/* mpfr_pow_ui-- compute the power of a floating-point
                                  by a machine integer

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 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., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

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

/* sets x to y^n, and return 0 if exact, non-zero otherwise */
int
mpfr_pow_ui (mpfr_ptr x, mpfr_srcptr y, unsigned long int n, mp_rnd_t rnd)
{
  unsigned long m;
  mpfr_t res;
  mp_prec_t prec, err;
  int inexact;
  mp_rnd_t rnd1;
  MPFR_SAVE_EXPO_DECL (expo);
  MPFR_ZIV_DECL (loop);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (y)))
    {
      if (MPFR_IS_NAN (y))
        {
          MPFR_SET_NAN (x);
          MPFR_RET_NAN;
        }
      else if (n == 0) /* y^0 = 1 for any y except NAN */
        {
          /* The return mpfr_set_ui is important as 1 isn't necessarily
             in the exponent range. */
          return mpfr_set_ui (x, 1, rnd);
        }
      else if (MPFR_IS_INF (y))
        {
          /* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
          if ((MPFR_IS_NEG (y)) && ((n & 1) == 1))
            MPFR_SET_NEG (x);
          else
            MPFR_SET_POS (x);
          MPFR_SET_INF (x);
          MPFR_RET (0);
        }
      else /* y is zero */
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (y));
          /* 0^n = 0 for any n */
          MPFR_SET_ZERO (x);
          if (MPFR_IS_POS (y) || ((n & 1) == 0))
            MPFR_SET_POS (x);
          else
            MPFR_SET_NEG (x);
          MPFR_RET (0);
        }
    }
  else if (MPFR_UNLIKELY (n <= 2))
    {
      if (n < 1)
        /* y^0 = 1 for any y */
        return mpfr_set_ui (x, 1, rnd);
      else if (n == 1)
        /* y^1 = y */
        return mpfr_set (x, y, rnd);
      else
        /* y^2 = sqr(y) */
        return mpfr_mul (x, y, y, rnd);
    }

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

  /* setup initial precision */
  prec = MPFR_PREC (x) + 3 + BITS_PER_MP_LIMB
    + MPFR_INT_CEIL_LOG2 (MPFR_PREC (x));
  mpfr_init2 (res, prec);

  rnd1 = MPFR_IS_POS (y) ? GMP_RNDU : GMP_RNDD; /* away */

  MPFR_ZIV_INIT (loop, prec);
  for (;;)
    {
      int i;
      for (m = n, i = 0; m; i++, m >>= 1)
        ;
      /* now 2^(i-1) <= n < 2^i */
      MPFR_ASSERTD (prec > (mpfr_prec_t) i);
      err = prec - 1 - (mpfr_prec_t) i;
      MPFR_ASSERTD (i >= 1);
      mpfr_clear_overflow ();
      mpfr_clear_underflow ();
      /* First step: compute square from y */
      inexact = mpfr_mul (res, y, y, GMP_RNDU);
      if (n & (1UL << (i-2)))
        inexact |= mpfr_mul (res, res, y, rnd1);
      for (i -= 3; i >= 0 && !mpfr_overflow_p () && !mpfr_underflow_p (); i--)
        {
          inexact |= mpfr_mul (res, res, res, GMP_RNDU);
          if (n & (1UL << i))
            inexact |= mpfr_mul (res, res, y, rnd1);
        }
      /* let r(n) be the number of roundings: we have r(2)=1, r(3)=2,
         and r(2n)=2r(n)+1, r(2n+1)=2r(n)+2, thus r(n)=n-1.
         Using Higham's method, to each rounding corresponds a factor
         (1-theta) with 0 <= theta <= 2^(1-p), thus at the end the
         absolute error is bounded by (n-1)*2^(1-p)*res <= 2*(n-1)*ulp(res)
         since 2^(-p)*x <= ulp(x). Since n < 2^i, this gives a maximal
         error of 2^(1+i)*ulp(res).
      */
      if (MPFR_LIKELY (inexact == 0
                       || mpfr_overflow_p () || mpfr_underflow_p ()
                       || MPFR_CAN_ROUND (res, err, MPFR_PREC (x), rnd)))
        break;
      /* Actualisation of the precision */
      MPFR_ZIV_NEXT (loop, prec);
      mpfr_set_prec (res, prec);
    }
  MPFR_ZIV_FREE (loop);

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

  /* Check Overflow */
  if (MPFR_UNLIKELY (mpfr_overflow_p ()))
    {
      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_overflow (x, rnd,
                            (n % 2) ? MPFR_SIGN (y) : MPFR_SIGN_POS);
    }
  /* Check Underflow  */
  else if (MPFR_UNLIKELY (mpfr_underflow_p ()))
    {
      if (rnd == GMP_RNDN)
        rnd = GMP_RNDZ;
      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_underflow (x, rnd,
                             (n % 2) ? MPFR_SIGN(y) : MPFR_SIGN_POS);
    }

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