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/* mpn_divexact(qp,np,nn,dp,dn,tp) -- Divide N = {np,nn} by D = {dp,dn} storing
the result in Q = {qp,nn-dn+1} expecting no remainder. Overlap allowed
between Q and N; all other overlap disallowed.
Contributed to the GNU project by Torbjorn 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/. */
/* We use the Jebelean's bidirectional exact division algorithm. This is
somewhat naively implemented, with equal quotient parts done by 2-adic
division and truncating division. Since 2-adic division is faster, it
should be used for a larger chunk.
This code is horrendously ugly, in all sorts of ways.
* It was hacked without much care or thought, but with a testing program.
* It handles scratch space frivolously, and furthermore the itch function
is broken.
* Doesn't provide any measures to deal with mu_divappr_q's +3 error. We
have yet to provoke an error due to this, though.
* Algorithm selection leaves a lot to be desired. In particular, the choice
between DC and MU isn't a point, but we treat it like one.
* It makes the msb part 1 or 2 limbs larger than the lsb part, in spite of
that the latter is faster. We should at least reverse this, but perhaps
we should make the lsb part considerably larger. (How do we tune this?)
Perhaps we could somehow use 2-adic division for both parts, not as now
truncating division for the upper part and 2-adic for the lower part.
*/
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
mp_size_t
mpn_divexact_itch (mp_size_t nn, mp_size_t dn)
{
return nn + dn; /* FIXME this is not right */
}
void
mpn_divexact (mp_ptr qp,
mp_srcptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn,
mp_ptr scratch)
{
mp_size_t qn;
mp_size_t nn0, qn0;
mp_size_t nn1, qn1;
mp_ptr tp;
mp_limb_t qml;
mp_limb_t qh;
int cnt;
mp_ptr xdp;
mp_limb_t di;
mp_limb_t dip[2], xp[2], cy;
TMP_DECL;
TMP_MARK;
qn = nn - dn + 1;
/* For small divisors, and small quotients, don't use Jebelean's algorithm. */
if (dn < DIVEXACT_JEB_THRESHOLD || qn < DIVEXACT_JEB_THRESHOLD)
{
tp = scratch;
MPN_COPY (tp, np, qn);
binvert_limb (di, dp[0]); di = -di;
dn = MIN (dn, qn);
mpn_sb_bdiv_q (qp, tp, qn, dp, dn, di);
TMP_FREE;
return;
}
qn0 = ((nn - dn) >> 1) + 1; /* low quotient size */
/* If quotient is much larger than the divisor, the bidirectional algorithm
does not work as currently implemented. Fall back to plain bdiv. */
if (qn0 > dn)
{
if (BELOW_THRESHOLD (dn, DC_BDIV_Q_THRESHOLD))
{
tp = scratch;
MPN_COPY (tp, np, qn);
binvert_limb (di, dp[0]); di = -di;
dn = MIN (dn, qn);
mpn_sb_bdiv_q (qp, tp, qn, dp, dn, di);
}
else if (BELOW_THRESHOLD (dn, MU_BDIV_Q_THRESHOLD))
{
tp = scratch;
MPN_COPY (tp, np, qn);
binvert_limb (di, dp[0]); di = -di;
mpn_dc_bdiv_q (qp, tp, qn, dp, dn, di);
}
else
{
mpn_mu_bdiv_q (qp, np, qn, dp, dn, scratch);
}
TMP_FREE;
return;
}
nn0 = qn0 + qn0;
nn1 = nn0 - 1 + ((nn-dn) & 1);
qn1 = qn0;
if (LIKELY (qn0 != dn))
{
nn1 = nn1 + 1;
qn1 = qn1 + 1;
if (UNLIKELY (dp[dn - 1] == 1 && qn1 != dn))
{
/* If the leading divisor limb == 1, i.e. has just one bit, we have
to include an extra limb in order to get the needed overlap. */
/* FIXME: Now with the mu_divappr_q function, we should really need
more overlap. That indicates one of two things: (1) The test code
is not good. (2) We actually overlap too much by default. */
nn1 = nn1 + 1;
qn1 = qn1 + 1;
}
}
tp = TMP_ALLOC_LIMBS (nn1 + 1);
count_leading_zeros (cnt, dp[dn - 1]);
/* Normalize divisor, store into tmp area. */
if (cnt != 0)
{
xdp = TMP_ALLOC_LIMBS (qn1);
mpn_lshift (xdp, dp + dn - qn1, qn1, cnt);
}
else
{
xdp = (mp_ptr) dp + dn - qn1;
}
/* Shift dividend according to the divisor normalization. */
/* FIXME: We compute too much here for XX_divappr_q, but these functions'
interfaces want a pointer to the imaginative least significant limb, not
to the least significant *used* limb. Of course, we could leave nn1-qn1
rubbish limbs in the low part, to save some time. */
if (cnt != 0)
{
cy = mpn_lshift (tp, np + nn - nn1, nn1, cnt);
if (cy != 0)
{
tp[nn1] = cy;
nn1++;
}
}
else
{
/* FIXME: This copy is not needed for mpn_mu_divappr_q, except when the
mpn_sub_n right before is executed. */
MPN_COPY (tp, np + nn - nn1, nn1);
}
if (BELOW_THRESHOLD (qn1, DC_DIVAPPR_Q_THRESHOLD))
{
/* Compute divisor inverse. */
cy = mpn_add_1 (xp, xdp + qn1 - 2, 2, 1);
if (cy != 0)
dip[0] = dip[1] = 0;
else
{
mp_limb_t scratch[10]; /* FIXME */
mpn_invert (dip, xp, 2, scratch);
}
qp[qn0 - 1 + nn1 - qn1] = mpn_sb_divappr_q (qp + qn0 - 1, tp, nn1, xdp, qn1, dip);
}
else if (BELOW_THRESHOLD (qn1, MU_DIVAPPR_Q_THRESHOLD))
{
qp[qn0 - 1 + nn1 - qn1] = mpn_dc_divappr_q (qp + qn0 - 1, tp, nn1, xdp, qn1);
}
else
{
/* FIXME: mpn_mu_divappr_q doesn't handle qh != 0. Work around it with a
conditional subtraction here. */
qh = mpn_cmp (tp + nn1 - qn1, xdp, qn1) >= 0;
if (qh)
mpn_sub_n (tp + nn1 - qn1, tp + nn1 - qn1, xdp, qn1);
mpn_mu_divappr_q (qp + qn0 - 1, tp, nn1, xdp, qn1, scratch);
qp[qn0 - 1 + nn1 - qn1] = qh;
}
qml = qp[qn0 - 1];
binvert_limb (di, dp[0]); di = -di;
if (BELOW_THRESHOLD (qn0, DC_BDIV_Q_THRESHOLD))
{
MPN_COPY (tp, np, qn0);
mpn_sb_bdiv_q (qp, tp, qn0, dp, qn0, di);
}
else if (BELOW_THRESHOLD (qn0, MU_BDIV_Q_THRESHOLD))
{
MPN_COPY (tp, np, qn0);
mpn_dc_bdiv_q (qp, tp, qn0, dp, qn0, di);
}
else
{
mpn_mu_bdiv_q (qp, np, qn0, dp, qn0, scratch);
}
if (qml < qp[qn0 - 1])
mpn_decr_u (qp + qn0, 1);
TMP_FREE;
}
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