1  /* mpz_gcdext(g, s, t, a, b) -- Set G to gcd(a, b), and S and T such that
       2     g = as + bt.
       3  
       4  Copyright 1991, 1993-1997, 2000, 2001, 2005, 2011, 2012, 2015 Free
       5  Software Foundation, Inc.
       6  
       7  This file is part of the GNU MP Library.
       8  
       9  The GNU MP Library is free software; you can redistribute it and/or modify
      10  it under the terms of either:
      11  
      12    * the GNU Lesser General Public License as published by the Free
      13      Software Foundation; either version 3 of the License, or (at your
      14      option) any later version.
      15  
      16  or
      17  
      18    * the GNU General Public License as published by the Free Software
      19      Foundation; either version 2 of the License, or (at your option) any
      20      later version.
      21  
      22  or both in parallel, as here.
      23  
      24  The GNU MP Library is distributed in the hope that it will be useful, but
      25  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
      26  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
      27  for more details.
      28  
      29  You should have received copies of the GNU General Public License and the
      30  GNU Lesser General Public License along with the GNU MP Library.  If not,
      31  see https://www.gnu.org/licenses/.  */
      32  
      33  #include <stdio.h> /* for NULL */
      34  #include "gmp-impl.h"
      35  
      36  void
      37  mpz_gcdext (mpz_ptr g, mpz_ptr s, mpz_ptr t, mpz_srcptr a, mpz_srcptr b)
      38  {
      39    mp_size_t asize, bsize;
      40    mp_ptr tmp_ap, tmp_bp;
      41    mp_size_t gsize, ssize, tmp_ssize;
      42    mp_ptr gp, tmp_gp, tmp_sp;
      43    TMP_DECL;
      44  
      45    /* mpn_gcdext requires that Usize >= Vsize.  Therefore, we often
      46       have to swap U and V.  The computed cofactor will be the
      47       "smallest" one, which is faster to produce.  The wanted one will
      48       be computed here; this is needed anyway when both are requested.  */
      49  
      50    asize = ABSIZ (a);
      51    bsize = ABSIZ (b);
      52  
      53    ASSERT (s != NULL);
      54  
      55    if (asize < bsize)
      56      {
      57        MPZ_SRCPTR_SWAP (a, b);
      58        MP_SIZE_T_SWAP (asize, bsize);
      59        MPZ_PTR_SWAP (s, t);
      60      }
      61  
      62    if (bsize == 0)
      63      {
      64        /* g = |a|, s = sgn(a), t = 0. */
      65        ssize = SIZ (a) >= 0 ? (asize != 0) : -1;
      66  
      67        if (g != NULL)
      68  	{
      69  	  /* If g == a, then ALLOC(g) == ALLOC(a) >= asize, i.e.
      70  	     the next MPZ_NEWALLOC returns the old PTR(a) .*/
      71  	  gp = MPZ_NEWALLOC (g, asize);
      72  	  MPN_COPY (gp, PTR (a), asize);
      73  	  SIZ (g) = asize;
      74  	}
      75        if (t != NULL)
      76  	SIZ (t) = 0;
      77        if (s != NULL)
      78  	{
      79  	  SIZ (s) = ssize;
      80  	  MPZ_NEWALLOC (s, 1)[0] = 1;
      81  	}
      82        return;
      83      }
      84  
      85    TMP_MARK;
      86  
      87    TMP_ALLOC_LIMBS_2 (tmp_gp, bsize, tmp_sp, asize + bsize + bsize + 1);
      88    tmp_bp = tmp_sp + bsize + 1;
      89    tmp_ap = tmp_bp + bsize;
      90    MPN_COPY (tmp_ap, PTR (a), asize);
      91    MPN_COPY (tmp_bp, PTR (b), bsize);
      92  
      93    gsize = mpn_gcdext (tmp_gp, tmp_sp, &tmp_ssize, tmp_ap, asize, tmp_bp, bsize);
      94  
      95    ssize = ABS (tmp_ssize);
      96    tmp_ssize = SIZ (a) >= 0 ? tmp_ssize : -tmp_ssize;
      97  
      98    if (t != NULL)
      99      {
     100        mpz_t x;
     101        mpz_t gtmp, stmp;
     102  
     103        PTR (gtmp) = tmp_gp;
     104        SIZ (gtmp) = gsize;
     105  
     106        PTR (stmp) = tmp_sp;
     107        SIZ (stmp) = tmp_ssize;
     108  
     109        ASSERT (ssize <= bsize); /* ssize*2 + asize + 1 <= asize + bsize*2 + 1 */
     110        PTR (x) = tmp_sp + ssize;
     111        ALLOC (x) = ssize + asize + 1;
     112  
     113        mpz_mul (x, stmp, a);
     114        mpz_sub (x, gtmp, x);
     115        mpz_divexact (t, x, b);
     116      }
     117  
     118    if (s != NULL)
     119      {
     120        mp_ptr sp;
     121  
     122        sp = MPZ_NEWALLOC (s, ssize);
     123        MPN_COPY (sp, tmp_sp, ssize);
     124        SIZ (s) = tmp_ssize;
     125      }
     126  
     127    if (g != NULL)
     128      {
     129        gp = MPZ_NEWALLOC (g, gsize);
     130        MPN_COPY (gp, tmp_gp, gsize);
     131        SIZ (g) = gsize;
     132      }
     133  
     134    TMP_FREE;
     135  }