kronuz.c
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上传日期:2022-08-06
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- /* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
- Copyright 1999, 2000, 2001, 2002 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 "gmp.h"
- #include "gmp-impl.h"
- #include "longlong.h"
- int
- mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
- {
- mp_srcptr b_ptr;
- mp_limb_t b_low;
- int b_abs_size;
- mp_limb_t b_rem;
- int twos;
- int result_bit1;
- /* (a/-1)=1 when a>=0, so the sign of b is ignored */
- b_abs_size = ABSIZ (b);
- if (b_abs_size == 0)
- return JACOBI_U0 (a); /* (a/0) */
- if (a > GMP_NUMB_MAX)
- {
- mp_limb_t alimbs[2];
- mpz_t az;
- ALLOC(az) = numberof (alimbs);
- PTR(az) = alimbs;
- mpz_set_ui (az, a);
- return mpz_kronecker (az, b);
- }
- b_ptr = PTR(b);
- b_low = b_ptr[0];
- result_bit1 = 0;
- if (! (b_low & 1))
- {
- /* (0/b)=0 for b!=+/-1; and (even/even)=0 */
- if (! (a & 1))
- return 0;
- /* a odd, b even
- Establish shifted b_low with valid bit1 for the RECIP below. Zero
- limbs stripped are accounted for, but zero bits on b_low are not
- because they remain in {b_ptr,b_abs_size} for
- JACOBI_MOD_OR_MODEXACT_1_ODD. */
- JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
- if (! (b_low & 1))
- {
- if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
- {
- /* need b_ptr[1] to get bit1 in b_low */
- if (b_abs_size == 1)
- {
- /* (a/0x80...00) == (a/2)^(NUMB-1) */
- if ((GMP_NUMB_BITS % 2) == 0)
- {
- /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
- when GMP_NUMB_BITS is even, so it's still 0. */
- ASSERT (result_bit1 == 0);
- result_bit1 = JACOBI_TWO_U_BIT1 (a);
- }
- return JACOBI_BIT1_TO_PN (result_bit1);
- }
- /* b_abs_size > 1 */
- b_low = b_ptr[1] << 1;
- }
- else
- {
- count_trailing_zeros (twos, b_low);
- b_low >>= twos;
- }
- }
- }
- else
- {
- if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */
- return (b_abs_size == 1 && b_low == 1);
- if (! (a & 1))
- {
- /* a even, b odd */
- count_trailing_zeros (twos, a);
- a >>= twos;
- /* (a*2^n/b) = (a/b) * (2/a)^n */
- result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
- }
- }
- if (a == 1)
- return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
- /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
- JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
- result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
- return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
- }