sbpi1_div_q.c
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- /* mpn_sbpi1_div_q -- Schoolbook division using the M鰈ler-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 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.
- 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 Lesser General Public
- License for more details.
- You should have received a copy of the GNU Lesser General Public License
- along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
- #include "gmp.h"
- #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;
- }