1 /* mpz_ui_kronecker -- Kronecker/Jacobi symbol. */
4 Copyright (C) 1999, 2000 Free Software Foundation, Inc.
6 This file is part of the GNU MP Library.
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of the GNU Lesser General Public License as published by
10 the Free Software Foundation; either version 2.1 of the License, or (at your
11 option) any later version.
13 The GNU MP Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
18 You should have received a copy of the GNU Lesser General Public License
19 along with the GNU MP Library; see the file COPYING.LIB. If not, write to
20 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
31 mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
33 mpz_ui_kronecker (a, b)
45 b_abs_size = ABSIZ (b);
49 /* (a/-1)=1 when a>=0, so the sign of b is ignored */
53 /* (0/1)=1; (0/-1)=1; (0/b)=0 for b!=+/-1
56 return (a == 1) | ((b_abs_size == 1) & (b_low == 1));
60 /* (a/1) = 1 for any a */
61 if (b_abs_size == 1 && b_low == 1)
64 count_trailing_zeros (twos, a);
67 return JACOBI_TWOS_U (twos, b_low); /* powers of (2/b) only */
69 /* powers of (2/b); reciprocity to (b/a); (b/a) == (b mod a / a) */
70 return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
72 JACOBI_TWOS_U_BIT1 (twos, b_low)
73 ^ JACOBI_RECIP_UU_BIT1 (b_low, a));
76 /* b is even; (a/2)=0 if a is even */
80 /* Require MP_BITS_PER_LIMB even, so (a/2)^MP_BITS_PER_LIMB = 1, and so we
81 don't have to pay attention to how many trailing zero limbs are
83 ASSERT ((BITS_PER_MP_LIMB & 1) == 0);
85 MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size);
89 /* reciprocity to (b/a); (b/a) == (b mod a / a) */
90 return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
92 JACOBI_RECIP_UU_BIT1 (b_low, a));
94 count_trailing_zeros (twos, b_low);
96 /* reciprocity to get (b/a) */
97 if (twos == BITS_PER_MP_LIMB-1)
101 /* b==0x800...00, one limb high bit only, so (a/2)^(BPML-1) */
102 return JACOBI_TWOS_U (BITS_PER_MP_LIMB-1, a);
106 result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_ptr[1] << 1);
109 result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_low >> twos);
111 /* powers of (a/2); reciprocity to (b/a); (b/a) == (b mod a / a) */
112 return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size, twos, a),
114 JACOBI_TWOS_U_BIT1 (twos, a) ^ result_bit1);