223 lines
6.0 KiB
C
223 lines
6.0 KiB
C
/* mpn_inv_divappr_q -- divide-and-conquer division, returning approximate
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quotient. The quotient returned is either correct, or one too large.
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Contributed to the GNU project by Torbjorn Granlund.
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THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
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SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
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Copyright 2006, 2007, 2009, 2010 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 the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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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 Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
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#include "mpir.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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mp_limb_t
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mpn_inv_divappr_q (mp_ptr qp, mp_ptr np, mp_size_t nn,
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mp_srcptr dp, mp_size_t dn, mp_srcptr dinv)
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{
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mp_size_t qn;
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mp_limb_t qh, cy, qsave, dinv2;
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mp_ptr tp, temp;
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TMP_DECL;
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TMP_MARK;
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ASSERT (dn >= 6);
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ASSERT (nn > dn);
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ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);
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qn = nn - dn;
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qp += qn;
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np += nn;
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dp += dn;
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if (qn >= dn)
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{
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qn++; /* pretend we'll need an extra limb */
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/* Reduce qn mod dn without division, optimizing small operations. */
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do
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qn -= dn;
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while (qn > dn);
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qp -= qn; /* point at low limb of next quotient block */
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np -= qn; /* point in the middle of partial remainder */
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tp = TMP_ALLOC_LIMBS (10*dn);
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/* Perform the typically smaller block first. */
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if (qn == 1)
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{
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mp_limb_t q, n2, n1, n0, d1, d0;
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/* Handle qh up front, for simplicity. */
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qh = mpn_cmp (np - dn + 1, dp - dn, dn) >= 0;
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if (qh)
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ASSERT_NOCARRY (mpn_sub_n (np - dn + 1, np - dn + 1, dp - dn, dn));
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/* A single iteration of schoolbook: One 3/2 division,
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followed by the bignum update and adjustment. */
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n2 = np[0];
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n1 = np[-1];
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n0 = np[-2];
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d1 = dp[-1];
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d0 = dp[-2];
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ASSERT (n2 < d1 || (n2 == d1 && n1 <= d0));
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if (UNLIKELY (n2 == d1) && n1 == d0)
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{
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q = GMP_NUMB_MASK;
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cy = mpn_submul_1 (np - dn, dp - dn, dn, q);
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ASSERT (cy == n2);
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}
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else
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{
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invert_1(dinv2, d1, d0);
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tdiv_qr_3by2 (q, n1, n0, n2, n1, n0, d1, d0, dinv2);
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if (dn > 2)
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{
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mp_limb_t cy, cy1;
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cy = mpn_submul_1 (np - dn, dp - dn, dn - 2, q);
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cy1 = n0 < cy;
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n0 = (n0 - cy) & GMP_NUMB_MASK;
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cy = n1 < cy1;
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n1 = (n1 - cy1) & GMP_NUMB_MASK;
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np[-2] = n0;
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if (UNLIKELY (cy != 0))
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{
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n1 += d1 + mpn_add_n (np - dn, np - dn, dp - dn, dn - 1);
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qh -= (q == 0);
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q = (q - 1) & GMP_NUMB_MASK;
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}
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}
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else
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np[-2] = n0;
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np[-1] = n1;
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}
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qp[0] = q;
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}
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else
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{
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invert_1(dinv2, dp[-1], dp[-2]);
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if (qn == 2)
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qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2);
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else if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
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qh = mpn_sb_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv2);
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else if (BELOW_THRESHOLD (qn, INV_DIV_QR_THRESHOLD))
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qh = mpn_dc_div_qr_n (qp, np - qn, dp - qn, qn, dinv2, tp);
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else
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{
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if (mpn_is_invert(dinv + dn - qn, dp - qn, qn))
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qh = mpn_inv_div_qr_n (qp, np - qn, dp - qn, qn, dinv + dn - qn);
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else
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{
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mpn_add_1(tp, dinv + dn - qn, qn, 1);
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qh = mpn_inv_div_qr_n (qp, np - qn, dp - qn, qn, tp);
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}
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}
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if (qn != dn)
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{
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if (qn > dn - qn)
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mpn_mul (tp, qp, qn, dp - dn, dn - qn);
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else
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mpn_mul (tp, dp - dn, dn - qn, qp, qn);
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cy = mpn_sub_n (np - dn, np - dn, tp, dn);
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if (qh != 0)
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cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
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while (cy != 0)
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{
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qh -= mpn_sub_1 (qp, qp, qn, 1);
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cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
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}
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}
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}
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qn = nn - dn - qn + 1;
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while (qn > dn)
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{
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qp -= dn;
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np -= dn;
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mpn_inv_div_qr_n (qp, np - dn, dp - dn, dn, dinv);
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qn -= dn;
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}
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/* Since we pretended we'd need an extra quotient limb before, we now
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have made sure the code above left just dn-1=qn quotient limbs to
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develop. Develop that plus a guard limb. */
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qn--;
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qp -= qn;
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np -= dn;
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qsave = qp[qn];
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mpn_inv_divappr_q_n (qp, np - dn, dp - dn, dn, dinv);
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MPN_COPY_INCR (qp, qp + 1, qn);
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qp[qn] = qsave;
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}
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else /* (qn < dn) */
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{
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mp_ptr q2p;
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qp -= qn; /* point at low limb of next quotient block */
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np -= qn; /* point in the middle of partial remainder */
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q2p = TMP_ALLOC_LIMBS (qn + 1);
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invert_1(dinv2, dp[-1], dp[-2]);
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if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD))
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{
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qh = mpn_sb_divappr_q (q2p, np - qn - 2, 2 * (qn + 1),
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dp - (qn + 1), qn + 1, dinv2);
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}
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else if (BELOW_THRESHOLD (qn, INV_DIVAPPR_Q_N_THRESHOLD))
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{
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/* It is tempting to use qp for recursive scratch and put quotient in
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tp, but the recursive scratch needs one limb too many. */
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tp = TMP_ALLOC_LIMBS (10*(qn + 1));
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qh = mpn_dc_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, dinv2, tp);
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}
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else
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{
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tp = TMP_ALLOC_LIMBS (qn + 1);
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if (mpn_is_invert(dinv + dn - (qn + 1), dp - (qn + 1), qn + 1))
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qh = mpn_inv_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, dinv + dn - (qn + 1));
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else
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{
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mpn_add_1(tp, dinv + dn - (qn + 1), qn + 1, 1);
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qh = mpn_inv_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, tp);
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}
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}
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MPN_COPY (qp, q2p + 1, qn);
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}
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TMP_FREE;
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return qh;
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}
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