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+/* mpn_mu_div_q.
+
+ Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
+
+ THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
+ SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
+ GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
+
+Copyright 2005-2007, 2009, 2010, 2013 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 either:
+
+ * 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.
+
+or
+
+ * the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any
+ later version.
+
+or both in parallel, as here.
+
+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 General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library. If not,
+see https://www.gnu.org/licenses/. */
+
+
+/*
+ The idea of the algorithm used herein is to compute a smaller inverted value
+ than used in the standard Barrett algorithm, and thus save time in the
+ Newton iterations, and pay just a small price when using the inverted value
+ for developing quotient bits. This algorithm was presented at ICMS 2006.
+*/
+
+/*
+ Things to work on:
+
+ 1. This is a rudimentary implementation of mpn_mu_div_q. The algorithm is
+ probably close to optimal, except when mpn_mu_divappr_q fails.
+
+ 2. We used to fall back to mpn_mu_div_qr when we detect a possible
+ mpn_mu_divappr_q rounding problem, now we multiply and compare.
+ Unfortunately, since mpn_mu_divappr_q does not return the partial
+ remainder, this also doesn't become optimal. A mpn_mu_divappr_qr could
+ solve that.
+
+ 3. The allocations done here should be made from the scratch area, which
+ then would need to be amended.
+*/
+
+#include <stdlib.h> /* for NULL */
+#include "gmp.h"
+#include "gmp-impl.h"
+
+
+mp_limb_t
+mpn_mu_div_q (mp_ptr qp,
+ mp_srcptr np, mp_size_t nn,
+ mp_srcptr dp, mp_size_t dn,
+ mp_ptr scratch)
+{
+ mp_ptr tp, rp;
+ mp_size_t qn;
+ mp_limb_t cy, qh;
+ TMP_DECL;
+
+ TMP_MARK;
+
+ qn = nn - dn;
+
+ tp = TMP_BALLOC_LIMBS (qn + 1);
+
+ if (qn >= dn) /* nn >= 2*dn + 1 */
+ {
+ /* |_______________________| dividend
+ |________| divisor */
+
+ rp = TMP_BALLOC_LIMBS (nn + 1);
+ MPN_COPY (rp + 1, np, nn);
+ rp[0] = 0;
+
+ qh = mpn_cmp (rp + 1 + nn - dn, dp, dn) >= 0;
+ if (qh != 0)
+ mpn_sub_n (rp + 1 + nn - dn, rp + 1 + nn - dn, dp, dn);
+
+ cy = mpn_mu_divappr_q (tp, rp, nn + 1, dp, dn, scratch);
+
+ if (UNLIKELY (cy != 0))
+ {
+ /* Since the partial remainder fed to mpn_preinv_mu_divappr_q was
+ canonically reduced, replace the returned value of B^(qn-dn)+eps
+ by the largest possible value. */
+ mp_size_t i;
+ for (i = 0; i < qn + 1; i++)
+ tp[i] = GMP_NUMB_MAX;
+ }
+
+ /* The max error of mpn_mu_divappr_q is +4. If the low quotient limb is
+ greater than the max error, we cannot trust the quotient. */
+ if (tp[0] > 4)
+ {
+ MPN_COPY (qp, tp + 1, qn);
+ }
+ else
+ {
+ mp_limb_t cy;
+ mp_ptr pp;
+
+ pp = rp;
+ mpn_mul (pp, tp + 1, qn, dp, dn);
+
+ cy = (qh != 0) ? mpn_add_n (pp + qn, pp + qn, dp, dn) : 0;
+
+ if (cy || mpn_cmp (pp, np, nn) > 0) /* At most is wrong by one, no cycle. */
+ qh -= mpn_sub_1 (qp, tp + 1, qn, 1);
+ else /* Same as above */
+ MPN_COPY (qp, tp + 1, qn);
+ }
+ }
+ else
+ {
+ /* |_______________________| dividend
+ |________________| divisor */
+
+ /* FIXME: When nn = 2dn-1, qn becomes dn-1, and the numerator size passed
+ here becomes 2dn, i.e., more than nn. This shouldn't hurt, since only
+ the most significant dn-1 limbs will actually be read, but it is not
+ pretty. */
+
+ qh = mpn_mu_divappr_q (tp, np + nn - (2 * qn + 2), 2 * qn + 2,
+ dp + dn - (qn + 1), qn + 1, scratch);
+
+ /* The max error of mpn_mu_divappr_q is +4, but we get an additional
+ error from the divisor truncation. */
+ if (tp[0] > 6)
+ {
+ MPN_COPY (qp, tp + 1, qn);
+ }
+ else
+ {
+ mp_limb_t cy;
+
+ /* FIXME: a shorter product should be enough; we may use already
+ allocated space... */
+ rp = TMP_BALLOC_LIMBS (nn);
+ mpn_mul (rp, dp, dn, tp + 1, qn);
+
+ cy = (qh != 0) ? mpn_add_n (rp + qn, rp + qn, dp, dn) : 0;
+
+ if (cy || mpn_cmp (rp, np, nn) > 0) /* At most is wrong by one, no cycle. */
+ qh -= mpn_sub_1 (qp, tp + 1, qn, 1);
+ else /* Same as above */
+ MPN_COPY (qp, tp + 1, qn);
+ }
+ }
+
+ TMP_FREE;
+ return qh;
+}
+
+mp_size_t
+mpn_mu_div_q_itch (mp_size_t nn, mp_size_t dn, int mua_k)
+{
+ mp_size_t qn;
+
+ qn = nn - dn;
+ if (qn >= dn)
+ {
+ return mpn_mu_divappr_q_itch (nn + 1, dn, mua_k);
+ }
+ else
+ {
+ return mpn_mu_divappr_q_itch (2 * qn + 2, qn + 1, mua_k);
+ }
+}