| /* mpn_dc_div_qr -- recursive divide-and-conquer division for arbitrary size |
| operands. |
| |
| Contributed to the GNU project by Torbjörn Granlund. |
| |
| THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH A MUTABLE INTERFACE. 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 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" |
| |
| |
| mp_limb_t |
| mpn_dc_div_qr_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n, |
| mp_srcptr dip, 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_sb_div_qr (qp + lo, np + 2 * lo, 2 * hi, dp + lo, hi, dip); |
| else |
| qh = mpn_dc_div_qr_n (qp + lo, np + 2 * lo, dp + lo, hi, dip, 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_sb_div_qr (qp, np + hi, 2 * lo, dp + hi, lo, dip); |
| else |
| ql = mpn_dc_div_qr_n (qp, np + hi, dp + hi, lo, dip, 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_preinv_dc_div_qr (mp_ptr qp, |
| mp_ptr np, mp_size_t nn, |
| mp_srcptr dp, mp_size_t dn, |
| mp_srcptr dip) |
| { |
| mp_size_t qn; |
| mp_limb_t qh, cy; |
| mp_ptr tp; |
| TMP_DECL; |
| |
| TMP_MARK; |
| |
| tp = TMP_SALLOC_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 (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD)) |
| qh = mpn_sb_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dip); |
| else |
| qh = mpn_dc_div_qr_n (qp, np - qn, dp - qn, qn, dip, 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_dc_div_qr_n (qp, np - dn, dp - dn, dn, dip, tp); |
| qn -= dn; |
| } |
| while (qn > 0); |
| } |
| else |
| { |
| 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; |
| } |
| |
| 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_sb_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dip); |
| else |
| qh = mpn_dc_div_qr_n (qp, np - qn, dp - qn, qn, dip, 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; |
| } |
| |
| mp_limb_t |
| mpn_dc_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn) |
| { |
| mp_limb_t cy; |
| mp_limb_t xp[2], dip[2]; |
| |
| ASSERT (dn >= 2); |
| |
| cy = mpn_add_1 (xp, dp + dn - 2, 2, 1); |
| if (cy != 0) |
| dip[0] = dip[1] = 0; |
| else |
| { |
| mp_limb_t scratch[10]; /* FIXME */ |
| mpn_invert (dip, xp, 2, scratch); |
| } |
| |
| return mpn_preinv_dc_div_qr (qp, np, nn, dp, dn, dip); |
| } |