/* mpz_powm_ui(res,base,exp,mod) -- Set R to (B^E) mod M.

   Contributed to the GNU project by Torbjörn Granlund.

Copyright 1991, 1993, 1994, 1996, 1997, 2000-2002, 2005, 2008, 2009,

2011-2013, 2015 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 either:

  * 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.

or

  * the GNU General Public License as published by the Free Software

    Foundation; either version 2 of the License, or (at your option) any

    later version.

or both in parallel, as here.

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 General Public License

for more details.

You should have received copies of the GNU General Public License and the

GNU Lesser General Public License along with the GNU MP Library.  If not,

see https://www.gnu.org/licenses/.  */

#include "gmp-impl.h"

#include "longlong.h"

/* This code is very old, and should be rewritten to current GMP standard.  It

   is slower than mpz_powm for large exponents, but also for small exponents

   when the mod argument is small.

   As an intermediate solution, we now deflect to mpz_powm for exponents >= 20.

*/

/*

  b ^ e mod m   res

  0   0     0    ?

  0   e     0    ?

  0   0     m    ?

  0   e     m    0

  b   0     0    ?

  b   e     0    ?

  b   0     m    1 mod m

  b   e     m    b^e mod m

*/

static void

mod (mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn, gmp_pi1_t *dinv, mp_ptr tp)

{

  mp_ptr qp = tp;

  if (dn == 1)

    {

      np[0] = mpn_divrem_1 (qp, (mp_size_t) 0, np, nn, dp[0]);

    }

  else if (dn == 2)

    {

      mpn_div_qr_2n_pi1 (qp, np, np, nn, dp[1], dp[0], dinv->inv32);

    }

  else if (BELOW_THRESHOLD (dn, DC_DIV_QR_THRESHOLD) ||

     BELOW_THRESHOLD (nn - dn, DC_DIV_QR_THRESHOLD))

    {

      mpn_sbpi1_div_qr (qp, np, nn, dp, dn, dinv->inv32);

    }

  else if (BELOW_THRESHOLD (dn, MUPI_DIV_QR_THRESHOLD) ||   /* fast condition */

     BELOW_THRESHOLD (nn, 2 * MU_DIV_QR_THRESHOLD) || /* fast condition */

     (double) (2 * (MU_DIV_QR_THRESHOLD - MUPI_DIV_QR_THRESHOLD)) * dn /* slow... */

     + (double) MUPI_DIV_QR_THRESHOLD * nn > (double) dn * nn)    /* ...condition */

    {

      mpn_dcpi1_div_qr (qp, np, nn, dp, dn, dinv);

    }

  else

    {

      /* We need to allocate separate remainder area, since mpn_mu_div_qr does

   not handle overlap between the numerator and remainder areas.

   FIXME: Make it handle such overlap.  */

      mp_ptr rp, scratch;

      mp_size_t itch;

      TMP_DECL;

      TMP_MARK;

      itch = mpn_mu_div_qr_itch (nn, dn, 0);

      rp = TMP_BALLOC_LIMBS (dn);

      scratch = TMP_BALLOC_LIMBS (itch);

      mpn_mu_div_qr (qp, rp, np, nn, dp, dn, scratch);

      MPN_COPY (np, rp, dn);

      TMP_FREE;

    }

}

/* Compute t = a mod m, a is defined by (ap,an), m is defined by (mp,mn), and

   t is defined by (tp,mn).  */

static void

reduce (mp_ptr tp, mp_srcptr ap, mp_size_t an, mp_srcptr mp, mp_size_t mn, gmp_pi1_t *dinv)

{

  mp_ptr rp, scratch;

  TMP_DECL;

  TMP_MARK;

  TMP_ALLOC_LIMBS_2 (rp, an, scratch, an - mn + 1);

  MPN_COPY (rp, ap, an);

  mod (rp, an, mp, mn, dinv, scratch);

  MPN_COPY (tp, rp, mn);

  TMP_FREE;

}

void

mpz_powm_ui (mpz_ptr r, mpz_srcptr b, unsigned long int el, mpz_srcptr m)

{

  if (el < 20)

    {

      mp_ptr xp, tp, mp, bp, scratch;

      mp_size_t xn, tn, mn, bn;

      int m_zero_cnt;

      int c;

      mp_limb_t e, m2;

      gmp_pi1_t dinv;

      TMP_DECL;

      mp = PTR(m);

      mn = ABSIZ(m);

      if (UNLIKELY (mn == 0))

  DIVIDE_BY_ZERO;

      if (el <= 1)

  {

    if (el == 1)

      {

        mpz_mod (r, b, m);

        return;

      }

    /* Exponent is zero, result is 1 mod M, i.e., 1 or 0 depending on if

       M equals 1.  */

    SIZ(r) = mn != 1 || mp[0] != 1;

    MPZ_NEWALLOC (r, 1)[0] = 1;

    return;

  }

      TMP_MARK;

      /* Normalize m (i.e. make its most significant bit set) as required by

   division functions below.  */

      count_leading_zeros (m_zero_cnt, mp[mn - 1]);

      m_zero_cnt -= GMP_NAIL_BITS;

      if (m_zero_cnt != 0)

  {

    mp_ptr new_mp = TMP_ALLOC_LIMBS (mn);

    mpn_lshift (new_mp, mp, mn, m_zero_cnt);

    mp = new_mp;

  }

      m2 = mn == 1 ? 0 : mp[mn - 2];

      invert_pi1 (dinv, mp[mn - 1], m2);

      bn = ABSIZ(b);

      bp = PTR(b);

      if (bn > mn)

  {

    /* Reduce possibly huge base.  Use a function call to reduce, since we

       don't want the quotient allocation to live until function return.  */

    mp_ptr new_bp = TMP_ALLOC_LIMBS (mn);

    reduce (new_bp, bp, bn, mp, mn, &dinv);

    bp = new_bp;

    bn = mn;

    /* Canonicalize the base, since we are potentially going to multiply with

       it quite a few times.  */

    MPN_NORMALIZE (bp, bn);

  }

      if (bn == 0)

  {

    SIZ(r) = 0;

    TMP_FREE;

    return;

  }

      TMP_ALLOC_LIMBS_3 (xp, mn, scratch, mn + 1, tp, 2 * mn + 1);

      MPN_COPY (xp, bp, bn);

      xn = bn;

      e = el;

      count_leading_zeros (c, e);

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

      c = GMP_LIMB_BITS - 1 - c;

      ASSERT (c != 0); /* el > 1 */

  {

    /* Main loop. */

    do

      {

        mpn_sqr (tp, xp, xn);

        tn = 2 * xn; tn -= tp[tn - 1] == 0;

        if (tn < mn)

    {

      MPN_COPY (xp, tp, tn);

      xn = tn;

    }

        else

    {

      mod (tp, tn, mp, mn, &dinv, scratch);

      MPN_COPY (xp, tp, mn);

      xn = mn;

    }

        if ((mp_limb_signed_t) e < 0)

    {

      mpn_mul (tp, xp, xn, bp, bn);

      tn = xn + bn; tn -= tp[tn - 1] == 0;

      if (tn < mn)

        {

          MPN_COPY (xp, tp, tn);

          xn = tn;

        }

      else

        {

          mod (tp, tn, mp, mn, &dinv, scratch);

          MPN_COPY (xp, tp, mn);

          xn = mn;

        }

    }

        e <<= 1;

        c--;

      }

    while (c != 0);

  }

      /* We shifted m left m_zero_cnt steps.  Adjust the result by reducing it

   with the original M.  */

      if (m_zero_cnt != 0)

  {

    mp_limb_t cy;

    cy = mpn_lshift (tp, xp, xn, m_zero_cnt);

    tp[xn] = cy; xn += cy != 0;

    if (xn >= mn)

      {

        mod (tp, xn, mp, mn, &dinv, scratch);

        xn = mn;

      }

    mpn_rshift (xp, tp, xn, m_zero_cnt);

  }

      MPN_NORMALIZE (xp, xn);

      if ((el & 1) != 0 && SIZ(b) < 0 && xn != 0)

  {

    mp = PTR(m);      /* want original, unnormalized m */

    mpn_sub (xp, mp, mn, xp, xn);

    xn = mn;

    MPN_NORMALIZE (xp, xn);

  }

      MPZ_NEWALLOC (r, xn);

      SIZ (r) = xn;

      MPN_COPY (PTR(r), xp, xn);

      TMP_FREE;

    }

  else

    {

      /* For large exponents, fake an mpz_t exponent and deflect to the more

   sophisticated mpz_powm.  */

      mpz_t e;

      mp_limb_t ep[LIMBS_PER_ULONG];

      MPZ_FAKE_UI (e, ep, el);

      mpz_powm (r, b, e, m);

    }

}