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/* mpz_congruent_p -- test congruence of two mpz's.
Copyright 2001, 2002, 2005 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 https://www.gnu.org/licenses/. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
/* For big divisors this code is only very slightly better than the user
doing a combination of mpz_sub and mpz_tdiv_r, but it's quite convenient,
and perhaps in the future can be improved, in similar ways to
mpn_divisible_p perhaps.
The csize==1 / dsize==1 special case makes mpz_congruent_p as good as
mpz_congruent_ui_p on relevant operands, though such a combination
probably doesn't occur often.
Alternatives:
If c<d then it'd work to just form a%d and compare a and c (either as
a==c or a+c==d depending on the signs), but the saving from avoiding the
abs(a-c) calculation would be small compared to the division.
Similarly if both a<d and c<d then it would work to just compare a and c
(a==c or a+c==d), but this isn't considered a particularly important case
and so isn't done for the moment.
Low zero limbs on d could be stripped and the corresponding limbs of a
and c tested and skipped, but doing so would introduce a borrow when a
and c differ in sign and have non-zero skipped limbs. It doesn't seem
worth the complications to do this, since low zero limbs on d should
occur only rarely. */
int
mpz_congruent_p (mpz_srcptr a, mpz_srcptr c, mpz_srcptr d)
{
mp_size_t asize, csize, dsize, sign;
mp_srcptr ap, cp, dp;
mp_ptr xp;
mp_limb_t alow, clow, dlow, dmask, r;
int result;
TMP_DECL;
dsize = SIZ(d);
if (UNLIKELY (dsize == 0))
return (mpz_cmp (a, c) == 0);
dsize = ABS(dsize);
dp = PTR(d);
if (ABSIZ(a) < ABSIZ(c))
MPZ_SRCPTR_SWAP (a, c);
asize = SIZ(a);
csize = SIZ(c);
sign = (asize ^ csize);
asize = ABS(asize);
ap = PTR(a);
if (csize == 0)
return mpn_divisible_p (ap, asize, dp, dsize);
csize = ABS(csize);
cp = PTR(c);
alow = ap[0];
clow = cp[0];
dlow = dp[0];
/* Check a==c mod low zero bits of dlow. This might catch a few cases of
a!=c quickly, and it helps the csize==1 special cases below. */
dmask = LOW_ZEROS_MASK (dlow) & GMP_NUMB_MASK;
alow = (sign >= 0 ? alow : -alow);
if (((alow-clow) & dmask) != 0)
return 0;
if (csize == 1)
{
if (dsize == 1)
{
cong_1:
if (sign < 0)
NEG_MOD (clow, clow, dlow);
if (ABOVE_THRESHOLD (asize, BMOD_1_TO_MOD_1_THRESHOLD))
{
r = mpn_mod_1 (ap, asize, dlow);
if (clow < dlow)
return r == clow;
else
return r == (clow % dlow);
}
if ((dlow & 1) == 0)
{
/* Strip low zero bits to get odd d required by modexact. If
d==e*2^n then a==c mod d if and only if both a==c mod e and
a==c mod 2^n, the latter having been done above. */
unsigned twos;
count_trailing_zeros (twos, dlow);
dlow >>= twos;
}
r = mpn_modexact_1c_odd (ap, asize, dlow, clow);
return r == 0 || r == dlow;
}
/* dlow==0 is avoided since we don't want to bother handling extra low
zero bits if dsecond is even (would involve borrow if a,c differ in
sign and alow,clow!=0). */
if (dsize == 2 && dlow != 0)
{
mp_limb_t dsecond = dp[1];
if (dsecond <= dmask)
{
unsigned twos;
count_trailing_zeros (twos, dlow);
dlow = (dlow >> twos) | (dsecond << (GMP_NUMB_BITS-twos));
ASSERT_LIMB (dlow);
/* dlow will be odd here, so the test for it even under cong_1
is unnecessary, but the rest of that code is wanted. */
goto cong_1;
}
}
}
TMP_MARK;
xp = TMP_ALLOC_LIMBS (asize+1);
/* calculate abs(a-c) */
if (sign >= 0)
{
/* same signs, subtract */
if (asize > csize || mpn_cmp (ap, cp, asize) >= 0)
ASSERT_NOCARRY (mpn_sub (xp, ap, asize, cp, csize));
else
ASSERT_NOCARRY (mpn_sub_n (xp, cp, ap, asize));
MPN_NORMALIZE (xp, asize);
}
else
{
/* different signs, add */
mp_limb_t carry;
carry = mpn_add (xp, ap, asize, cp, csize);
xp[asize] = carry;
asize += (carry != 0);
}
result = mpn_divisible_p (xp, asize, dp, dsize);
TMP_FREE;
return result;
}
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