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+/* mpn_sbpi1_div_q -- Schoolbook division using the Möller-Granlund 3/2
+ division algorithm.
+
+ Contributed to the GNU project by Torbjorn Granlund.
+
+ THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
+ SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
+ GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
+
+Copyright 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_sbpi1_div_q (mp_ptr qp,
+ mp_ptr np, mp_size_t nn,
+ mp_srcptr dp, mp_size_t dn,
+ mp_limb_t dinv)
+{
+ mp_limb_t qh;
+ mp_size_t qn, i;
+ mp_limb_t n1, n0;
+ mp_limb_t d1, d0;
+ mp_limb_t cy, cy1;
+ mp_limb_t q;
+ mp_limb_t flag;
+
+ mp_size_t dn_orig = dn;
+ mp_srcptr dp_orig = dp;
+ mp_ptr np_orig = np;
+
+ ASSERT (dn > 2);
+ ASSERT (nn >= dn);
+ ASSERT ((dp[dn-1] & GMP_NUMB_HIGHBIT) != 0);
+
+ np += nn;
+
+ qn = nn - dn;
+ if (qn + 1 < dn)
+ {
+ dp += dn - (qn + 1);
+ dn = qn + 1;
+ }
+
+ qh = mpn_cmp (np - dn, dp, dn) >= 0;
+ if (qh != 0)
+ mpn_sub_n (np - dn, np - dn, dp, dn);
+
+ qp += qn;
+
+ dn -= 2; /* offset dn by 2 for main division loops,
+ saving two iterations in mpn_submul_1. */
+ d1 = dp[dn + 1];
+ d0 = dp[dn + 0];
+
+ np -= 2;
+
+ n1 = np[1];
+
+ for (i = qn - (dn + 2); i >= 0; i--)
+ {
+ np--;
+ if (UNLIKELY (n1 == d1) && np[1] == d0)
+ {
+ q = GMP_NUMB_MASK;
+ mpn_submul_1 (np - dn, dp, dn + 2, q);
+ n1 = np[1]; /* update n1, last loop's value will now be invalid */
+ }
+ else
+ {
+ udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);
+
+ cy = mpn_submul_1 (np - dn, dp, dn, q);
+
+ cy1 = n0 < cy;
+ n0 = (n0 - cy) & GMP_NUMB_MASK;
+ cy = n1 < cy1;
+ n1 -= cy1;
+ np[0] = n0;
+
+ if (UNLIKELY (cy != 0))
+ {
+ n1 += d1 + mpn_add_n (np - dn, np - dn, dp, dn + 1);
+ q--;
+ }
+ }
+
+ *--qp = q;
+ }
+
+ flag = ~CNST_LIMB(0);
+
+ if (dn >= 0)
+ {
+ for (i = dn; i > 0; i--)
+ {
+ np--;
+ if (UNLIKELY (n1 >= (d1 & flag)))
+ {
+ q = GMP_NUMB_MASK;
+ cy = mpn_submul_1 (np - dn, dp, dn + 2, q);
+
+ if (UNLIKELY (n1 != cy))
+ {
+ if (n1 < (cy & flag))
+ {
+ q--;
+ mpn_add_n (np - dn, np - dn, dp, dn + 2);
+ }
+ else
+ flag = 0;
+ }
+ n1 = np[1];
+ }
+ else
+ {
+ udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);
+
+ cy = mpn_submul_1 (np - dn, dp, dn, q);
+
+ cy1 = n0 < cy;
+ n0 = (n0 - cy) & GMP_NUMB_MASK;
+ cy = n1 < cy1;
+ n1 -= cy1;
+ np[0] = n0;
+
+ if (UNLIKELY (cy != 0))
+ {
+ n1 += d1 + mpn_add_n (np - dn, np - dn, dp, dn + 1);
+ q--;
+ }
+ }
+
+ *--qp = q;
+
+ /* Truncate operands. */
+ dn--;
+ dp++;
+ }
+
+ np--;
+ if (UNLIKELY (n1 >= (d1 & flag)))
+ {
+ q = GMP_NUMB_MASK;
+ cy = mpn_submul_1 (np, dp, 2, q);
+
+ if (UNLIKELY (n1 != cy))
+ {
+ if (n1 < (cy & flag))
+ {
+ q--;
+ add_ssaaaa (np[1], np[0], np[1], np[0], dp[1], dp[0]);
+ }
+ else
+ flag = 0;
+ }
+ n1 = np[1];
+ }
+ else
+ {
+ udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);
+
+ np[0] = n0;
+ np[1] = n1;
+ }
+
+ *--qp = q;
+ }
+ ASSERT_ALWAYS (np[1] == n1);
+ np += 2;
+
+
+ dn = dn_orig;
+ if (UNLIKELY (n1 < (dn & flag)))
+ {
+ mp_limb_t q, x;
+
+ /* The quotient may be too large if the remainder is small. Recompute
+ for above ignored operand parts, until the remainder spills.
+
+ FIXME: The quality of this code isn't the same as the code above.
+ 1. We don't compute things in an optimal order, high-to-low, in order
+ to terminate as quickly as possible.
+ 2. We mess with pointers and sizes, adding and subtracting and
+ adjusting to get things right. It surely could be streamlined.
+ 3. The only termination criteria are that we determine that the
+ quotient needs to be adjusted, or that we have recomputed
+ everything. We should stop when the remainder is so large
+ that no additional subtracting could make it spill.
+ 4. If nothing else, we should not do two loops of submul_1 over the
+ data, instead handle both the triangularization and chopping at
+ once. */
+
+ x = n1;
+
+ if (dn > 2)
+ {
+ /* Compensate for triangularization. */
+ mp_limb_t y;
+
+ dp = dp_orig;
+ if (qn + 1 < dn)
+ {
+ dp += dn - (qn + 1);
+ dn = qn + 1;
+ }
+
+ y = np[-2];
+
+ for (i = dn - 3; i >= 0; i--)
+ {
+ q = qp[i];
+ cy = mpn_submul_1 (np - (dn - i), dp, dn - i - 2, q);
+
+ if (y < cy)
+ {
+ if (x == 0)
+ {
+ cy = mpn_sub_1 (qp, qp, qn, 1);
+ ASSERT_ALWAYS (cy == 0);
+ return qh - cy;
+ }
+ x--;
+ }
+ y -= cy;
+ }
+ np[-2] = y;
+ }
+
+ dn = dn_orig;
+ if (qn + 1 < dn)
+ {
+ /* Compensate for ignored dividend and divisor tails. */
+
+ dp = dp_orig;
+ np = np_orig;
+
+ if (qh != 0)
+ {
+ cy = mpn_sub_n (np + qn, np + qn, dp, dn - (qn + 1));
+ if (cy != 0)
+ {
+ if (x == 0)
+ {
+ if (qn != 0)
+ cy = mpn_sub_1 (qp, qp, qn, 1);
+ return qh - cy;
+ }
+ x--;
+ }
+ }
+
+ if (qn == 0)
+ return qh;
+
+ for (i = dn - qn - 2; i >= 0; i--)
+ {
+ cy = mpn_submul_1 (np + i, qp, qn, dp[i]);
+ cy = mpn_sub_1 (np + qn + i, np + qn + i, dn - qn - i - 1, cy);
+ if (cy != 0)
+ {
+ if (x == 0)
+ {
+ cy = mpn_sub_1 (qp, qp, qn, 1);
+ return qh;
+ }
+ x--;
+ }
+ }
+ }
+ }
+
+ return qh;
+}
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