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/* mpz_divexact_gcd -- exact division optimized for GCDs.
THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE AND ARE ALMOST CERTAIN TO
BE SUBJECT TO INCOMPATIBLE CHANGES IN FUTURE GNU MP RELEASES.
Copyright 2000, 2005, 2011, 2012 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 either:
* 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.
or
* the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any
later version.
or both in parallel, as here.
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 copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library. If not,
see https://www.gnu.org/licenses/. */
#include "gmp-impl.h"
#include "longlong.h"
/* Set q to a/d, expecting d to be from a GCD and therefore usually small.
The distribution of GCDs of random numbers can be found in Knuth volume 2
section 4.5.2 theorem D.
GCD chance
1 60.8%
2^k 20.2% (1<=k<32)
3*2^k 9.0% (1<=k<32)
other 10.1%
Only the low limb is examined for optimizations, since GCDs bigger than
2^32 (or 2^64) will occur very infrequently.
Future: This could change to an mpn_divexact_gcd, possibly partly
inlined, if/when the relevant mpq functions change to an mpn based
implementation. */
#if GMP_NUMB_BITS % 2 == 0
static void
mpz_divexact_by3 (mpz_ptr q, mpz_srcptr a)
{
mp_size_t size = SIZ(a);
mp_size_t abs_size = ABS(size);
mp_ptr qp;
qp = MPZ_REALLOC (q, abs_size);
mpn_bdiv_dbm1 (qp, PTR(a), abs_size, GMP_NUMB_MASK / 3);
abs_size -= (qp[abs_size-1] == 0);
SIZ(q) = (size>0 ? abs_size : -abs_size);
}
#endif
#if GMP_NUMB_BITS % 4 == 0
static void
mpz_divexact_by5 (mpz_ptr q, mpz_srcptr a)
{
mp_size_t size = SIZ(a);
mp_size_t abs_size = ABS(size);
mp_ptr qp;
qp = MPZ_REALLOC (q, abs_size);
mpn_bdiv_dbm1 (qp, PTR(a), abs_size, GMP_NUMB_MASK / 5);
abs_size -= (qp[abs_size-1] == 0);
SIZ(q) = (size>0 ? abs_size : -abs_size);
}
#endif
static void
mpz_divexact_limb (mpz_ptr q, mpz_srcptr a, mp_limb_t d)
{
mp_size_t size = SIZ(a);
mp_size_t abs_size = ABS(size);
mp_ptr qp;
qp = MPZ_REALLOC (q, abs_size);
MPN_DIVREM_OR_DIVEXACT_1 (qp, PTR(a), abs_size, d);
abs_size -= (qp[abs_size-1] == 0);
SIZ(q) = (size > 0 ? abs_size : -abs_size);
}
void
mpz_divexact_gcd (mpz_ptr q, mpz_srcptr a, mpz_srcptr d)
{
ASSERT (mpz_sgn (d) > 0);
if (SIZ(a) == 0)
{
SIZ(q) = 0;
return;
}
if (SIZ(d) == 1)
{
mp_limb_t dl = PTR(d)[0];
int twos;
if ((dl & 1) == 0)
{
count_trailing_zeros (twos, dl);
dl >>= twos;
mpz_tdiv_q_2exp (q, a, twos);
a = q;
}
if (dl == 1)
{
if (q != a)
mpz_set (q, a);
return;
}
#if GMP_NUMB_BITS % 2 == 0
if (dl == 3)
{
mpz_divexact_by3 (q, a);
return;
}
#endif
#if GMP_NUMB_BITS % 4 == 0
if (dl == 5)
{
mpz_divexact_by5 (q, a);
return;
}
#endif
mpz_divexact_limb (q, a, dl);
return;
}
mpz_divexact (q, a, d);
}
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