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/* mpn_mu_div_q.
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Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
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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 2005-2007, 2009, 2010, 2013 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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/*
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The idea of the algorithm used herein is to compute a smaller inverted value
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than used in the standard Barrett algorithm, and thus save time in the
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Newton iterations, and pay just a small price when using the inverted value
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for developing quotient bits. This algorithm was presented at ICMS 2006.
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*/
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/*
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Things to work on:
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1. This is a rudimentary implementation of mpn_mu_div_q. The algorithm is
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probably close to optimal, except when mpn_mu_divappr_q fails.
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2. We used to fall back to mpn_mu_div_qr when we detect a possible
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mpn_mu_divappr_q rounding problem, now we multiply and compare.
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Unfortunately, since mpn_mu_divappr_q does not return the partial
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remainder, this also doesn't become optimal. A mpn_mu_divappr_qr could
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solve that.
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3. The allocations done here should be made from the scratch area, which
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then would need to be amended.
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*/
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#include <stdlib.h> /* for NULL */
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#include "gmp.h"
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#include "gmp-impl.h"
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mp_limb_t
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mpn_mu_div_q (mp_ptr qp,
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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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mp_ptr scratch)
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{
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mp_ptr tp, rp;
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mp_size_t qn;
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mp_limb_t cy, qh;
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TMP_DECL;
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TMP_MARK;
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qn = nn - dn;
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tp = TMP_BALLOC_LIMBS (qn + 1);
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if (qn >= dn) /* nn >= 2*dn + 1 */
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{
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/* |_______________________| dividend
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|________| divisor */
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rp = TMP_BALLOC_LIMBS (nn + 1);
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MPN_COPY (rp + 1, np, nn);
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rp[0] = 0;
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qh = mpn_cmp (rp + 1 + nn - dn, dp, dn) >= 0;
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if (qh != 0)
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mpn_sub_n (rp + 1 + nn - dn, rp + 1 + nn - dn, dp, dn);
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cy = mpn_mu_divappr_q (tp, rp, nn + 1, dp, dn, scratch);
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if (UNLIKELY (cy != 0))
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{
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/* Since the partial remainder fed to mpn_preinv_mu_divappr_q was
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canonically reduced, replace the returned value of B^(qn-dn)+eps
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by the largest possible value. */
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mp_size_t i;
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for (i = 0; i < qn + 1; i++)
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tp[i] = GMP_NUMB_MAX;
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}
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/* The max error of mpn_mu_divappr_q is +4. If the low quotient limb is
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smaller than the max error, we cannot trust the quotient. */
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if (tp[0] > 4)
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{
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MPN_COPY (qp, tp + 1, qn);
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}
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else
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{
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mp_limb_t cy;
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mp_ptr pp;
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pp = rp;
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mpn_mul (pp, tp + 1, qn, dp, dn);
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cy = (qh != 0) ? mpn_add_n (pp + qn, pp + qn, dp, dn) : 0;
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if (cy || mpn_cmp (pp, np, nn) > 0) /* At most is wrong by one, no cycle. */
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qh -= mpn_sub_1 (qp, tp + 1, qn, 1);
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else /* Same as above */
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MPN_COPY (qp, tp + 1, qn);
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}
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}
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else
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{
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/* |_______________________| dividend
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|________________| divisor */
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/* FIXME: When nn = 2dn-1, qn becomes dn-1, and the numerator size passed
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here becomes 2dn, i.e., more than nn. This shouldn't hurt, since only
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the most significant dn-1 limbs will actually be read, but it is not
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pretty. */
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qh = mpn_mu_divappr_q (tp, np + nn - (2 * qn + 2), 2 * qn + 2,
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dp + dn - (qn + 1), qn + 1, scratch);
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/* The max error of mpn_mu_divappr_q is +4, but we get an additional
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error from the divisor truncation. */
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if (tp[0] > 6)
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{
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MPN_COPY (qp, tp + 1, qn);
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}
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else
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{
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mp_limb_t cy;
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/* FIXME: a shorter product should be enough; we may use already
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allocated space... */
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rp = TMP_BALLOC_LIMBS (nn);
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mpn_mul (rp, dp, dn, tp + 1, qn);
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cy = (qh != 0) ? mpn_add_n (rp + qn, rp + qn, dp, dn) : 0;
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if (cy || mpn_cmp (rp, np, nn) > 0) /* At most is wrong by one, no cycle. */
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qh -= mpn_sub_1 (qp, tp + 1, qn, 1);
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else /* Same as above */
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MPN_COPY (qp, tp + 1, qn);
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}
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}
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TMP_FREE;
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return qh;
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}
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mp_size_t
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mpn_mu_div_q_itch (mp_size_t nn, mp_size_t dn, int mua_k)
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{
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mp_size_t qn;
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qn = nn - dn;
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if (qn >= dn)
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{
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return mpn_mu_divappr_q_itch (nn + 1, dn, mua_k);
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}
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else
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{
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return mpn_mu_divappr_q_itch (2 * qn + 2, qn + 1, mua_k);
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}
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}
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