| Austin Schuh | dace2a6 | 2020-08-18 10:56:48 -0700 | [diff] [blame] | 1 | /* mpz_kronecker_si -- mpz+long Kronecker/Jacobi symbol. |
| 2 | |
| 3 | Copyright 1999-2002 Free Software Foundation, Inc. |
| 4 | |
| 5 | This file is part of the GNU MP Library. |
| 6 | |
| 7 | The GNU MP Library is free software; you can redistribute it and/or modify |
| 8 | it under the terms of either: |
| 9 | |
| 10 | * the GNU Lesser General Public License as published by the Free |
| 11 | Software Foundation; either version 3 of the License, or (at your |
| 12 | option) any later version. |
| 13 | |
| 14 | or |
| 15 | |
| 16 | * the GNU General Public License as published by the Free Software |
| 17 | Foundation; either version 2 of the License, or (at your option) any |
| 18 | later version. |
| 19 | |
| 20 | or both in parallel, as here. |
| 21 | |
| 22 | The GNU MP Library is distributed in the hope that it will be useful, but |
| 23 | WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
| 24 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| 25 | for more details. |
| 26 | |
| 27 | You should have received copies of the GNU General Public License and the |
| 28 | GNU Lesser General Public License along with the GNU MP Library. If not, |
| 29 | see https://www.gnu.org/licenses/. */ |
| 30 | |
| 31 | #include "gmp-impl.h" |
| 32 | #include "longlong.h" |
| 33 | |
| 34 | |
| 35 | /* After the absolute value of b is established it's treated as an unsigned |
| 36 | long, because 0x80..00 doesn't fit in a signed long. */ |
| 37 | |
| 38 | int |
| 39 | mpz_kronecker_si (mpz_srcptr a, long b) |
| 40 | { |
| 41 | mp_srcptr a_ptr; |
| 42 | mp_size_t a_size; |
| 43 | mp_limb_t a_rem, b_limb; |
| 44 | int result_bit1; |
| 45 | |
| 46 | a_size = SIZ(a); |
| 47 | if (a_size == 0) |
| 48 | return JACOBI_0S (b); |
| 49 | |
| 50 | #if GMP_NUMB_BITS < BITS_PER_ULONG |
| 51 | if (b > GMP_NUMB_MAX || b < -GMP_NUMB_MAX) |
| 52 | { |
| 53 | mp_limb_t blimbs[2]; |
| 54 | mpz_t bz; |
| 55 | ALLOC(bz) = numberof (blimbs); |
| 56 | PTR(bz) = blimbs; |
| 57 | mpz_set_si (bz, b); |
| 58 | return mpz_kronecker (a, bz); |
| 59 | } |
| 60 | #endif |
| 61 | |
| 62 | result_bit1 = JACOBI_BSGN_SS_BIT1 (a_size, b); |
| 63 | b_limb = ABS_CAST (unsigned long, b); |
| 64 | a_ptr = PTR(a); |
| 65 | |
| 66 | if ((b_limb & 1) == 0) |
| 67 | { |
| 68 | mp_limb_t a_low = a_ptr[0]; |
| 69 | int twos; |
| 70 | |
| 71 | if (b_limb == 0) |
| 72 | return JACOBI_LS0 (a_low, a_size); /* (a/0) */ |
| 73 | |
| 74 | if (! (a_low & 1)) |
| 75 | return 0; /* (even/even)=0 */ |
| 76 | |
| 77 | /* (a/2)=(2/a) for a odd */ |
| 78 | count_trailing_zeros (twos, b_limb); |
| 79 | b_limb >>= twos; |
| 80 | result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, a_low); |
| 81 | } |
| 82 | |
| 83 | if (b_limb == 1) |
| 84 | return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1)=1 for any a */ |
| 85 | |
| 86 | result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a_size, b_limb); |
| 87 | a_size = ABS(a_size); |
| 88 | |
| 89 | /* (a/b) = (a mod b / b) */ |
| 90 | JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b_limb); |
| 91 | return mpn_jacobi_base (a_rem, b_limb, result_bit1); |
| 92 | } |