1 /* mpz_ui_kronecker -- ulong+mpz 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.h" 32 #include "gmp-impl.h" 33 #include "longlong.h" 34 35 36 int 37 mpz_ui_kronecker (unsigned long a, mpz_srcptr b) 38 { 39 mp_srcptr b_ptr; 40 mp_limb_t b_low; 41 int b_abs_size; 42 mp_limb_t b_rem; 43 int twos; 44 int result_bit1; 45 46 /* (a/-1)=1 when a>=0, so the sign of b is ignored */ 47 b_abs_size = ABSIZ (b); 48 49 if (b_abs_size == 0) 50 return JACOBI_U0 (a); /* (a/0) */ 51 52 if (a > GMP_NUMB_MAX) 53 { 54 mp_limb_t alimbs[2]; 55 mpz_t az; 56 ALLOC(az) = numberof (alimbs); 57 PTR(az) = alimbs; 58 mpz_set_ui (az, a); 59 return mpz_kronecker (az, b); 60 } 61 62 b_ptr = PTR(b); 63 b_low = b_ptr[0]; 64 result_bit1 = 0; 65 66 if (! (b_low & 1)) 67 { 68 /* (0/b)=0 for b!=+/-1; and (even/even)=0 */ 69 if (! (a & 1)) 70 return 0; 71 72 /* a odd, b even 73 74 Establish shifted b_low with valid bit1 for the RECIP below. Zero 75 limbs stripped are accounted for, but zero bits on b_low are not 76 because they remain in {b_ptr,b_abs_size} for 77 JACOBI_MOD_OR_MODEXACT_1_ODD. */ 78 79 JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low); 80 if (! (b_low & 1)) 81 { 82 if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT)) 83 { 84 /* need b_ptr[1] to get bit1 in b_low */ 85 if (b_abs_size == 1) 86 { 87 /* (a/0x80...00) == (a/2)^(NUMB-1) */ 88 if ((GMP_NUMB_BITS % 2) == 0) 89 { 90 /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1 91 when GMP_NUMB_BITS is even, so it's still 0. */ 92 ASSERT (result_bit1 == 0); 93 result_bit1 = JACOBI_TWO_U_BIT1 (a); 94 } 95 return JACOBI_BIT1_TO_PN (result_bit1); 96 } 97 98 /* b_abs_size > 1 */ 99 b_low = b_ptr[1] << 1; 100 } 101 else 102 { 103 count_trailing_zeros (twos, b_low); 104 b_low >>= twos; 105 } 106 } 107 } 108 else 109 { 110 if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */ 111 return (b_abs_size == 1 && b_low == 1); 112 113 if (! (a & 1)) 114 { 115 /* a even, b odd */ 116 count_trailing_zeros (twos, a); 117 a >>= twos; 118 /* (a*2^n/b) = (a/b) * (2/a)^n */ 119 result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low); 120 } 121 } 122 123 if (a == 1) 124 return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */ 125 126 /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */ 127 JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a); 128 result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low); 129 return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1); 130 } 131