147 lines
3.3 KiB
C
147 lines
3.3 KiB
C
/* 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 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 "mpir.h"
|
|
#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_divexact_byfobm1 (qp, PTR(a), abs_size, 3, 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_divexact_byfobm1 (qp, PTR(a), abs_size, 5, 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_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);
|
|
}
|