/* mpc_pow_ui -- Raise a complex number to an integer power.

Copyright (C) 2009, 2010, 2011, 2012 INRIA

This file is part of GNU MPC.

GNU MPC 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 3 of the License, or (at your

option) any later version.

GNU MPC 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 this program. If not, see http://www.gnu.org/licenses/ .

*/

#include <limits.h> /* for CHAR_BIT */

#include "mpc-impl.h"

static int

mpc_pow_usi_naive (mpc_ptr z, mpc_srcptr x, unsigned long y, int sign,

   mpc_rnd_t rnd)

{

   int inex;

   mpc_t t;

   mpc_init3 (t, sizeof (unsigned long) * CHAR_BIT, MPFR_PREC_MIN);

   if (sign > 0)

      mpc_set_ui (t, y, MPC_RNDNN); /* exact */

   else

      mpc_set_si (t, - (signed long) y, MPC_RNDNN);

   inex = mpc_pow (z, x, t, rnd);

   mpc_clear (t);

   return inex;

}

int

mpc_pow_usi (mpc_ptr z, mpc_srcptr x, unsigned long y, int sign,

   mpc_rnd_t rnd)

   /* computes z = x^(sign*y) */

{

   int inex;

   mpc_t t, x3;

   mpfr_prec_t p, l, l0;

   long unsigned int u;

   int has3; /* non-zero if y has '11' in its binary representation */

   int loop, done;

   /* let mpc_pow deal with special values */

   if (!mpc_fin_p (x) || mpfr_zero_p (mpc_realref (x)) || mpfr_zero_p (mpc_imagref(x))

       || y == 0)

      return mpc_pow_usi_naive (z, x, y, sign, rnd);

   /* easy special cases */

   else if (y == 1) {

      if (sign > 0)

         return mpc_set (z, x, rnd);

      else

         return mpc_ui_div (z, 1ul, x, rnd);

   }

   else if (y == 2 && sign > 0)

      return mpc_sqr (z, x, rnd);

   /* let mpc_pow treat potential over- and underflows */

   else {

      mpfr_exp_t exp_r = mpfr_get_exp (mpc_realref (x)),

                 exp_i = mpfr_get_exp (mpc_imagref (x));

      if (   MPC_MAX (exp_r, exp_i) > mpfr_get_emax () / (mpfr_exp_t) y

             /* heuristic for overflow */

          || MPC_MAX (-exp_r, -exp_i) > (-mpfr_get_emin ()) / (mpfr_exp_t) y

             /* heuristic for underflow */

         )

         return mpc_pow_usi_naive (z, x, y, sign, rnd);

   }

   has3 = (y & (y >> 1)) != 0;

   for (l = 0, u = y; u > 3; l ++, u >>= 1);

   /* l>0 is the number of bits of y, minus 2, thus y has bits:

      y_{l+1} y_l y_{l-1} ... y_1 y_0 */

   l0 = l + 2;

   p = MPC_MAX_PREC(z) + l0 + 32; /* l0 ensures that y*2^{-p} <= 1 below */

   mpc_init2 (t, p);

   if (has3)

      mpc_init2 (x3, p);

   loop = 0;

   done = 0;

   while (!done) {

      loop++;

      mpc_sqr (t, x, MPC_RNDNN);

      if (has3) {

         mpc_mul (x3, t, x, MPC_RNDNN);

         if ((y >> l) & 1) /* y starts with 11... */

            mpc_set (t, x3, MPC_RNDNN);

      }

      while (l-- > 0) {

         mpc_sqr (t, t, MPC_RNDNN);

         if ((y >> l) & 1) {

            if ((l > 0) && ((y >> (l-1)) & 1)) /* implies has3 <> 0 */ {

               l--;

               mpc_sqr (t, t, MPC_RNDNN);

               mpc_mul (t, t, x3, MPC_RNDNN);

            }

            else

               mpc_mul (t, t, x, MPC_RNDNN);

         }

      }

      if (sign < 0)

         mpc_ui_div (t, 1ul, t, MPC_RNDNN);

      if (mpfr_zero_p (mpc_realref(t)) || mpfr_zero_p (mpc_imagref(t))) {

         inex = mpc_pow_usi_naive (z, x, y, sign, rnd);

            /* since mpfr_get_exp() is not defined for zero */

         done = 1;

      }

      else {

         /* see error bound in algorithms.tex; we use y<2^l0 instead of y-1

            also when sign>0                                                */

         mpfr_exp_t diff;

         mpfr_prec_t er, ei;

         diff = mpfr_get_exp (mpc_realref(t)) - mpfr_get_exp (mpc_imagref(t));

         /* the factor on the real part is 2+2^(-diff+2) <= 4 for diff >= 1

            and < 2^(-diff+3) for diff <= 0 */

         er = (diff >= 1) ? l0 + 3 : l0 + (-diff) + 3;

         /* the factor on the imaginary part is 2+2^(diff+2) <= 4 for diff <= -1

            and < 2^(diff+3) for diff >= 0 */

         ei = (diff <= -1) ? l0 + 3 : l0 + diff + 3;

         if (mpfr_can_round (mpc_realref(t), p - er, MPFR_RNDN, MPFR_RNDZ,

                              MPC_PREC_RE(z) + (MPC_RND_RE(rnd) == MPFR_RNDN))

               && mpfr_can_round (mpc_imagref(t), p - ei, MPFR_RNDN, MPFR_RNDZ,

                              MPC_PREC_IM(z) + (MPC_RND_IM(rnd) == MPFR_RNDN))) {

            inex = mpc_set (z, t, rnd);

            done = 1;

         }

         else if (loop == 1 && SAFE_ABS(mpfr_prec_t, diff) < MPC_MAX_PREC(z)) {

            /* common case, make a second trial at higher precision */

            p += MPC_MAX_PREC(x);

            mpc_set_prec (t, p);

            if (has3)

               mpc_set_prec (x3, p);

            l = l0 - 2;

         }

         else {

            /* stop the loop and use mpc_pow */

            inex = mpc_pow_usi_naive (z, x, y, sign, rnd);

            done = 1;

         }

      }

   }

   mpc_clear (t);

   if (has3)

      mpc_clear (x3);

   return inex;

}

int

mpc_pow_ui (mpc_ptr z, mpc_srcptr x, unsigned long y, mpc_rnd_t rnd)

{

  return mpc_pow_usi (z, x, y, 1, rnd);

}