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      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 }
    136