1 /* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
3 Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
5 This file is part of the GNU MP Library.
7 The GNU MP Library is free software; you can redistribute it and/or modify
8 it under the terms of the GNU Lesser General Public License as published by
9 the Free Software Foundation; either version 3 of the License, or (at your
10 option) any later version.
12 The GNU MP Library is distributed in the hope that it will be useful, but
13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
15 License for more details.
17 You should have received a copy of the GNU Lesser General Public License
18 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
26 mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
35 /* (a/-1)=1 when a>=0, so the sign of b is ignored */
36 b_abs_size = ABSIZ (b);
39 return JACOBI_U0 (a); /* (a/0) */
45 ALLOC(az) = numberof (alimbs);
48 return mpz_kronecker (az, b);
57 /* (0/b)=0 for b!=+/-1; and (even/even)=0 */
63 Establish shifted b_low with valid bit1 for the RECIP below. Zero
64 limbs stripped are accounted for, but zero bits on b_low are not
65 because they remain in {b_ptr,b_abs_size} for
66 JACOBI_MOD_OR_MODEXACT_1_ODD. */
68 JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
71 if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
73 /* need b_ptr[1] to get bit1 in b_low */
76 /* (a/0x80...00) == (a/2)^(NUMB-1) */
77 if ((GMP_NUMB_BITS % 2) == 0)
79 /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
80 when GMP_NUMB_BITS is even, so it's still 0. */
81 ASSERT (result_bit1 == 0);
82 result_bit1 = JACOBI_TWO_U_BIT1 (a);
84 return JACOBI_BIT1_TO_PN (result_bit1);
88 b_low = b_ptr[1] << 1;
92 count_trailing_zeros (twos, b_low);
99 if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */
100 return (b_abs_size == 1 && b_low == 1);
105 count_trailing_zeros (twos, a);
107 /* (a*2^n/b) = (a/b) * (2/a)^n */
108 result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
113 return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
115 /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
116 JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
117 result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
118 return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);