122 lines
3.7 KiB
C
122 lines
3.7 KiB
C
/* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
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Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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int
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mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
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{
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mp_srcptr b_ptr;
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mp_limb_t b_low;
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int b_abs_size;
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mp_limb_t b_rem;
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int twos;
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int result_bit1;
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/* (a/-1)=1 when a>=0, so the sign of b is ignored */
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b_abs_size = ABSIZ (b);
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if (b_abs_size == 0)
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return JACOBI_U0 (a); /* (a/0) */
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if (a > GMP_NUMB_MAX)
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{
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mp_limb_t alimbs[2];
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mpz_t az;
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ALLOC(az) = numberof (alimbs);
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PTR(az) = alimbs;
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mpz_set_ui (az, a);
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return mpz_kronecker (az, b);
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}
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b_ptr = PTR(b);
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b_low = b_ptr[0];
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result_bit1 = 0;
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if (! (b_low & 1))
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{
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/* (0/b)=0 for b!=+/-1; and (even/even)=0 */
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if (! (a & 1))
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return 0;
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/* a odd, b even
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Establish shifted b_low with valid bit1 for the RECIP below. Zero
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limbs stripped are accounted for, but zero bits on b_low are not
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because they remain in {b_ptr,b_abs_size} for
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JACOBI_MOD_OR_MODEXACT_1_ODD. */
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JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
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if (! (b_low & 1))
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{
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if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
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{
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/* need b_ptr[1] to get bit1 in b_low */
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if (b_abs_size == 1)
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{
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/* (a/0x80...00) == (a/2)^(NUMB-1) */
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if ((GMP_NUMB_BITS % 2) == 0)
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{
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/* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
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when GMP_NUMB_BITS is even, so it's still 0. */
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ASSERT (result_bit1 == 0);
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result_bit1 = JACOBI_TWO_U_BIT1 (a);
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}
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return JACOBI_BIT1_TO_PN (result_bit1);
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}
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/* b_abs_size > 1 */
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b_low = b_ptr[1] << 1;
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}
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else
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{
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count_trailing_zeros (twos, b_low);
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b_low >>= twos;
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}
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}
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}
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else
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{
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if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */
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return (b_abs_size == 1 && b_low == 1);
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if (! (a & 1))
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{
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/* a even, b odd */
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count_trailing_zeros (twos, a);
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a >>= twos;
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/* (a*2^n/b) = (a/b) * (2/a)^n */
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result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
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}
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}
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if (a == 1)
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return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
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/* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
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JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
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result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
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return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
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}
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