/* mpn_dc_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 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 "mpir.h" #include "gmp-impl.h" #include "longlong.h" #define DC_DIVAPPR_Q_THRESHOLD 41 /*FIXME: tune these */ #define DC_DIVAPPR_QR_THRESHOLD 45 mp_limb_t mpn_dc_divappr_q (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn, mp_srcptr 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 (10*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. */ ASSERT (np[0] < dp[-1] || (np[0] == dp[-1] && np[-1] <= dp[-2])); if (UNLIKELY (n2 == d1) && n1 == d0) { q = GMP_NUMB_MASK; cy = mpn_submul_1 (np - dn, dp - dn, dn, q); ASSERT (cy == n2); } else { mp_limb_t q1[1]; mp_limb_t r2[3]; r2[0] = np[-2]; r2[1] = np[-1]; r2[2] = np[0]; mpn_sb_divrem_mn(q1, r2, 3, dp - 2, 2); q = q1[0]; if (dn > 2) { mp_limb_t cy, cy1; cy = mpn_submul_1 (np - dn, dp - dn, dn - 2, q); cy1 = r2[0] < cy; np[-2] = (r2[0] - cy) & GMP_NUMB_MASK; cy = r2[1] < cy1; np[-1] = (r2[1] - cy1) & GMP_NUMB_MASK; if (UNLIKELY (cy != 0)) { np[-1] += dp[-1] + mpn_add_n (np - dn, np - dn, dp - dn, dn - 1); qh -= (q == 0); q = (q - 1) & GMP_NUMB_MASK; } } else { np[-2] = r2[0]; np[-1] = r2[1]; } } qp[0] = q; } else { if (qn == 2) qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2); else qh = mpn_divrem (qp, 0, np - qn, 2 * qn, dp - qn, qn); 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_divrem (qp, 0, np - dn, 2 * dn, dp - dn, dn); 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_dc_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); if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD)) { qh = mpn_sb_divappr_q (q2p, np - qn - 2, 2 * (qn + 1), dp - (qn + 1), qn + 1, dinv); } 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 (10*(qn + 1)); qh = mpn_dc_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, dinv, tp); } MPN_COPY (qp, q2p + 1, qn); } TMP_FREE; return qh; }