/* mpfr_pow_z -- power function x^z with z a MPZ

Copyright 2005 Free Software Foundation, Inc.

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. */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

static int
mpfr_pow_pos_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mp_rnd_t rnd)
{
  mpfr_t res;
  mp_prec_t prec, err;
  int inexact;
  mp_rnd_t rnd1;
  mpz_t absz;
  mp_size_t size_z;
  MPFR_ZIV_DECL (loop);

  MPFR_ASSERTD (mpz_sgn (z) != 0);

  if (MPFR_UNLIKELY (mpz_cmpabs_ui (z, 1) == 0))
    return mpfr_set (y, x, rnd);

  rnd1 = MPFR_IS_POS (x) ? GMP_RNDU : GMP_RNDD; /* away */
  absz[0] = z[0];
  SIZ (absz) = ABS(SIZ(absz)); /* Hack to get abs(z) */
  MPFR_MPZ_SIZEINBASE2 (size_z, z);

  prec = MPFR_PREC (y) + 3 + size_z + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y));
  mpfr_init2 (res, prec);

  MPFR_ZIV_INIT (loop, prec);
  for (;;)
    {
      mp_size_t i = size_z;
      /* now 2^(i-1) <= z < 2^i */
      /* see pow_ui.c for the error analusis, which is identical */
      MPFR_ASSERTD (prec > (mpfr_prec_t) i);
      err = prec - 1 - (mpfr_prec_t) i;
      MPFR_ASSERTD (i >= 2);
      mpfr_clear_overflow ();
      mpfr_clear_underflow ();

      /* First step: compute square from y */
      inexact = mpfr_mul (res, x, x, GMP_RNDU);
      if (mpz_tstbit (absz, i-2))
        inexact |= mpfr_mul (res, res, x, rnd1);
      for (i -= 3; i >= 0 && !mpfr_underflow_p() && !mpfr_overflow_p (); i--)
        {
          inexact |= mpfr_mul (res, res, res, GMP_RNDU);
          if (mpz_tstbit (absz, i))
            inexact |= mpfr_mul (res, res, x, rnd1);
        }
      /*    printf ("pow_z ");
            mpfr_dump_mant (MPFR_MANT (res), prec, MPFR_PREC (x), err); */
      if (MPFR_LIKELY (inexact == 0
                       || mpfr_overflow_p () || mpfr_underflow_p ()
                       || MPFR_CAN_ROUND (res, err, MPFR_PREC (y), rnd)))
        break;
      /* Actualisation of the precision */
      MPFR_ZIV_NEXT (loop, prec);
      mpfr_set_prec (res, prec);
    }
  MPFR_ZIV_FREE (loop);

  inexact = mpfr_set (y, res, rnd);
  mpfr_clear (res);

  /* Check Overflow */
  if (MPFR_UNLIKELY (mpfr_overflow_p ()))
    return mpfr_overflow (y, rnd,
              mpz_odd_p (absz) ? MPFR_SIGN (x) : MPFR_SIGN_POS);
  /* Check Underflow */
  else if (MPFR_UNLIKELY (mpfr_underflow_p ()))
    {
      if (rnd == GMP_RNDN)
        rnd = GMP_RNDZ;
      return mpfr_underflow (y, rnd,
         mpz_odd_p (absz) ? MPFR_SIGN (x) : MPFR_SIGN_POS);
    }
  return inexact;
}

/* The computation of y=pow(x,z) is done by
 *    y=pow_ui(x,z) if z>0
 * else
 *    y=1/pow_ui(x,z) if z<0
 */

int
mpfr_pow_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mp_rnd_t rnd)
{
  int   inexact;
  mpz_t tmp;
  MPFR_SAVE_EXPO_DECL (expo);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      if (MPFR_IS_NAN (x))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      else if (mpz_sgn (z) == 0)  /* y^0 = 1 for any y except NAN */
        return mpfr_set_ui (y, 1, rnd);
      else if (MPFR_IS_INF (x))
        {
          /* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
          /* Inf ^(-n) = 0, sign = + if x>0 or z even */
          if (mpz_sgn (z) > 0)
            MPFR_SET_INF (y);
          else
            MPFR_SET_ZERO (y);
          if (MPFR_UNLIKELY (MPFR_IS_NEG (x) && mpz_odd_p (z)))
            MPFR_SET_NEG (y);
          else
            MPFR_SET_POS (y);
          MPFR_RET (0);
        }
      else /* x is zero */
        {
          MPFR_ASSERTD (MPFR_IS_ZERO(x));
          if (mpz_sgn (z) > 0)
            /* 0^n = +/-0 for any n */
            MPFR_SET_ZERO (y);
          else
            /* 0^(-n) if +/- INF */
            MPFR_SET_INF (y);
          if (MPFR_LIKELY (MPFR_IS_POS (x) || mpz_even_p (z)))
            MPFR_SET_POS (y);
          else
            MPFR_SET_NEG (y);
          MPFR_RET(0);
        }
    }

  if (MPFR_UNLIKELY (mpz_sgn (z) == 0))
    /* y^0 = 1 for any y except NAN */
    return mpfr_set_ui (y, 1, rnd);

  /* detect exact powers: x^-n is exact iff x is a power of 2
     Do it if n > 0 too (faster). */
  if (MPFR_UNLIKELY (mpfr_cmp_si_2exp (x, MPFR_SIGN (x),
                                       MPFR_EXP (x) - 1) == 0))
    {
      mp_exp_t expx = MPFR_EXP (x); /* warning: x and y may be the same
                                       variable */
      mpfr_set_si (y, mpz_odd_p (z) ? MPFR_INT_SIGN(x) : 1, rnd);
      MPFR_ASSERTD (MPFR_IS_FP (y));
      mpz_init (tmp);
      mpz_mul_si (tmp, z, expx-1);
      MPFR_ASSERTD (MPFR_GET_EXP (y) == 1);
      mpz_add_ui (tmp, tmp, 1);
      inexact = 0;
      if (MPFR_UNLIKELY (mpz_cmp_si (tmp, __gmpfr_emin) < 0))
        {
          /* The following test is necessary because in the rounding to the
           * nearest mode, mpfr_underflow always rounds away from 0. In
           * this rounding mode, we need to round to 0 if:
           *   _ |y| < 2^(emin-2), or
           *   _ |y| = 2^(emin-2) and the absolute value of the exact
           *     result is <= 2^(emin-2).
           * NOTE: y is a power of 2 and inexact = 0!
           */
          if (rnd == GMP_RNDN && mpz_cmp_si (tmp, __gmpfr_emin-1) < 0)
            rnd = GMP_RNDZ;
          inexact = mpfr_underflow (y, rnd, MPFR_SIGN (y));
        }
      else if (MPFR_UNLIKELY (mpz_cmp_si (tmp, __gmpfr_emax) > 0))
        inexact = mpfr_overflow (y, rnd, MPFR_SIGN(x));
      else
        MPFR_SET_EXP (y, mpz_get_si (tmp));
      mpz_clear (tmp);
      MPFR_RET (inexact);
    }

  MPFR_SAVE_EXPO_MARK (expo);
  __gmpfr_emin -= 3; /* So that we can check for underflow properly */

  if (mpz_sgn (z) > 0)
    inexact = mpfr_pow_pos_z (y, x, z, rnd);
  else
    {
      /* Declaration of the intermediary variable */
      mpfr_t t;
      mp_prec_t Nt;   /* Precision of the intermediary variable */
      MPFR_ZIV_DECL (loop);

      /* compute the precision of intermediary variable */
      Nt = MAX (MPFR_PREC (x), MPFR_PREC (y));

      /* the optimal number of bits : see algorithms.ps */
      Nt = Nt + 3 + MPFR_INT_CEIL_LOG2 (Nt);

      /* initialise of intermediary     variable */
      mpfr_init2 (t, Nt);

      MPFR_ZIV_INIT (loop, Nt);
      for (;;)
        {
          /* compute 1/(x^n) n>0 */
          mpfr_pow_pos_z (t, x, z, GMP_RNDN);
          inexact = MPFR_IS_ZERO (t) || MPFR_IS_INF (t);
          mpfr_ui_div (t, 1, t, GMP_RNDN);
          inexact = inexact || MPFR_IS_ZERO (t) || MPFR_IS_INF (t);

          if (MPFR_LIKELY (inexact != 0
                           || MPFR_CAN_ROUND (t, Nt-3, MPFR_PREC (y), rnd)))
            break;
          /* actualisation of the precision */
          MPFR_ZIV_NEXT (loop, Nt);
          mpfr_set_prec (t, Nt);
        }
      MPFR_ZIV_FREE (loop);

      inexact = mpfr_set (y, t, rnd);
      mpfr_clear (t);
    }

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, inexact, rnd);
}