancel is the amount of bit that will be flushed */
    estimated_cancel= (long) ceil(ecCST*A);
    Prec = prec_nec + estimated_cancel+20;


    mpfr_init2(xp, Prec);
    if (compared == -1)
      {
	mpfr_ui_sub(xp, 1, x, GMP_RNDN);
      }
    else
      {
	mpfr_sub_ui(xp, x, 1, GMP_RNDN);
      }
    /* Initialisation    */
    mpfr_init2(tmp, Prec);
    mpfr_init2(tmp2, Prec);
    mpfr_init2(the_pi, Prec);
    mpfr_init2(product, Prec);
    mpfr_init2(GammaTrial, Prec);


    mpfr_set_ui(GammaTrial, 0, GMP_RNDN);
    sign=1;
    for (k = 1; k<=N; k++)
      {
	mpfr_set_ui(tmp, A-k, GMP_RNDN);
	mpfr_exp(product, tmp, GMP_RNDN);
	mpfr_ui_pow_ui(tmp, A-k, k-1, GMP_RNDN);
	mpfr_mul(product, product, tmp, GMP_RNDN);
	mpfr_sqrt_ui(tmp, A-k, GMP_RNDN);
	mpfr_mul(product, product, tmp, GMP_RNDN);
	mpfr_fac_ui(tmp, k-1, GMP_RNDN);
	mpfr_div(product, product, tmp, GMP_RNDN);
	mpfr_add_ui(tmp, xp, k, GMP_RNDN);
	mpfr_div(product, product, tmp, GMP_RNDN);
	sign=-sign;
	if (sign == 1)
	  {
	    mpfr_neg(product, product, GMP_RNDN);
#ifdef DEBUG
	    /*	    printf(" k=%u", k);
		    printf("\n");*/
#endif
	  }
	mpfr_add(GammaTrial, GammaTrial, product, GMP_RNDN);
      }
#ifdef DEBUG
    printf("GammaTrial =");
    mpfr_out_str (stdout, 10, 0, GammaTrial, GMP_RNDD);
    printf ("\n");
#endif
    mpfr_const_pi(the_pi, GMP_RNDN);
    mpfr_const_pi(tmp, GMP_RNDN);
    mpfr_mul_2ui(tmp, tmp, 1, GMP_RNDN);
    mpfr_sqrt(tmp, tmp, GMP_RNDN);
    mpfr_add(GammaTrial, GammaTrial, tmp, GMP_RNDN);
    mpfr_add_ui(tmp2, xp, A, GMP_RNDN);
    mpfr_set_ui(tmp, 1, GMP_RNDN);
    mpfr_div_2ui(tmp, tmp, 1, GMP_RNDN);
    mpfr_add(tmp, tmp, xp, GMP_RNDN);
    mpfr_pow(tmp, tmp2, tmp, GMP_RNDN);
    mpfr_mul(GammaTrial, GammaTrial, tmp, GMP_RNDN);
    mpfr_neg(tmp, tmp2, GMP_RNDN);
    mpfr_exp(tmp, tmp, GMP_RNDN);
    mpfr_mul(GammaTrial, GammaTrial, tmp, GMP_RNDN);
    if (compared == -1)
      {
	mpfr_init2(Csin, Prec);
	mpfr_sub_ui(tmp, x, 1, GMP_RNDN);
	mpfr_mul(tmp, the_pi, tmp, GMP_RNDN);
	mpfr_div(GammaTrial, tmp, GammaTrial, GMP_RNDN);
	mpfr_sin(tmp, tmp, GMP_RNDN);
	mpfr_div(GammaTrial, GammaTrial, tmp, GMP_RNDN);
	mpfr_neg(GammaTrial, GammaTrial, GMP_RNDN);
      }
#ifdef DEBUG
    printf("GammaTrial =");
    mpfr_out_str (stdout, 10, 0, GammaTrial, GMP_RNDD);
    printf ("\n");
#endif
    if (mpfr_can_round(GammaTrial, realprec, GMP_RNDD, rnd_mode, MPFR_PREC(gamma)))
      {
	mpfr_set(gamma, GammaTrial, rnd_mode);
	good = 1;
      }
    else
      {
	realprec += _mpfr_ceil_log2 ((double) realprec);
#ifdef DEBUG
	printf("RETRY\n");
#endif
      }
    mpfr_clear(tmp);
    mpfr_clear(tmp2);
    mpfr_clear(the_pi);
    mpfr_clear(product);
    mpfr_clear(GammaTrial);
  }

  mpfr_clear(xp);

  return 1; /* inexact result */
}