| 1 | /* mpz_kronecker_si -- mpz+long 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 | /* After the absolute value of b is established it's treated as an unsigned |
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| 36 | long, because 0x80..00 doesn't fit in a signed long. */ |
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| 37 | |
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| 38 | int |
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| 39 | mpz_kronecker_si (mpz_srcptr a, long b) |
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| 40 | { |
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| 41 | mp_srcptr a_ptr = PTR(a); |
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| 42 | mp_size_t a_size; |
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| 43 | mp_limb_t a_rem, b_limb; |
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| 44 | int result_bit1; |
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| 45 | |
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| 46 | a_size = SIZ(a); |
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| 47 | if (a_size == 0) |
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| 48 | return JACOBI_0S (b); |
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| 49 | |
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| 50 | #if GMP_NUMB_BITS < BITS_PER_ULONG |
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| 51 | if (b > GMP_NUMB_MAX || b < -GMP_NUMB_MAX) |
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| 52 | { |
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| 53 | mp_limb_t blimbs[2]; |
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| 54 | mpz_t bz; |
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| 55 | ALLOC(bz) = numberof (blimbs); |
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| 56 | PTR(bz) = blimbs; |
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| 57 | mpz_set_si (bz, b); |
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| 58 | return mpz_kronecker (a, bz); |
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| 59 | } |
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| 60 | #endif |
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| 61 | |
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| 62 | result_bit1 = JACOBI_BSGN_SS_BIT1 (a_size, b); |
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| 63 | b_limb = (unsigned long) ABS (b); |
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| 64 | |
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| 65 | if ((b_limb & 1) == 0) |
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| 66 | { |
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| 67 | mp_limb_t a_low = a_ptr[0]; |
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| 68 | int twos; |
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| 69 | |
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| 70 | if (b_limb == 0) |
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| 71 | return JACOBI_LS0 (a_low, a_size); /* (a/0) */ |
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| 72 | |
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| 73 | if (! (a_low & 1)) |
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| 74 | return 0; /* (even/even)=0 */ |
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| 75 | |
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| 76 | /* (a/2)=(2/a) for a odd */ |
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| 77 | count_trailing_zeros (twos, b_limb); |
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| 78 | b_limb >>= twos; |
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| 79 | result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, a_low); |
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| 80 | } |
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| 81 | |
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| 82 | if (b_limb == 1) |
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| 83 | return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1)=1 for any a */ |
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| 84 | |
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| 85 | result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a_size, b_limb); |
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| 86 | a_size = ABS(a_size); |
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| 87 | |
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| 88 | /* (a/b) = (a mod b / b) */ |
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| 89 | JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b_limb); |
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| 90 | return mpn_jacobi_base (a_rem, b_limb, result_bit1); |
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| 91 | } |
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| 92 | |
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| 93 | |
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