| 1 | /* mpz_kronecker_ui -- mpz+ulong Kronecker/Jacobi symbol. |
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| 2 | |
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| 3 | Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc. |
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| 4 | |
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| 5 | This file is part of the GNU MP Library. |
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| 6 | |
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| 7 | The GNU MP Library is free software; you can redistribute it and/or modify |
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| 8 | it under the terms of the GNU Lesser General Public License as published by |
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| 9 | the Free Software Foundation; either version 2.1 of the License, or (at your |
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| 10 | option) any later version. |
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| 11 | |
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| 12 | The GNU MP Library is distributed in the hope that it will be useful, but |
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| 13 | WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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| 14 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public |
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| 15 | License for more details. |
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| 16 | |
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| 17 | You should have received a copy of the GNU Lesser General Public License |
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| 18 | along with the GNU MP Library; see the file COPYING.LIB. If not, write to |
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| 19 | the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
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| 20 | MA 02111-1307, USA. */ |
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| 21 | |
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| 22 | #include "gmp.h" |
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| 23 | #include "gmp-impl.h" |
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| 24 | #include "longlong.h" |
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| 25 | |
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| 26 | |
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| 27 | /* This implementation depends on BITS_PER_MP_LIMB being even, so that |
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| 28 | (a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how |
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| 29 | many low zero limbs are stripped. */ |
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| 30 | #if BITS_PER_MP_LIMB % 2 != 0 |
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| 31 | Error, error, unsupported BITS_PER_MP_LIMB |
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| 32 | #endif |
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| 33 | |
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| 34 | |
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| 35 | int |
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| 36 | mpz_kronecker_ui (mpz_srcptr a, unsigned long b) |
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| 37 | { |
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| 38 | mp_srcptr a_ptr = PTR(a); |
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| 39 | mp_size_t a_size; |
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| 40 | mp_limb_t a_rem; |
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| 41 | int result_bit1; |
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| 42 | |
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| 43 | a_size = SIZ(a); |
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| 44 | if (a_size == 0) |
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| 45 | return JACOBI_0U (b); |
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| 46 | |
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| 47 | if (b > GMP_NUMB_MAX) |
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| 48 | { |
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| 49 | mp_limb_t blimbs[2]; |
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| 50 | mpz_t bz; |
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| 51 | ALLOC(bz) = numberof (blimbs); |
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| 52 | PTR(bz) = blimbs; |
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| 53 | mpz_set_ui (bz, b); |
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| 54 | return mpz_kronecker (a, bz); |
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| 55 | } |
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| 56 | |
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| 57 | if ((b & 1) != 0) |
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| 58 | { |
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| 59 | result_bit1 = JACOBI_ASGN_SU_BIT1 (a_size, b); |
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| 60 | } |
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| 61 | else |
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| 62 | { |
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| 63 | mp_limb_t a_low = a_ptr[0]; |
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| 64 | int twos; |
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| 65 | |
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| 66 | if (b == 0) |
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| 67 | return JACOBI_LS0 (a_low, a_size); /* (a/0) */ |
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| 68 | |
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| 69 | if (! (a_low & 1)) |
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| 70 | return 0; /* (even/even)=0 */ |
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| 71 | |
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| 72 | /* (a/2)=(2/a) for a odd */ |
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| 73 | count_trailing_zeros (twos, b); |
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| 74 | b >>= twos; |
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| 75 | result_bit1 = (JACOBI_TWOS_U_BIT1 (twos, a_low) |
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| 76 | ^ JACOBI_ASGN_SU_BIT1 (a_size, b)); |
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| 77 | } |
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| 78 | |
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| 79 | if (b == 1) |
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| 80 | return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1)=1 for any a */ |
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| 81 | |
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| 82 | a_size = ABS(a_size); |
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| 83 | |
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| 84 | /* (a/b) = (a mod b / b) */ |
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| 85 | JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b); |
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| 86 | return mpn_jacobi_base (a_rem, (mp_limb_t) b, result_bit1); |
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| 87 | } |
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