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/* Reference mpz functions.
Copyright 1997, 1999-2002 Free Software Foundation, Inc.
This file is part of the GNU MP Library test suite.
The GNU MP Library test suite 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 test suite 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 test suite. If not, see https://www.gnu.org/licenses/. */
/* always do assertion checking */
#define WANT_ASSERT 1
#include <stdio.h>
#include <stdlib.h> /* for free */
#include "gmp-impl.h"
#include "longlong.h"
#include "tests.h"
/* Change this to "#define TRACE(x) x" for some traces. */
#define TRACE(x)
/* FIXME: Shouldn't use plain mpz functions in a reference routine. */
void
refmpz_combit (mpz_ptr r, unsigned long bit)
{
if (mpz_tstbit (r, bit))
mpz_clrbit (r, bit);
else
mpz_setbit (r, bit);
}
unsigned long
refmpz_hamdist (mpz_srcptr x, mpz_srcptr y)
{
mp_size_t xsize, ysize, tsize;
mp_ptr xp, yp;
unsigned long ret;
if ((SIZ(x) < 0 && SIZ(y) >= 0)
|| (SIZ(y) < 0 && SIZ(x) >= 0))
return ULONG_MAX;
xsize = ABSIZ(x);
ysize = ABSIZ(y);
tsize = MAX (xsize, ysize);
xp = refmpn_malloc_limbs (tsize);
refmpn_zero (xp, tsize);
refmpn_copy (xp, PTR(x), xsize);
yp = refmpn_malloc_limbs (tsize);
refmpn_zero (yp, tsize);
refmpn_copy (yp, PTR(y), ysize);
if (SIZ(x) < 0)
refmpn_neg (xp, xp, tsize);
if (SIZ(x) < 0)
refmpn_neg (yp, yp, tsize);
ret = refmpn_hamdist (xp, yp, tsize);
free (xp);
free (yp);
return ret;
}
void
refmpz_gcd (mpz_ptr g, mpz_srcptr a_orig, mpz_srcptr b_orig)
{
mp_bitcnt_t a_twos, b_twos, common_twos;
mpz_t a;
mpz_t b;
mpz_init (a);
mpz_init (b);
mpz_abs (a, a_orig);
mpz_abs (b, b_orig);
if (mpz_sgn (a) == 0)
{
mpz_set (g, b);
return;
}
if (mpz_sgn (b) == 0)
{
mpz_set (g, a);
return;
}
a_twos = mpz_scan1 (a, 0);
mpz_tdiv_q_2exp (a, a, a_twos);
b_twos = mpz_scan1 (b, 0);
mpz_tdiv_q_2exp (b, b, b_twos);
common_twos = MIN(a_twos, b_twos);
for (;;)
{
int c;
mp_bitcnt_t twos;
c = mpz_cmp (a, b);
if (c == 0)
break;
if (c < 0)
mpz_swap (a, b);
mpz_sub (a, a, b);
twos = mpz_scan1 (a, 0);
mpz_tdiv_q_2exp (a, a, twos);
}
mpz_mul_2exp (g, a, common_twos);
mpz_clear (a);
mpz_clear (b);
}
/* (0/b), with mpz b; is 1 if b=+/-1, 0 otherwise */
#define JACOBI_0Z(b) JACOBI_0LS (PTR(b)[0], SIZ(b))
/* (a/b) effect due to sign of b: mpz/mpz */
#define JACOBI_BSGN_ZZ_BIT1(a, b) JACOBI_BSGN_SS_BIT1 (SIZ(a), SIZ(b))
/* (a/b) effect due to sign of a: mpz/unsigned-mpz, b odd;
is (-1/b) if a<0, or +1 if a>=0 */
#define JACOBI_ASGN_ZZU_BIT1(a, b) JACOBI_ASGN_SU_BIT1 (SIZ(a), PTR(b)[0])
int
refmpz_kronecker (mpz_srcptr a_orig, mpz_srcptr b_orig)
{
unsigned long twos;
mpz_t a, b;
int result_bit1 = 0;
if (mpz_sgn (b_orig) == 0)
return JACOBI_Z0 (a_orig); /* (a/0) */
if (mpz_sgn (a_orig) == 0)
return JACOBI_0Z (b_orig); /* (0/b) */
if (mpz_even_p (a_orig) && mpz_even_p (b_orig))
return 0;
if (mpz_cmp_ui (b_orig, 1) == 0)
return 1;
mpz_init_set (a, a_orig);
mpz_init_set (b, b_orig);
if (mpz_sgn (b) < 0)
{
result_bit1 ^= JACOBI_BSGN_ZZ_BIT1 (a, b);
mpz_neg (b, b);
}
if (mpz_even_p (b))
{
twos = mpz_scan1 (b, 0L);
mpz_tdiv_q_2exp (b, b, twos);
result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(a)[0]);
}
if (mpz_sgn (a) < 0)
{
result_bit1 ^= JACOBI_N1B_BIT1 (PTR(b)[0]);
mpz_neg (a, a);
}
if (mpz_even_p (a))
{
twos = mpz_scan1 (a, 0L);
mpz_tdiv_q_2exp (a, a, twos);
result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(b)[0]);
}
for (;;)
{
ASSERT (mpz_odd_p (a));
ASSERT (mpz_odd_p (b));
ASSERT (mpz_sgn (a) > 0);
ASSERT (mpz_sgn (b) > 0);
TRACE (printf ("top\n");
mpz_trace (" a", a);
mpz_trace (" b", b));
if (mpz_cmp (a, b) < 0)
{
TRACE (printf ("swap\n"));
mpz_swap (a, b);
result_bit1 ^= JACOBI_RECIP_UU_BIT1 (PTR(a)[0], PTR(b)[0]);
}
if (mpz_cmp_ui (b, 1) == 0)
break;
mpz_sub (a, a, b);
TRACE (printf ("sub\n");
mpz_trace (" a", a));
if (mpz_sgn (a) == 0)
goto zero;
twos = mpz_scan1 (a, 0L);
mpz_fdiv_q_2exp (a, a, twos);
TRACE (printf ("twos %lu\n", twos);
mpz_trace (" a", a));
result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(b)[0]);
}
mpz_clear (a);
mpz_clear (b);
return JACOBI_BIT1_TO_PN (result_bit1);
zero:
mpz_clear (a);
mpz_clear (b);
return 0;
}
/* Same as mpz_kronecker, but ignoring factors of 2 on b */
int
refmpz_jacobi (mpz_srcptr a, mpz_srcptr b)
{
ASSERT_ALWAYS (mpz_sgn (b) > 0);
ASSERT_ALWAYS (mpz_odd_p (b));
return refmpz_kronecker (a, b);
}
/* Legendre symbol via powm. p must be an odd prime. */
int
refmpz_legendre (mpz_srcptr a, mpz_srcptr p)
{
int res;
mpz_t r;
mpz_t e;
ASSERT_ALWAYS (mpz_sgn (p) > 0);
ASSERT_ALWAYS (mpz_odd_p (p));
mpz_init (r);
mpz_init (e);
mpz_fdiv_r (r, a, p);
mpz_set (e, p);
mpz_sub_ui (e, e, 1);
mpz_fdiv_q_2exp (e, e, 1);
mpz_powm (r, r, e, p);
/* Normalize to a more or less symmetric range around zero */
if (mpz_cmp (r, e) > 0)
mpz_sub (r, r, p);
ASSERT_ALWAYS (mpz_cmpabs_ui (r, 1) <= 0);
res = mpz_sgn (r);
mpz_clear (r);
mpz_clear (e);
return res;
}
int
refmpz_kronecker_ui (mpz_srcptr a, unsigned long b)
{
mpz_t bz;
int ret;
mpz_init_set_ui (bz, b);
ret = refmpz_kronecker (a, bz);
mpz_clear (bz);
return ret;
}
int
refmpz_kronecker_si (mpz_srcptr a, long b)
{
mpz_t bz;
int ret;
mpz_init_set_si (bz, b);
ret = refmpz_kronecker (a, bz);
mpz_clear (bz);
return ret;
}
int
refmpz_ui_kronecker (unsigned long a, mpz_srcptr b)
{
mpz_t az;
int ret;
mpz_init_set_ui (az, a);
ret = refmpz_kronecker (az, b);
mpz_clear (az);
return ret;
}
int
refmpz_si_kronecker (long a, mpz_srcptr b)
{
mpz_t az;
int ret;
mpz_init_set_si (az, a);
ret = refmpz_kronecker (az, b);
mpz_clear (az);
return ret;
}
void
refmpz_pow_ui (mpz_ptr w, mpz_srcptr b, unsigned long e)
{
mpz_t s, t;
unsigned long i;
mpz_init_set_ui (t, 1L);
mpz_init_set (s, b);
if ((e & 1) != 0)
mpz_mul (t, t, s);
for (i = 2; i <= e; i <<= 1)
{
mpz_mul (s, s, s);
if ((i & e) != 0)
mpz_mul (t, t, s);
}
mpz_set (w, t);
mpz_clear (s);
mpz_clear (t);
}
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