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/* mpn_remove -- divide out all multiples of odd mpn number from another mpn
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number.
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Contributed to the GNU project by Torbjorn Granlund.
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THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
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SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
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Copyright 2009, 2012-2014 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#if GMP_LIMB_BITS > 50
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#define LOG 50
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#else
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#define LOG GMP_LIMB_BITS
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#endif
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/* Input: U = {up,un}, V = {vp,vn} must be odd, cap
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Ouput W = {wp,*wn} allocation need is exactly *wn
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Set W = U / V^k, where k is the largest integer <= cap such that the
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division yields an integer.
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FIXME: We currently allow any operand overlap. This is quite non mpn-ish
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and might be changed, since it cost significant temporary space.
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* If we require W to have space for un + 1 limbs, we could save qp or qp2
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(but we will still need to copy things into wp 50% of the time).
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* If we allow ourselves to clobber U, we could save the other of qp and qp2,
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and the initial COPY (but also here we would need un + 1 limbs).
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*/
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/* FIXME: We need to wrap mpn_bdiv_qr due to the itch interface. This need
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indicates a flaw in the current itch mechanism: Which operands not greater
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than un,un will incur the worst itch? We need a parallel foo_maxitch set
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of functions. */
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static void
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mpn_bdiv_qr_wrap (mp_ptr qp, mp_ptr rp,
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mp_srcptr np, mp_size_t nn,
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mp_srcptr dp, mp_size_t dn)
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{
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mp_ptr scratch_out;
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TMP_DECL;
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TMP_MARK;
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scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (nn, dn));
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mpn_bdiv_qr (qp, rp, np, nn, dp, dn, scratch_out);
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TMP_FREE;
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}
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mp_bitcnt_t
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mpn_remove (mp_ptr wp, mp_size_t *wn,
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mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn,
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mp_bitcnt_t cap)
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{
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mp_srcptr pwpsp[LOG];
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mp_size_t pwpsn[LOG];
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mp_size_t npowers;
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mp_ptr tp, qp, np, qp2;
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mp_srcptr pp;
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mp_size_t pn, nn, qn, i;
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mp_bitcnt_t pwr;
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TMP_DECL;
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ASSERT (un > 0);
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ASSERT (vn > 0);
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ASSERT (vp[0] % 2 != 0); /* 2-adic division wants odd numbers */
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ASSERT (vn > 1 || vp[0] > 1); /* else we would loop indefinitely */
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TMP_MARK;
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TMP_ALLOC_LIMBS_3 (qp, un + 1, /* quotient, alternating */
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qp2, un + 1, /* quotient, alternating */
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tp, (un + 1 + vn) / 2); /* remainder */
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pp = vp;
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pn = vn;
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MPN_COPY (qp, up, un);
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qn = un;
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npowers = 0;
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while (qn >= pn)
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{
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qp[qn] = 0;
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mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pp, pn);
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if (!mpn_zero_p (tp, pn))
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break; /* could not divide by V^npowers */
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MP_PTR_SWAP (qp, qp2);
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qn = qn - pn;
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qn += qp[qn] != 0;
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pwpsp[npowers] = pp;
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pwpsn[npowers] = pn;
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++npowers;
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if (((mp_bitcnt_t) 2 << npowers) - 1 > cap)
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break;
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nn = 2 * pn - 1; /* next power will be at least this large */
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if (nn > qn)
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break; /* next power would be overlarge */
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if (npowers == 1) /* Alloc once, but only if it's needed */
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np = TMP_ALLOC_LIMBS (qn + LOG); /* powers of V */
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else
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np += pn;
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mpn_sqr (np, pp, pn);
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pn = nn + (np[nn] != 0);
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pp = np;
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}
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pwr = ((mp_bitcnt_t) 1 << npowers) - 1;
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for (i = npowers; --i >= 0;)
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{
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pn = pwpsn[i];
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if (qn < pn)
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continue;
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if (pwr + ((mp_bitcnt_t) 1 << i) > cap)
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continue; /* V^i would bring us past cap */
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qp[qn] = 0;
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mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pwpsp[i], pn);
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if (!mpn_zero_p (tp, pn))
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continue; /* could not divide by V^i */
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MP_PTR_SWAP (qp, qp2);
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qn = qn - pn;
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qn += qp[qn] != 0;
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pwr += (mp_bitcnt_t) 1 << i;
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}
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MPN_COPY (wp, qp, qn);
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*wn = qn;
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TMP_FREE;
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return pwr;
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}
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