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/* 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 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 General Public License for more
details.
You should have received a copy of the GNU 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 "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);
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);
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;
}
|
