/* mpfr_exp2 -- power of 2 function 2^y 

Copyright 2001, 2002, 2003 Free Software Foundation.

This file is part of the MPFR Library.

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 <limits.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"

 /* The computation of y = 2^z is done by

    y = exp(z*log(2)). The result is exact iff z is an integer.
 */

int
mpfr_exp2 (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) 
{    

    int inexact;

    if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) ))
      {
	if (MPFR_IS_NAN(x))
	  {
	    MPFR_SET_NAN(y);
	    MPFR_RET_NAN;
	  }
	else if (MPFR_IS_INF(x))
	  {
	    if (MPFR_IS_POS(x))
	      MPFR_SET_INF(y);
	    else
	      MPFR_SET_ZERO(y);
	    MPFR_SET_POS(y);
	    MPFR_RET(0);
	  }
	/* 2^0 = 1 */
	else if (MPFR_IS_ZERO(x))
	  return mpfr_set_ui (y, 1, rnd_mode);
	else
	  MPFR_ASSERTN(0);
      }
    /* Useless due to mpfr_set 
       MPFR_CLEAR_FLAGS(y);*/
    
    /* since the smallest representable non-zero float is 1/2*2^__gmpfr_emin,
       if x < __gmpfr_emin - 1, the result is either 1/2*2^__gmpfr_emin or 0 */
    MPFR_ASSERTN(MPFR_EMIN_MIN - 2 >= LONG_MIN);
    if (mpfr_cmp_si_2exp (x, __gmpfr_emin - 1, 0) < 0)
      {
        mp_rnd_t rnd2 = rnd_mode;
        /* in round to nearest mode, round to zero when x <= __gmpfr_emin-2 */
        if (rnd_mode == GMP_RNDN &&
            mpfr_cmp_si_2exp (x, __gmpfr_emin - 2, 0) <= 0)
          rnd2 = GMP_RNDZ;
        return mpfr_set_underflow (y, rnd2, 1);
      }

    if (mpfr_integer_p (x)) /* we know that x >= 2^(emin-1) */
      {
        double xd;

        MPFR_ASSERTN(MPFR_EMAX_MAX <= LONG_MAX);
        if (mpfr_cmp_si_2exp (x, __gmpfr_emax, 0) > 0)
          return mpfr_set_overflow (y, rnd_mode, 1);

        xd = mpfr_get_d1 (x);
        
        mpfr_set_ui (y, 1, GMP_RNDZ);
        return mpfr_mul_2si (y, y, (long) xd, rnd_mode);
      }

    /* General case */
    {
    /* Declaration of the intermediary variable */
      mpfr_t t, te;

      /* Declaration of the size variable */
      mp_prec_t Nx = MPFR_PREC(x);   /* Precision of input variable */
      mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */

      mp_prec_t Nt;   /* Precision of the intermediary variable */
      long int err;  /* Precision of error */
                
      /* compute the precision of intermediary variable */
      Nt = MAX(Nx, Ny);
      /* the optimal number of bits : see algorithms.ps */
      Nt = Nt + 5 + __gmpfr_ceil_log2 (Nt);


      /* initialise of intermediary	variable */
      mpfr_init (t);
      mpfr_init (te);

      /* First computation */
      do
        {

          /* reactualisation of the precision */
          mpfr_set_prec (t, Nt);             
          mpfr_set_prec (te, Nt);             

          /* compute   exp(x*ln(2))*/
          mpfr_const_log2 (t, GMP_RNDU);    /* ln(2) */
          mpfr_mul (te, x, t, GMP_RNDU);    /* x*ln(2) */
          mpfr_exp (t, te, GMP_RNDN);       /* exp(x*ln(2))*/

          /* estimate of the error -- see pow function in algorithms.ps*/
          err = Nt - (MPFR_GET_EXP (te) + 2);

          /* actualisation of the precision */
          Nt += __gmpfr_isqrt (Nt) + 10;

        }
      while ((err < 0) || !mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
                                           Ny + (rnd_mode == GMP_RNDN)));
 
      inexact = mpfr_set (y, t, rnd_mode);

      mpfr_clear (t);
      mpfr_clear (te);
    }

    return inexact;
}