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/* mpz_kronecker_ui -- mpz+ulong Kronecker/Jacobi symbol. */
/*
Copyright 1999, 2000, 2001 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 2.1 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; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA.
*/
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
/* This implementation depends on BITS_PER_MP_LIMB being even, so that
(a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how
many low zero limbs are stripped. */
#if BITS_PER_MP_LIMB % 2 != 0
Error, error, unsupported BITS_PER_MP_LIMB
#endif
int
mpz_kronecker_ui (mpz_srcptr a, unsigned long b)
{
mp_srcptr a_ptr = PTR(a);
int a_size;
mp_limb_t a_rem;
int result_bit1;
a_size = SIZ(a);
if (a_size == 0)
return JACOBI_0U (b);
if ((b & 1) != 0)
{
result_bit1 = JACOBI_ASGN_SU_BIT1 (a_size, b);
}
else
{
mp_limb_t a_low = a_ptr[0];
int twos;
if (b == 0)
return JACOBI_LS0 (a_low, a_size); /* (a/0) */
if (! (a_low & 1))
return 0; /* (even/even)=0 */
/* (a/2)=(2/a) for a odd */
count_trailing_zeros (twos, b);
b >>= twos;
result_bit1 = (JACOBI_TWOS_U_BIT1 (twos, a_low)
^ JACOBI_ASGN_SU_BIT1 (a_size, b));
}
if (b == 1)
return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1)=1 for any a */
a_size = ABS(a_size);
/* (a/b) = (a mod b / b) */
JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b);
return mpn_jacobi_base (a_rem, (mp_limb_t) b, result_bit1);
}
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