macssh/gmp/mpz/powm_ui.c

/* mpz_powm_ui(res,base,exp,mod) -- Set RES to (base**exp) mod MOD.

Copyright (C) 1991, 1993, 1994, 1996, 1997, 2000 Free Software Foundation,
Inc.

This file is part of the GNU MP Library.

The GNU MP 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 GNU MP 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 GNU MP 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> /* for NULL */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"

void
#if __STDC__
mpz_powm_ui (mpz_ptr res, mpz_srcptr base, unsigned long int exp, mpz_srcptr mod)
#else
mpz_powm_ui (res, base, exp, mod)
     mpz_ptr res;
     mpz_srcptr base;
     unsigned long int exp;
     mpz_srcptr mod;
#endif
{
  mp_ptr rp, mp, bp;
  mp_size_t msize, bsize, rsize;
  mp_size_t size;
  int mod_shift_cnt;
  int negative_result;
  mp_limb_t *free_me = NULL;
  size_t free_me_size;
  TMP_DECL (marker);

  msize = ABS (mod->_mp_size);
  size = 2 * msize;

  rp = res->_mp_d;

  if (msize == 0)
    DIVIDE_BY_ZERO;

  if (exp == 0)
    {
      /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
	 depending on if MOD equals 1.  */
      res->_mp_size = (msize == 1 && (mod->_mp_d)[0] == 1) ? 0 : 1;
      rp[0] = 1;
      return;
    }

  TMP_MARK (marker);

  /* Normalize MOD (i.e. make its most significant bit set) as required by
     mpn_divmod.  This will make the intermediate values in the calculation
     slightly larger, but the correct result is obtained after a final
     reduction using the original MOD value.  */

  mp = (mp_ptr) TMP_ALLOC (msize * BYTES_PER_MP_LIMB);
  count_leading_zeros (mod_shift_cnt, mod->_mp_d[msize - 1]);
  if (mod_shift_cnt != 0)
    mpn_lshift (mp, mod->_mp_d, msize, mod_shift_cnt);
  else
    MPN_COPY (mp, mod->_mp_d, msize);

  bsize = ABS (base->_mp_size);
  if (bsize > msize)
    {
      /* The base is larger than the module.  Reduce it.  */

      /* Allocate (BSIZE + 1) with space for remainder and quotient.
	 (The quotient is (bsize - msize + 1) limbs.)  */
      bp = (mp_ptr) TMP_ALLOC ((bsize + 1) * BYTES_PER_MP_LIMB);
      MPN_COPY (bp, base->_mp_d, bsize);
      /* We don't care about the quotient, store it above the remainder,
	 at BP + MSIZE.  */
      mpn_divmod (bp + msize, bp, bsize, mp, msize);
      bsize = msize;
      /* Canonicalize the base, since we are going to multiply with it
	 quite a few times.  */
      MPN_NORMALIZE (bp, bsize);
    }
  else
    bp = base->_mp_d;

  if (bsize == 0)
    {
      res->_mp_size = 0;
      TMP_FREE (marker);
      return;
    }

  if (res->_mp_alloc < size)
    {
      /* We have to allocate more space for RES.  If any of the input
	 parameters are identical to RES, defer deallocation of the old
	 space.  */

      if (rp == mp || rp == bp)
	{
	  free_me = rp;
	  free_me_size = res->_mp_alloc;
	}
      else
	(*_mp_free_func) (rp, res->_mp_alloc * BYTES_PER_MP_LIMB);

      rp = (mp_ptr) (*_mp_allocate_func) (size * BYTES_PER_MP_LIMB);
      res->_mp_alloc = size;
      res->_mp_d = rp;
    }
  else
    {
      /* Make BASE, EXP and MOD not overlap with RES.  */
      if (rp == bp)
	{
	  /* RES and BASE are identical.  Allocate temp. space for BASE.  */
	  bp = (mp_ptr) TMP_ALLOC (bsize * BYTES_PER_MP_LIMB);
	  MPN_COPY (bp, rp, bsize);
	}
      if (rp == mp)
	{
	  /* RES and MOD are identical.  Allocate temporary space for MOD.  */
	  mp = (mp_ptr) TMP_ALLOC (msize * BYTES_PER_MP_LIMB);
	  MPN_COPY (mp, rp, msize);
	}
    }

  MPN_COPY (rp, bp, bsize);
  rsize = bsize;

  {
    mp_ptr xp = (mp_ptr) TMP_ALLOC (2 * (msize + 1) * BYTES_PER_MP_LIMB);
    int c;
    mp_limb_t e;
    mp_limb_t carry_limb;

    negative_result = (exp & 1) && base->_mp_size < 0;

    e = exp;
    count_leading_zeros (c, e);
    e = (e << c) << 1;		/* shift the exp bits to the left, lose msb */
    c = BITS_PER_MP_LIMB - 1 - c;

    /* Main loop.

       Make the result be pointed to alternately by XP and RP.  This
       helps us avoid block copying, which would otherwise be necessary
       with the overlap restrictions of mpn_divmod.  With 50% probability
       the result after this loop will be in the area originally pointed
       by RP (==RES->_mp_d), and with 50% probability in the area originally
       pointed to by XP.  */

    while (c != 0)
      {
	mp_ptr tp;
	mp_size_t xsize;

	mpn_mul_n (xp, rp, rp, rsize);
	xsize = 2 * rsize;
	xsize -= xp[xsize - 1] == 0;
	if (xsize > msize)
	  {
	    mpn_divmod (xp + msize, xp, xsize, mp, msize);
	    xsize = msize;
	  }

	tp = rp; rp = xp; xp = tp;
	rsize = xsize;

	if ((mp_limb_signed_t) e < 0)
	  {
	    mpn_mul (xp, rp, rsize, bp, bsize);
	    xsize = rsize + bsize;
	    xsize -= xp[xsize - 1] == 0;
	    if (xsize > msize)
	      {
		mpn_divmod (xp + msize, xp, xsize, mp, msize);
		xsize = msize;
	      }

	    tp = rp; rp = xp; xp = tp;
	    rsize = xsize;
	  }
	e <<= 1;
	c--;
      }

    /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
       steps.  Adjust the result by reducing it with the original MOD.

       Also make sure the result is put in RES->_mp_d (where it already
       might be, see above).  */

    if (mod_shift_cnt != 0)
      {
	carry_limb = mpn_lshift (res->_mp_d, rp, rsize, mod_shift_cnt);
	rp = res->_mp_d;
	if (carry_limb != 0)
	  {
	    rp[rsize] = carry_limb;
	    rsize++;
	  }
      }
    else
      {
	MPN_COPY (res->_mp_d, rp, rsize);
	rp = res->_mp_d;
      }

    if (rsize >= msize)
      {
	mpn_divmod (rp + msize, rp, rsize, mp, msize);
	rsize = msize;
      }

    /* Remove any leading zero words from the result.  */
    if (mod_shift_cnt != 0)
      mpn_rshift (rp, rp, rsize, mod_shift_cnt);
    MPN_NORMALIZE (rp, rsize);
  }

  if (negative_result && rsize != 0)
    {
      if (mod_shift_cnt != 0)
	mpn_rshift (mp, mp, msize, mod_shift_cnt);
      mpn_sub (rp, mp, msize, rp, rsize);
      rsize = msize;
      MPN_NORMALIZE (rp, rsize);
    }
  res->_mp_size = rsize;

  if (free_me != NULL)
    (*_mp_free_func) (free_me, free_me_size * BYTES_PER_MP_LIMB);
  TMP_FREE (marker);
}