| /* mpn_dcpi1_divappr_q -- divide-and-conquer division, returning approximate |
| quotient. The quotient returned is either correct, or one too large. |
| |
| 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, 2010 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.h" |
| #include "gmp-impl.h" |
| #include "longlong.h" |
| |
| |
| mp_limb_t |
| mpn_dcpi1_divappr_q_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_DIVAPPR_Q_THRESHOLD)) |
| ql = mpn_sbpi1_divappr_q (qp, np + hi, 2 * lo, dp + hi, lo, dinv->inv32); |
| else |
| ql = mpn_dcpi1_divappr_q_n (qp, np + hi, dp + hi, lo, dinv, tp); |
| |
| if (UNLIKELY (ql != 0)) |
| { |
| mp_size_t i; |
| for (i = 0; i < lo; i++) |
| qp[i] = GMP_NUMB_MASK; |
| } |
| |
| return qh; |
| } |
| |
| mp_limb_t |
| mpn_dcpi1_divappr_q (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, qsave; |
| mp_ptr tp; |
| TMP_DECL; |
| |
| TMP_MARK; |
| |
| ASSERT (dn >= 6); |
| ASSERT (nn > dn); |
| ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT); |
| |
| qn = nn - dn; |
| qp += qn; |
| np += nn; |
| dp += dn; |
| |
| if (qn >= dn) |
| { |
| qn++; /* pretend we'll need an extra limb */ |
| /* 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 */ |
| |
| tp = TMP_SALLOC_LIMBS (dn); |
| |
| /* 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 |
| { |
| if (qn == 2) |
| qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2); |
| 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 + 1; |
| while (qn > dn) |
| { |
| qp -= dn; |
| np -= dn; |
| mpn_dcpi1_div_qr_n (qp, np - dn, dp - dn, dn, dinv, tp); |
| qn -= dn; |
| } |
| |
| /* Since we pretended we'd need an extra quotient limb before, we now |
| have made sure the code above left just dn-1=qn quotient limbs to |
| develop. Develop that plus a guard limb. */ |
| qn--; |
| qp -= qn; |
| np -= dn; |
| qsave = qp[qn]; |
| mpn_dcpi1_divappr_q_n (qp, np - dn, dp - dn, dn, dinv, tp); |
| MPN_COPY_INCR (qp, qp + 1, qn); |
| qp[qn] = qsave; |
| } |
| else /* (qn < dn) */ |
| { |
| mp_ptr q2p; |
| #if 0 /* not possible since we demand nn > dn */ |
| if (qn == 0) |
| { |
| qh = mpn_cmp (np - dn, dp - dn, dn) >= 0; |
| if (qh) |
| mpn_sub_n (np - dn, np - dn, dp - dn, dn); |
| TMP_FREE; |
| return qh; |
| } |
| #endif |
| |
| qp -= qn; /* point at low limb of next quotient block */ |
| np -= qn; /* point in the middle of partial remainder */ |
| |
| q2p = TMP_SALLOC_LIMBS (qn + 1); |
| /* Should we at all check DC_DIVAPPR_Q_THRESHOLD here, or reply on |
| callers not to be silly? */ |
| if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD)) |
| { |
| qh = mpn_sbpi1_divappr_q (q2p, np - qn - 2, 2 * (qn + 1), |
| dp - (qn + 1), qn + 1, dinv->inv32); |
| } |
| else |
| { |
| /* It is tempting to use qp for recursive scratch and put quotient in |
| tp, but the recursive scratch needs one limb too many. */ |
| tp = TMP_SALLOC_LIMBS (qn + 1); |
| qh = mpn_dcpi1_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, dinv, tp); |
| } |
| MPN_COPY (qp, q2p + 1, qn); |
| } |
| |
| TMP_FREE; |
| return qh; |
| } |
