third_party/gmp/mpz/powm.c - RealtimeRoboticsGroup/test - Gitiles

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

    Contributed to the GNU project by Torbjorn Granlund.

 Copyright 1991, 1993, 1994, 1996, 1997, 2000-2002, 2005, 2008, 2009,
 2011, 2012, 2015, 2019 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"


 /* TODO

  * Improve handling of buffers.  It is pretty ugly now.

  * For even moduli, we compute a binvert of its odd part both here and in
    mpn_powm.  How can we avoid this recomputation?
 */

 /*
   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
 */

 #define HANDLE_NEGATIVE_EXPONENT 1

 void
 mpz_powm (mpz_ptr r, mpz_srcptr b, mpz_srcptr e, mpz_srcptr m)
 {
   mp_size_t n, nodd, ncnt;
   int cnt;
   mp_ptr rp, tp;
   mp_srcptr bp, ep, mp;
   mp_size_t rn, bn, es, en, itch;
   mpz_t new_b;			/* note: value lives long via 'b' */
   TMP_DECL;

   n = ABSIZ(m);
   if (UNLIKELY (n == 0))
     DIVIDE_BY_ZERO;

   mp = PTR(m);

   TMP_MARK;

   es = SIZ(e);
   if (UNLIKELY (es <= 0))
     {
       if (es == 0)
 	{
 	  /* b^0 mod m,  b is anything and m is non-zero.
 	     Result is 1 mod m, i.e., 1 or 0 depending on if m = 1.  */
 	  SIZ(r) = n != 1 || mp[0] != 1;
 	  MPZ_NEWALLOC (r, 1)[0] = 1;
 	  TMP_FREE;	/* we haven't really allocated anything here */
 	  return;
 	}
 #if HANDLE_NEGATIVE_EXPONENT
       MPZ_TMP_INIT (new_b, n + 1);

       if (UNLIKELY (! mpz_invert (new_b, b, m)))
 	DIVIDE_BY_ZERO;
       b = new_b;
       es = -es;
 #else
       DIVIDE_BY_ZERO;
 #endif
     }
   en = es;

   bn = ABSIZ(b);

   if (UNLIKELY (bn == 0))
     {
       SIZ(r) = 0;
       TMP_FREE;
       return;
     }

   ep = PTR(e);

   /* Handle (b^1 mod m) early, since mpn_pow* do not handle that case.  */
   if (UNLIKELY (en == 1 && ep[0] == 1))
     {
       rp = TMP_ALLOC_LIMBS (n);
       bp = PTR(b);
       if (bn >= n)
 	{
 	  mp_ptr qp = TMP_ALLOC_LIMBS (bn - n + 1);
 	  mpn_tdiv_qr (qp, rp, 0L, bp, bn, mp, n);
 	  rn = n;
 	  MPN_NORMALIZE (rp, rn);

 	  if (rn != 0 && SIZ(b) < 0)
 	    {
 	      mpn_sub (rp, mp, n, rp, rn);
 	      rn = n;
 	      MPN_NORMALIZE_NOT_ZERO (rp, rn);
 	    }
 	}
       else
 	{
 	  if (SIZ(b) < 0)
 	    {
 	      mpn_sub (rp, mp, n, bp, bn);
 	      rn = n;
 	      MPN_NORMALIZE_NOT_ZERO (rp, rn);
 	    }
 	  else
 	    {
 	      MPN_COPY (rp, bp, bn);
 	      rn = bn;
 	    }
 	}
       goto ret;
     }

   /* Remove low zero limbs from M.  This loop will terminate for correctly
      represented mpz numbers.  */
   ncnt = 0;
   while (UNLIKELY (mp[0] == 0))
     {
       mp++;
       ncnt++;
     }
   nodd = n - ncnt;
   cnt = 0;
   if (mp[0] % 2 == 0)
     {
       mp_ptr newmp = TMP_ALLOC_LIMBS (nodd);
       count_trailing_zeros (cnt, mp[0]);
       mpn_rshift (newmp, mp, nodd, cnt);
       nodd -= newmp[nodd - 1] == 0;
       mp = newmp;
       ncnt++;
     }

   if (ncnt != 0)
     {
       /* We will call both mpn_powm and mpn_powlo.  */
       /* rp needs n, mpn_powlo needs 4n, the 2 mpn_binvert might need more */
       mp_size_t n_largest_binvert = MAX (ncnt, nodd);
       mp_size_t itch_binvert = mpn_binvert_itch (n_largest_binvert);
       itch = 3 * n + MAX (itch_binvert, 2 * n);
     }
   else
     {
       /* We will call just mpn_powm.  */
       mp_size_t itch_binvert = mpn_binvert_itch (nodd);
       itch = n + MAX (itch_binvert, 2 * n);
     }
   tp = TMP_ALLOC_LIMBS (itch);

   rp = tp;  tp += n;

   bp = PTR(b);
   mpn_powm (rp, bp, bn, ep, en, mp, nodd, tp);

   rn = n;

   if (ncnt != 0)
     {
       mp_ptr r2, xp, yp, odd_inv_2exp;
       unsigned long t;
       int bcnt;

       if (bn < ncnt)
 	{
 	  mp_ptr newbp = TMP_ALLOC_LIMBS (ncnt);
 	  MPN_COPY (newbp, bp, bn);
 	  MPN_ZERO (newbp + bn, ncnt - bn);
 	  bp = newbp;
 	}

       r2 = tp;

       if (bp[0] % 2 == 0)
 	{
 	  if (en > 1)
 	    {
 	      MPN_ZERO (r2, ncnt);
 	      goto zero;
 	    }

 	  ASSERT (en == 1);
 	  t = (ncnt - (cnt != 0)) * GMP_NUMB_BITS + cnt;

 	  /* Count number of low zero bits in B, up to 3.  */
 	  bcnt = (0x1213 >> ((bp[0] & 7) << 1)) & 0x3;
 	  /* Note that ep[0] * bcnt might overflow, but that just results
 	     in a missed optimization.  */
 	  if (ep[0] * bcnt >= t)
 	    {
 	      MPN_ZERO (r2, ncnt);
 	      goto zero;
 	    }
 	}

       mpn_powlo (r2, bp, ep, en, ncnt, tp + ncnt);

     zero:
       if (nodd < ncnt)
 	{
 	  mp_ptr newmp = TMP_ALLOC_LIMBS (ncnt);
 	  MPN_COPY (newmp, mp, nodd);
 	  MPN_ZERO (newmp + nodd, ncnt - nodd);
 	  mp = newmp;
 	}

       odd_inv_2exp = tp + n;
       mpn_binvert (odd_inv_2exp, mp, ncnt, tp + 2 * n);

       mpn_sub (r2, r2, ncnt, rp, nodd > ncnt ? ncnt : nodd);

       xp = tp + 2 * n;
       mpn_mullo_n (xp, odd_inv_2exp, r2, ncnt);

       if (cnt != 0)
 	xp[ncnt - 1] &= (CNST_LIMB(1) << cnt) - 1;

       yp = tp;
       if (ncnt > nodd)
 	mpn_mul (yp, xp, ncnt, mp, nodd);
       else
 	mpn_mul (yp, mp, nodd, xp, ncnt);

       mpn_add (rp, yp, n, rp, nodd);

       ASSERT (nodd + ncnt >= n);
       ASSERT (nodd + ncnt <= n + 1);
     }

   MPN_NORMALIZE (rp, rn);

   if ((ep[0] & 1) && SIZ(b) < 0 && rn != 0)
     {
       mpn_sub (rp, PTR(m), n, rp, rn);
       rn = n;
       MPN_NORMALIZE (rp, rn);
     }

  ret:
   MPZ_NEWALLOC (r, rn);
   SIZ(r) = rn;
   MPN_COPY (PTR(r), rp, rn);

   TMP_FREE;
 }
	/* mpz_powm(res,base,exp,mod) -- Set R to (U^E) mod M.

	Contributed to the GNU project by Torbjorn Granlund.

	Copyright 1991, 1993, 1994, 1996, 1997, 2000-2002, 2005, 2008, 2009,
	2011, 2012, 2015, 2019 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"


	/* TODO

	* Improve handling of buffers. It is pretty ugly now.

	* For even moduli, we compute a binvert of its odd part both here and in
	mpn_powm. How can we avoid this recomputation?
	*/

	/*
	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
	*/

	#define HANDLE_NEGATIVE_EXPONENT 1

	void
	mpz_powm (mpz_ptr r, mpz_srcptr b, mpz_srcptr e, mpz_srcptr m)
	{
	mp_size_t n, nodd, ncnt;
	int cnt;
	mp_ptr rp, tp;
	mp_srcptr bp, ep, mp;
	mp_size_t rn, bn, es, en, itch;
	mpz_t new_b; /* note: value lives long via 'b' */
	TMP_DECL;

	n = ABSIZ(m);
	if (UNLIKELY (n == 0))
	DIVIDE_BY_ZERO;

	mp = PTR(m);

	TMP_MARK;

	es = SIZ(e);
	if (UNLIKELY (es <= 0))
	{
	if (es == 0)
	{
	/* b^0 mod m, b is anything and m is non-zero.
	Result is 1 mod m, i.e., 1 or 0 depending on if m = 1. */
	SIZ(r) = n != 1 \|\| mp[0] != 1;
	MPZ_NEWALLOC (r, 1)[0] = 1;
	TMP_FREE; /* we haven't really allocated anything here */
	return;
	}
	#if HANDLE_NEGATIVE_EXPONENT
	MPZ_TMP_INIT (new_b, n + 1);

	if (UNLIKELY (! mpz_invert (new_b, b, m)))
	DIVIDE_BY_ZERO;
	b = new_b;
	es = -es;
	#else
	DIVIDE_BY_ZERO;
	#endif
	}
	en = es;

	bn = ABSIZ(b);

	if (UNLIKELY (bn == 0))
	{
	SIZ(r) = 0;
	TMP_FREE;
	return;
	}

	ep = PTR(e);

	/* Handle (b^1 mod m) early, since mpn_pow* do not handle that case. */
	if (UNLIKELY (en == 1 && ep[0] == 1))
	{
	rp = TMP_ALLOC_LIMBS (n);
	bp = PTR(b);
	if (bn >= n)
	{
	mp_ptr qp = TMP_ALLOC_LIMBS (bn - n + 1);
	mpn_tdiv_qr (qp, rp, 0L, bp, bn, mp, n);
	rn = n;
	MPN_NORMALIZE (rp, rn);

	if (rn != 0 && SIZ(b) < 0)
	{
	mpn_sub (rp, mp, n, rp, rn);
	rn = n;
	MPN_NORMALIZE_NOT_ZERO (rp, rn);
	}
	}
	else
	{
	if (SIZ(b) < 0)
	{
	mpn_sub (rp, mp, n, bp, bn);
	rn = n;
	MPN_NORMALIZE_NOT_ZERO (rp, rn);
	}
	else
	{
	MPN_COPY (rp, bp, bn);
	rn = bn;
	}
	}
	goto ret;
	}

	/* Remove low zero limbs from M. This loop will terminate for correctly
	represented mpz numbers. */
	ncnt = 0;
	while (UNLIKELY (mp[0] == 0))
	{
	mp++;
	ncnt++;
	}
	nodd = n - ncnt;
	cnt = 0;
	if (mp[0] % 2 == 0)
	{
	mp_ptr newmp = TMP_ALLOC_LIMBS (nodd);
	count_trailing_zeros (cnt, mp[0]);
	mpn_rshift (newmp, mp, nodd, cnt);
	nodd -= newmp[nodd - 1] == 0;
	mp = newmp;
	ncnt++;
	}

	if (ncnt != 0)
	{
	/* We will call both mpn_powm and mpn_powlo. */
	/* rp needs n, mpn_powlo needs 4n, the 2 mpn_binvert might need more */
	mp_size_t n_largest_binvert = MAX (ncnt, nodd);
	mp_size_t itch_binvert = mpn_binvert_itch (n_largest_binvert);
	itch = 3 * n + MAX (itch_binvert, 2 * n);
	}
	else
	{
	/* We will call just mpn_powm. */
	mp_size_t itch_binvert = mpn_binvert_itch (nodd);
	itch = n + MAX (itch_binvert, 2 * n);
	}
	tp = TMP_ALLOC_LIMBS (itch);

	rp = tp; tp += n;

	bp = PTR(b);
	mpn_powm (rp, bp, bn, ep, en, mp, nodd, tp);

	rn = n;

	if (ncnt != 0)
	{
	mp_ptr r2, xp, yp, odd_inv_2exp;
	unsigned long t;
	int bcnt;

	if (bn < ncnt)
	{
	mp_ptr newbp = TMP_ALLOC_LIMBS (ncnt);
	MPN_COPY (newbp, bp, bn);
	MPN_ZERO (newbp + bn, ncnt - bn);
	bp = newbp;
	}

	r2 = tp;

	if (bp[0] % 2 == 0)
	{
	if (en > 1)
	{
	MPN_ZERO (r2, ncnt);
	goto zero;
	}

	ASSERT (en == 1);
	t = (ncnt - (cnt != 0)) * GMP_NUMB_BITS + cnt;

	/* Count number of low zero bits in B, up to 3. */
	bcnt = (0x1213 >> ((bp[0] & 7) << 1)) & 0x3;
	/* Note that ep[0] * bcnt might overflow, but that just results
	in a missed optimization. */
	if (ep[0] * bcnt >= t)
	{
	MPN_ZERO (r2, ncnt);
	goto zero;
	}
	}

	mpn_powlo (r2, bp, ep, en, ncnt, tp + ncnt);

	zero:
	if (nodd < ncnt)
	{
	mp_ptr newmp = TMP_ALLOC_LIMBS (ncnt);
	MPN_COPY (newmp, mp, nodd);
	MPN_ZERO (newmp + nodd, ncnt - nodd);
	mp = newmp;
	}

	odd_inv_2exp = tp + n;
	mpn_binvert (odd_inv_2exp, mp, ncnt, tp + 2 * n);

	mpn_sub (r2, r2, ncnt, rp, nodd > ncnt ? ncnt : nodd);

	xp = tp + 2 * n;
	mpn_mullo_n (xp, odd_inv_2exp, r2, ncnt);

	if (cnt != 0)
	xp[ncnt - 1] &= (CNST_LIMB(1) << cnt) - 1;

	yp = tp;
	if (ncnt > nodd)
	mpn_mul (yp, xp, ncnt, mp, nodd);
	else
	mpn_mul (yp, mp, nodd, xp, ncnt);

	mpn_add (rp, yp, n, rp, nodd);

	ASSERT (nodd + ncnt >= n);
	ASSERT (nodd + ncnt <= n + 1);
	}

	MPN_NORMALIZE (rp, rn);

	if ((ep[0] & 1) && SIZ(b) < 0 && rn != 0)
	{
	mpn_sub (rp, PTR(m), n, rp, rn);
	rn = n;
	MPN_NORMALIZE (rp, rn);
	}

	ret:
	MPZ_NEWALLOC (r, rn);
	SIZ(r) = rn;
	MPN_COPY (PTR(r), rp, rn);

	TMP_FREE;
	}