| /* mpn_mu_div_q, mpn_preinv_mu_div_q. |
| |
| 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 2005, 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/. */ |
| |
| |
| /* |
| Things to work on: |
| |
| 1. This is a rudimentary implementation of mpn_mu_div_q. The algorithm is |
| probably close to optimal, except when mpn_mu_divappr_q fails. |
| |
| An alternative which could be considered for much simpler code for the |
| complex qn>=dn arm would be to allocate a temporary nn+1 limb buffer, then |
| simply call mpn_mu_divappr_q. Such a temporary allocation is |
| unfortunately very large. |
| |
| 2. Instead of falling back to mpn_mu_div_qr when we detect a possible |
| mpn_mu_divappr_q rounding problem, we could multiply and compare. |
| Unfortunately, since mpn_mu_divappr_q does not return the partial |
| remainder, this also doesn't become optimal. A mpn_mu_divappr_qr |
| could solve that. |
| |
| 3. The allocations done here should be made from the scratch area. |
| */ |
| |
| #include <stdlib.h> /* for NULL */ |
| #include "gmp.h" |
| #include "gmp-impl.h" |
| |
| |
| mp_limb_t |
| mpn_mu_div_q (mp_ptr qp, |
| mp_ptr np, mp_size_t nn, |
| mp_srcptr dp, mp_size_t dn, |
| mp_ptr scratch) |
| { |
| mp_ptr tp, rp, ip, this_ip; |
| mp_size_t qn, in, this_in; |
| mp_limb_t cy; |
| TMP_DECL; |
| |
| TMP_MARK; |
| |
| qn = nn - dn; |
| |
| tp = TMP_BALLOC_LIMBS (qn + 1); |
| |
| if (qn >= dn) /* nn >= 2*dn + 1 */ |
| { |
| /* Find max inverse size needed by the two preinv calls. */ |
| if (dn != qn) |
| { |
| mp_size_t in1, in2; |
| |
| in1 = mpn_mu_div_qr_choose_in (qn - dn, dn, 0); |
| in2 = mpn_mu_divappr_q_choose_in (dn + 1, dn, 0); |
| in = MAX (in1, in2); |
| } |
| else |
| { |
| in = mpn_mu_divappr_q_choose_in (dn + 1, dn, 0); |
| } |
| |
| ip = TMP_BALLOC_LIMBS (in + 1); |
| |
| if (dn == in) |
| { |
| MPN_COPY (scratch + 1, dp, in); |
| scratch[0] = 1; |
| mpn_invert (ip, scratch, in + 1, NULL); |
| MPN_COPY_INCR (ip, ip + 1, in); |
| } |
| else |
| { |
| cy = mpn_add_1 (scratch, dp + dn - (in + 1), in + 1, 1); |
| if (UNLIKELY (cy != 0)) |
| MPN_ZERO (ip, in); |
| else |
| { |
| mpn_invert (ip, scratch, in + 1, NULL); |
| MPN_COPY_INCR (ip, ip + 1, in); |
| } |
| } |
| |
| /* |_______________________| dividend |
| |________| divisor */ |
| rp = TMP_BALLOC_LIMBS (2 * dn + 1); |
| if (dn != qn) /* FIXME: perhaps mpn_mu_div_qr should DTRT */ |
| { |
| this_in = mpn_mu_div_qr_choose_in (qn - dn, dn, 0); |
| this_ip = ip + in - this_in; |
| mpn_preinv_mu_div_qr (tp + dn + 1, rp + dn + 1, np + dn, qn, dp, dn, |
| this_ip, this_in, scratch); |
| } |
| else |
| MPN_COPY (rp + dn + 1, np + dn, dn); |
| |
| MPN_COPY (rp + 1, np, dn); |
| rp[0] = 0; |
| this_in = mpn_mu_divappr_q_choose_in (dn + 1, dn, 0); |
| this_ip = ip + in - this_in; |
| mpn_preinv_mu_divappr_q (tp, rp, 2*dn + 1, dp, dn, this_ip, this_in, scratch); |
| |
| /* The max error of mpn_mu_divappr_q is +4. If the low quotient limb is |
| greater than the max error, we cannot trust the quotient. */ |
| if (tp[0] > 4) |
| { |
| MPN_COPY (qp, tp + 1, qn); |
| } |
| else |
| { |
| /* Fall back to plain mpn_mu_div_qr. */ |
| mpn_mu_div_qr (qp, rp, np, nn, dp, dn, scratch); |
| } |
| } |
| else |
| { |
| /* |_______________________| dividend |
| |________________| divisor */ |
| mpn_mu_divappr_q (tp, np + nn - (2*qn + 2), 2*qn + 2, dp + dn - (qn + 1), qn + 1, scratch); |
| |
| if (tp[0] > 4) |
| { |
| MPN_COPY (qp, tp + 1, qn); |
| } |
| else |
| { |
| rp = TMP_BALLOC_LIMBS (dn); |
| mpn_mu_div_qr (qp, rp, np, nn, dp, dn, scratch); |
| } |
| } |
| |
| TMP_FREE; |
| return 0; |
| } |