/* mpz_congruent_p -- test congruence of two mpz's.

Copyright 2001, 2002, 2005 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 3 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.  If not, see https://www.gnu.org/licenses/.  */

#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"


/* For big divisors this code is only very slightly better than the user
   doing a combination of mpz_sub and mpz_tdiv_r, but it's quite convenient,
   and perhaps in the future can be improved, in similar ways to
   mpn_divisible_p perhaps.

   The csize==1 / dsize==1 special case makes mpz_congruent_p as good as
   mpz_congruent_ui_p on relevant operands, though such a combination
   probably doesn't occur often.

   Alternatives:

   If c<d then it'd work to just form a%d and compare a and c (either as
   a==c or a+c==d depending on the signs), but the saving from avoiding the
   abs(a-c) calculation would be small compared to the division.

   Similarly if both a<d and c<d then it would work to just compare a and c
   (a==c or a+c==d), but this isn't considered a particularly important case
   and so isn't done for the moment.

   Low zero limbs on d could be stripped and the corresponding limbs of a
   and c tested and skipped, but doing so would introduce a borrow when a
   and c differ in sign and have non-zero skipped limbs.  It doesn't seem
   worth the complications to do this, since low zero limbs on d should
   occur only rarely.  */

int
mpz_congruent_p (mpz_srcptr a, mpz_srcptr c, mpz_srcptr d)
{
  mp_size_t  asize, csize, dsize, sign;
  mp_srcptr  ap, cp, dp;
  mp_ptr     xp;
  mp_limb_t  alow, clow, dlow, dmask, r;
  int        result;
  TMP_DECL;

  dsize = SIZ(d);
  if (UNLIKELY (dsize == 0))
    return (mpz_cmp (a, c) == 0);

  dsize = ABS(dsize);
  dp = PTR(d);

  if (ABSIZ(a) < ABSIZ(c))
    MPZ_SRCPTR_SWAP (a, c);

  asize = SIZ(a);
  csize = SIZ(c);
  sign = (asize ^ csize);

  asize = ABS(asize);
  ap = PTR(a);

  if (csize == 0)
    return mpn_divisible_p (ap, asize, dp, dsize);

  csize = ABS(csize);
  cp = PTR(c);

  alow = ap[0];
  clow = cp[0];
  dlow = dp[0];

  /* Check a==c mod low zero bits of dlow.  This might catch a few cases of
     a!=c quickly, and it helps the csize==1 special cases below.  */
  dmask = LOW_ZEROS_MASK (dlow) & GMP_NUMB_MASK;
  alow = (sign >= 0 ? alow : -alow);
  if (((alow-clow) & dmask) != 0)
    return 0;

  if (csize == 1)
    {
      if (dsize == 1)
	{
	cong_1:
	  if (sign < 0)
	    NEG_MOD (clow, clow, dlow);

	  if (ABOVE_THRESHOLD (asize, BMOD_1_TO_MOD_1_THRESHOLD))
	    {
	      r = mpn_mod_1 (ap, asize, dlow);
	      if (clow < dlow)
		return r == clow;
	      else
		return r == (clow % dlow);
	    }

	  if ((dlow & 1) == 0)
	    {
	      /* Strip low zero bits to get odd d required by modexact.  If
		 d==e*2^n then a==c mod d if and only if both a==c mod e and
		 a==c mod 2^n, the latter having been done above.  */
	      unsigned	twos;
	      count_trailing_zeros (twos, dlow);
	      dlow >>= twos;
	    }

	  r = mpn_modexact_1c_odd (ap, asize, dlow, clow);
	  return r == 0 || r == dlow;
	}

      /* dlow==0 is avoided since we don't want to bother handling extra low
	 zero bits if dsecond is even (would involve borrow if a,c differ in
	 sign and alow,clow!=0).  */
      if (dsize == 2 && dlow != 0)
	{
	  mp_limb_t  dsecond = dp[1];

	  if (dsecond <= dmask)
	    {
	      unsigned	 twos;
	      count_trailing_zeros (twos, dlow);
	      dlow = (dlow >> twos) | (dsecond << (GMP_NUMB_BITS-twos));
	      ASSERT_LIMB (dlow);

	      /* dlow will be odd here, so the test for it even under cong_1
		 is unnecessary, but the rest of that code is wanted. */
	      goto cong_1;
	    }
	}
    }

  TMP_MARK;
  xp = TMP_ALLOC_LIMBS (asize+1);

  /* calculate abs(a-c) */
  if (sign >= 0)
    {
      /* same signs, subtract */
      if (asize > csize || mpn_cmp (ap, cp, asize) >= 0)
	ASSERT_NOCARRY (mpn_sub (xp, ap, asize, cp, csize));
      else
	ASSERT_NOCARRY (mpn_sub_n (xp, cp, ap, asize));
      MPN_NORMALIZE (xp, asize);
    }
  else
    {
      /* different signs, add */
      mp_limb_t  carry;
      carry = mpn_add (xp, ap, asize, cp, csize);
      xp[asize] = carry;
      asize += (carry != 0);
    }

  result = mpn_divisible_p (xp, asize, dp, dsize);

  TMP_FREE;
  return result;
}