1 /* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol. 2 3 Copyright 1999, 2000, 2001, 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 the GNU Lesser General Public License as published by 9 the Free Software Foundation; either version 3 of the License, or (at your 10 option) any later version. 11 12 The GNU MP Library is distributed in the hope that it will be useful, but 13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 15 License for more details. 16 17 You should have received a copy of the GNU Lesser General Public License 18 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 19 20 #include "gmp.h" 21 #include "gmp-impl.h" 22 #include "longlong.h" 23 24 25 int 26 mpz_ui_kronecker (unsigned long a, mpz_srcptr b) 27 { 28 mp_srcptr b_ptr; 29 mp_limb_t b_low; 30 int b_abs_size; 31 mp_limb_t b_rem; 32 int twos; 33 int result_bit1; 34 35 /* (a/-1)=1 when a>=0, so the sign of b is ignored */ 36 b_abs_size = ABSIZ (b); 37 38 if (b_abs_size == 0) 39 return JACOBI_U0 (a); /* (a/0) */ 40 41 if (a > GMP_NUMB_MAX) 42 { 43 mp_limb_t alimbs[2]; 44 mpz_t az; 45 ALLOC(az) = numberof (alimbs); 46 PTR(az) = alimbs; 47 mpz_set_ui (az, a); 48 return mpz_kronecker (az, b); 49 } 50 51 b_ptr = PTR(b); 52 b_low = b_ptr[0]; 53 result_bit1 = 0; 54 55 if (! (b_low & 1)) 56 { 57 /* (0/b)=0 for b!=+/-1; and (even/even)=0 */ 58 if (! (a & 1)) 59 return 0; 60 61 /* a odd, b even 62 63 Establish shifted b_low with valid bit1 for the RECIP below. Zero 64 limbs stripped are accounted for, but zero bits on b_low are not 65 because they remain in {b_ptr,b_abs_size} for 66 JACOBI_MOD_OR_MODEXACT_1_ODD. */ 67 68 JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low); 69 if (! (b_low & 1)) 70 { 71 if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT)) 72 { 73 /* need b_ptr[1] to get bit1 in b_low */ 74 if (b_abs_size == 1) 75 { 76 /* (a/0x80...00) == (a/2)^(NUMB-1) */ 77 if ((GMP_NUMB_BITS % 2) == 0) 78 { 79 /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1 80 when GMP_NUMB_BITS is even, so it's still 0. */ 81 ASSERT (result_bit1 == 0); 82 result_bit1 = JACOBI_TWO_U_BIT1 (a); 83 } 84 return JACOBI_BIT1_TO_PN (result_bit1); 85 } 86 87 /* b_abs_size > 1 */ 88 b_low = b_ptr[1] << 1; 89 } 90 else 91 { 92 count_trailing_zeros (twos, b_low); 93 b_low >>= twos; 94 } 95 } 96 } 97 else 98 { 99 if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */ 100 return (b_abs_size == 1 && b_low == 1); 101 102 if (! (a & 1)) 103 { 104 /* a even, b odd */ 105 count_trailing_zeros (twos, a); 106 a >>= twos; 107 /* (a*2^n/b) = (a/b) * (2/a)^n */ 108 result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low); 109 } 110 } 111 112 if (a == 1) 113 return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */ 114 115 /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */ 116 JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a); 117 result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low); 118 return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1); 119 } 120