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+/* mpn_dcpi1_div_qr_n -- recursive divide-and-conquer division for arbitrary
+ size operands.
+
+ Contributed to the GNU project by Torbjorn Granlund.
+
+ 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 2006, 2007, 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 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/. */
+
+#include "gmp-impl.h"
+#include "longlong.h"
+
+
+mp_limb_t
+mpn_dcpi1_div_qr_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n,
+ gmp_pi1_t *dinv, mp_ptr tp)
+{
+ mp_size_t lo, hi;
+ mp_limb_t cy, qh, ql;
+
+ lo = n >> 1; /* floor(n/2) */
+ hi = n - lo; /* ceil(n/2) */
+
+ if (BELOW_THRESHOLD (hi, DC_DIV_QR_THRESHOLD))
+ qh = mpn_sbpi1_div_qr (qp + lo, np + 2 * lo, 2 * hi, dp + lo, hi, dinv->inv32);
+ else
+ qh = mpn_dcpi1_div_qr_n (qp + lo, np + 2 * lo, dp + lo, hi, dinv, tp);
+
+ mpn_mul (tp, qp + lo, hi, dp, lo);
+
+ cy = mpn_sub_n (np + lo, np + lo, tp, n);
+ if (qh != 0)
+ cy += mpn_sub_n (np + n, np + n, dp, lo);
+
+ while (cy != 0)
+ {
+ qh -= mpn_sub_1 (qp + lo, qp + lo, hi, 1);
+ cy -= mpn_add_n (np + lo, np + lo, dp, n);
+ }
+
+ if (BELOW_THRESHOLD (lo, DC_DIV_QR_THRESHOLD))
+ ql = mpn_sbpi1_div_qr (qp, np + hi, 2 * lo, dp + hi, lo, dinv->inv32);
+ else
+ ql = mpn_dcpi1_div_qr_n (qp, np + hi, dp + hi, lo, dinv, tp);
+
+ mpn_mul (tp, dp, hi, qp, lo);
+
+ cy = mpn_sub_n (np, np, tp, n);
+ if (ql != 0)
+ cy += mpn_sub_n (np + lo, np + lo, dp, hi);
+
+ while (cy != 0)
+ {
+ mpn_sub_1 (qp, qp, lo, 1);
+ cy -= mpn_add_n (np, np, dp, n);
+ }
+
+ return qh;
+}
+
+mp_limb_t
+mpn_dcpi1_div_qr (mp_ptr qp,
+ mp_ptr np, mp_size_t nn,
+ mp_srcptr dp, mp_size_t dn,
+ gmp_pi1_t *dinv)
+{
+ mp_size_t qn;
+ mp_limb_t qh, cy;
+ mp_ptr tp;
+ TMP_DECL;
+
+ TMP_MARK;
+
+ ASSERT (dn >= 6); /* to adhere to mpn_sbpi1_div_qr's limits */
+ ASSERT (nn - dn >= 3); /* to adhere to mpn_sbpi1_div_qr's limits */
+ ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);
+
+ tp = TMP_ALLOC_LIMBS (dn);
+
+ qn = nn - dn;
+ qp += qn;
+ np += nn;
+ dp += dn;
+
+ if (qn > dn)
+ {
+ /* Reduce qn mod dn without division, optimizing small operations. */
+ do
+ qn -= dn;
+ while (qn > dn);
+
+ qp -= qn; /* point at low limb of next quotient block */
+ np -= qn; /* point in the middle of partial remainder */
+
+ /* Perform the typically smaller block first. */
+ if (qn == 1)
+ {
+ mp_limb_t q, n2, n1, n0, d1, d0;
+
+ /* Handle qh up front, for simplicity. */
+ qh = mpn_cmp (np - dn + 1, dp - dn, dn) >= 0;
+ if (qh)
+ ASSERT_NOCARRY (mpn_sub_n (np - dn + 1, np - dn + 1, dp - dn, dn));
+
+ /* A single iteration of schoolbook: One 3/2 division,
+ followed by the bignum update and adjustment. */
+ n2 = np[0];
+ n1 = np[-1];
+ n0 = np[-2];
+ d1 = dp[-1];
+ d0 = dp[-2];
+
+ ASSERT (n2 < d1 || (n2 == d1 && n1 <= d0));
+
+ if (UNLIKELY (n2 == d1) && n1 == d0)
+ {
+ q = GMP_NUMB_MASK;
+ cy = mpn_submul_1 (np - dn, dp - dn, dn, q);
+ ASSERT (cy == n2);
+ }
+ else
+ {
+ udiv_qr_3by2 (q, n1, n0, n2, n1, n0, d1, d0, dinv->inv32);
+
+ if (dn > 2)
+ {
+ mp_limb_t cy, cy1;
+ cy = mpn_submul_1 (np - dn, dp - dn, dn - 2, q);
+
+ cy1 = n0 < cy;
+ n0 = (n0 - cy) & GMP_NUMB_MASK;
+ cy = n1 < cy1;
+ n1 = (n1 - cy1) & GMP_NUMB_MASK;
+ np[-2] = n0;
+
+ if (UNLIKELY (cy != 0))
+ {
+ n1 += d1 + mpn_add_n (np - dn, np - dn, dp - dn, dn - 1);
+ qh -= (q == 0);
+ q = (q - 1) & GMP_NUMB_MASK;
+ }
+ }
+ else
+ np[-2] = n0;
+
+ np[-1] = n1;
+ }
+ qp[0] = q;
+ }
+ else
+ {
+ /* Do a 2qn / qn division */
+ if (qn == 2)
+ qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2); /* FIXME: obsolete function. Use 5/3 division? */
+ else if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
+ qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32);
+ else
+ qh = mpn_dcpi1_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);
+
+ if (qn != dn)
+ {
+ if (qn > dn - qn)
+ mpn_mul (tp, qp, qn, dp - dn, dn - qn);
+ else
+ mpn_mul (tp, dp - dn, dn - qn, qp, qn);
+
+ cy = mpn_sub_n (np - dn, np - dn, tp, dn);
+ if (qh != 0)
+ cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
+
+ while (cy != 0)
+ {
+ qh -= mpn_sub_1 (qp, qp, qn, 1);
+ cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
+ }
+ }
+ }
+
+ qn = nn - dn - qn;
+ do
+ {
+ qp -= dn;
+ np -= dn;
+ mpn_dcpi1_div_qr_n (qp, np - dn, dp - dn, dn, dinv, tp);
+ qn -= dn;
+ }
+ while (qn > 0);
+ }
+ else
+ {
+ qp -= qn; /* point at low limb of next quotient block */
+ np -= qn; /* point in the middle of partial remainder */
+
+ if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
+ qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32);
+ else
+ qh = mpn_dcpi1_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);
+
+ if (qn != dn)
+ {
+ if (qn > dn - qn)
+ mpn_mul (tp, qp, qn, dp - dn, dn - qn);
+ else
+ mpn_mul (tp, dp - dn, dn - qn, qp, qn);
+
+ cy = mpn_sub_n (np - dn, np - dn, tp, dn);
+ if (qh != 0)
+ cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
+
+ while (cy != 0)
+ {
+ qh -= mpn_sub_1 (qp, qp, qn, 1);
+ cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
+ }
+ }
+ }
+
+ TMP_FREE;
+ return qh;
+}