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remove.c revision 1.1.1.1 
      1 /* mpn_remove -- divide out all multiples of odd mpn number from another mpn
      2    number.
      3 
      4    Contributed to the GNU project by Torbjorn Granlund.
      5 
      6    THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY
      7    SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
      8    GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
      9 
     10 Copyright 2009 Free Software Foundation, Inc.
     11 
     12 This file is part of the GNU MP Library.
     13 
     14 The GNU MP Library is free software; you can redistribute it and/or modify
     15 it under the terms of the GNU Lesser General Public License as published by
     16 the Free Software Foundation; either version 3 of the License, or (at your
     17 option) any later version.
     18 
     19 The GNU MP Library is distributed in the hope that it will be useful, but
     20 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
     21 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
     22 License for more details.
     23 
     24 You should have received a copy of the GNU Lesser General Public License
     25 along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
     26 
     27 #include "gmp.h"
     28 #include "gmp-impl.h"
     29 
     30 #if GMP_LIMB_BITS > 50
     31 #define LOG 50
     32 #else
     33 #define LOG GMP_LIMB_BITS
     34 #endif
     35 
     36 
     37 /* Input: U = {up,un}, V = {vp,vn} must be odd, cap
     38    Ouput  W = {wp,*wn} allocation need is exactly *wn
     39 
     40    Set W = U / V^k, where k is the largest integer <= cap such that the
     41    division yields an integer.
     42 
     43    FIXME: We currently allow any operand overlap.  This is quite non mpn-ish
     44    and might be changed, since it cost significant temporary space.
     45    * If we require W to have space for un limbs, we could save qp or qp2 (but
     46      we will still need to copy things into wp 50% of the time).
     47    * If we allow ourselves to clobber U, we could save the other of qp and qp2.
     48 */
     49 
     50 mp_bitcnt_t
     51 mpn_remove (mp_ptr wp, mp_size_t *wn,
     52 	    mp_ptr up, mp_size_t un, mp_ptr vp, mp_size_t vn,
     53 	    mp_bitcnt_t cap)
     54 {
     55   mp_ptr    pwpsp[LOG];
     56   mp_size_t pwpsn[LOG];
     57   mp_size_t npowers;
     58   mp_ptr tp, qp, np, pp, qp2, scratch_out;
     59   mp_size_t pn, nn, qn, i;
     60   mp_bitcnt_t pwr;
     61   TMP_DECL;
     62 
     63   ASSERT (un > 0);
     64   ASSERT (vn > 0);
     65   ASSERT (vp[0] % 2 != 0);	/* 2-adic division wants odd numbers */
     66   ASSERT (vn > 1 || vp[0] > 1);	/* else we would loop indefinitely */
     67 
     68   TMP_MARK;
     69 
     70   tp = TMP_ALLOC_LIMBS ((un + vn) / 2); /* remainder */
     71   qp = TMP_ALLOC_LIMBS (un);		/* quotient, alternating */
     72   qp2 = TMP_ALLOC_LIMBS (un);		/* quotient, alternating */
     73   np = TMP_ALLOC_LIMBS (un + LOG);	/* powers of V */
     74   pp = vp;
     75   pn = vn;
     76 
     77   /* FIXME: This allocation need indicate a flaw in the current itch mechanism:
     78      Which operands not greater than un,un will incur the worst itch?  We need
     79      a parallel foo_maxitch set of functions.  */
     80   scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (un, un >> 1));
     81 
     82   MPN_COPY (qp, up, un);
     83   qn = un;
     84 
     85   npowers = 0;
     86   while (qn >= pn)
     87     {
     88       mpn_bdiv_qr (qp2, tp, qp, qn, pp, pn, scratch_out);
     89       if (!mpn_zero_p (tp, pn))
     90 	break;			/* could not divide by V^npowers */
     91 
     92       MP_PTR_SWAP (qp, qp2);
     93       qn = qn - pn;
     94       qn += qp[qn] != 0;
     95 
     96       pwpsp[npowers] = pp;
     97       pwpsn[npowers] = pn;
     98       npowers++;
     99 
    100       if (((mp_bitcnt_t) 2 << npowers) - 1 > cap)
    101 	break;
    102 
    103       nn = 2 * pn - 1;		/* next power will be at least this many limbs */
    104       if (nn > qn)
    105 	break;			/* next power would be overlarge */
    106 
    107       mpn_sqr (np, pp, pn);
    108       nn += np[nn] != 0;
    109       pp = np;
    110       pn = nn;
    111       np += nn;
    112     }
    113 
    114   pwr = ((mp_bitcnt_t) 1 << npowers) - 1;
    115 
    116   for (i = npowers - 1; i >= 0; i--)
    117     {
    118       pp = pwpsp[i];
    119       pn = pwpsn[i];
    120       if (qn < pn)
    121 	continue;
    122 
    123       if (pwr + ((mp_bitcnt_t) 1 << i) > cap)
    124 	continue;		/* V^i would bring us past cap */
    125 
    126       mpn_bdiv_qr (qp2, tp, qp, qn, pp, pn, scratch_out);
    127       if (!mpn_zero_p (tp, pn))
    128 	continue;		/* could not divide by V^i */
    129 
    130       MP_PTR_SWAP (qp, qp2);
    131       qn = qn - pn;
    132       qn += qp[qn] != 0;
    133 
    134       pwr += (mp_bitcnt_t) 1 << i;
    135     }
    136 
    137   MPN_COPY (wp, qp, qn);
    138   *wn = qn;
    139 
    140   TMP_FREE;
    141 
    142   return pwr;
    143 }
    144