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/* mpn_remove -- divide out all multiples of odd mpn number from another mpn
number.
Contributed to the GNU project by Torbjorn Granlund.
THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
Copyright 2009 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 http://www.gnu.org/licenses/. */
#include "gmp.h"
#include "gmp-impl.h"
#if GMP_LIMB_BITS > 50
#define LOG 50
#else
#define LOG GMP_LIMB_BITS
#endif
/* Input: U = {up,un}, V = {vp,vn} must be odd, cap
Ouput W = {wp,*wn} allocation need is exactly *wn
Set W = U / V^k, where k is the largest integer <= cap such that the
division yields an integer.
FIXME: We currently allow any operand overlap. This is quite non mpn-ish
and might be changed, since it cost significant temporary space.
* If we require W to have space for un limbs, we could save qp or qp2 (but
we will still need to copy things into wp 50% of the time).
* If we allow ourselves to clobber U, we could save the other of qp and qp2.
*/
mp_bitcnt_t
mpn_remove (mp_ptr wp, mp_size_t *wn,
mp_ptr up, mp_size_t un, mp_ptr vp, mp_size_t vn,
mp_bitcnt_t cap)
{
mp_ptr pwpsp[LOG];
mp_size_t pwpsn[LOG];
mp_size_t npowers;
mp_ptr tp, qp, np, pp, qp2, scratch_out;
mp_size_t pn, nn, qn, i;
mp_bitcnt_t pwr;
TMP_DECL;
ASSERT (un > 0);
ASSERT (vn > 0);
ASSERT (vp[0] % 2 != 0); /* 2-adic division wants odd numbers */
ASSERT (vn > 1 || vp[0] > 1); /* else we would loop indefinitely */
TMP_MARK;
tp = TMP_ALLOC_LIMBS ((un + vn) / 2); /* remainder */
qp = TMP_ALLOC_LIMBS (un); /* quotient, alternating */
qp2 = TMP_ALLOC_LIMBS (un); /* quotient, alternating */
np = TMP_ALLOC_LIMBS (un + LOG); /* powers of V */
pp = vp;
pn = vn;
/* FIXME: This allocation need indicate a flaw in the current itch mechanism:
Which operands not greater than un,un will incur the worst itch? We need
a parallel foo_maxitch set of functions. */
scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (un, un >> 1));
MPN_COPY (qp, up, un);
qn = un;
npowers = 0;
while (qn >= pn)
{
mpn_bdiv_qr (qp2, tp, qp, qn, pp, pn, scratch_out);
if (!mpn_zero_p (tp, pn))
break; /* could not divide by V^npowers */
MP_PTR_SWAP (qp, qp2);
qn = qn - pn;
qn += qp[qn] != 0;
pwpsp[npowers] = pp;
pwpsn[npowers] = pn;
npowers++;
if (((mp_bitcnt_t) 2 << npowers) - 1 > cap)
break;
nn = 2 * pn - 1; /* next power will be at least this many limbs */
if (nn > qn)
break; /* next power would be overlarge */
mpn_sqr (np, pp, pn);
nn += np[nn] != 0;
pp = np;
pn = nn;
np += nn;
}
pwr = ((mp_bitcnt_t) 1 << npowers) - 1;
for (i = npowers - 1; i >= 0; i--)
{
pp = pwpsp[i];
pn = pwpsn[i];
if (qn < pn)
continue;
if (pwr + ((mp_bitcnt_t) 1 << i) > cap)
continue; /* V^i would bring us past cap */
mpn_bdiv_qr (qp2, tp, qp, qn, pp, pn, scratch_out);
if (!mpn_zero_p (tp, pn))
continue; /* could not divide by V^i */
MP_PTR_SWAP (qp, qp2);
qn = qn - pn;
qn += qp[qn] != 0;
pwr += (mp_bitcnt_t) 1 << i;
}
MPN_COPY (wp, qp, qn);
*wn = qn;
TMP_FREE;
return pwr;
}
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