1/* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol. 2 3Copyright 1999-2002 Free Software Foundation, Inc. 4 5This file is part of the GNU MP Library. 6 7The GNU MP Library is free software; you can redistribute it and/or modify 8it 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 14or 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 20or both in parallel, as here. 21 22The GNU MP Library is distributed in the hope that it will be useful, but 23WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 24or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 25for more details. 26 27You should have received copies of the GNU General Public License and the 28GNU Lesser General Public License along with the GNU MP Library. If not, 29see https://www.gnu.org/licenses/. */ 30 31#include "gmp-impl.h" 32#include "longlong.h" 33 34 35int 36mpz_si_kronecker (long a, mpz_srcptr b) 37{ 38 mp_srcptr b_ptr; 39 mp_limb_t b_low; 40 mp_size_t b_size; 41 mp_size_t b_abs_size; 42 mp_limb_t a_limb, b_rem; 43 unsigned twos; 44 int result_bit1; 45 46#if GMP_NUMB_BITS < BITS_PER_ULONG 47 if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX) 48 { 49 mp_limb_t alimbs[2]; 50 mpz_t az; 51 ALLOC(az) = numberof (alimbs); 52 PTR(az) = alimbs; 53 mpz_set_si (az, a); 54 return mpz_kronecker (az, b); 55 } 56#endif 57 58 b_size = SIZ (b); 59 if (b_size == 0) 60 return JACOBI_S0 (a); /* (a/0) */ 61 62 /* account for the effect of the sign of b, then ignore it */ 63 result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size); 64 65 b_ptr = PTR(b); 66 b_low = b_ptr[0]; 67 b_abs_size = ABS (b_size); 68 69 if ((b_low & 1) != 0) 70 { 71 /* b odd */ 72 73 result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); 74 a_limb = ABS_CAST(mp_limb_t, a); 75 76 if ((a_limb & 1) == 0) 77 { 78 /* (0/b)=1 for b=+/-1, 0 otherwise */ 79 if (a_limb == 0) 80 return (b_abs_size == 1 && b_low == 1); 81 82 /* a even, b odd */ 83 count_trailing_zeros (twos, a_limb); 84 a_limb >>= twos; 85 /* (a*2^n/b) = (a/b) * twos(n,a) */ 86 result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low); 87 } 88 } 89 else 90 { 91 /* (even/even)=0, and (0/b)=0 for b!=+/-1 */ 92 if ((a & 1) == 0) 93 return 0; 94 95 /* a odd, b even 96 97 Establish shifted b_low with valid bit1 for ASGN and RECIP below. 98 Zero limbs stripped are accounted for, but zero bits on b_low are 99 not because they remain in {b_ptr,b_abs_size} for the 100 JACOBI_MOD_OR_MODEXACT_1_ODD. */ 101 102 JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low); 103 if ((b_low & 1) == 0) 104 { 105 if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT)) 106 { 107 /* need b_ptr[1] to get bit1 in b_low */ 108 if (b_abs_size == 1) 109 { 110 /* (a/0x80000000) = (a/2)^(BPML-1) */ 111 if ((GMP_NUMB_BITS % 2) == 0) 112 result_bit1 ^= JACOBI_TWO_U_BIT1 (a); 113 return JACOBI_BIT1_TO_PN (result_bit1); 114 } 115 116 /* b_abs_size > 1 */ 117 b_low = b_ptr[1] << 1; 118 } 119 else 120 { 121 count_trailing_zeros (twos, b_low); 122 b_low >>= twos; 123 } 124 } 125 126 result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); 127 a_limb = (unsigned long) ABS(a); 128 } 129 130 if (a_limb == 1) 131 return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */ 132 133 /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */ 134 JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb); 135 result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low); 136 return mpn_jacobi_base (b_rem, a_limb, result_bit1); 137} 138