Annotation of OpenXM_contrib/gmp/mpz/kronsz.c, Revision 1.1.1.2
1.1.1.2 ! ohara 1: /* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol.
1.1 maekawa 2:
1.1.1.2 ! ohara 3: Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
1.1 maekawa 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 2.1 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; see the file COPYING.LIB. If not, write to
19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
1.1.1.2 ! ohara 20: MA 02111-1307, USA. */
1.1 maekawa 21:
22: #include "gmp.h"
23: #include "gmp-impl.h"
24: #include "longlong.h"
25:
26:
1.1.1.2 ! ohara 27: /* This implementation depends on BITS_PER_MP_LIMB being even, so that
! 28: (a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how
! 29: many low zero limbs are stripped. */
! 30: #if BITS_PER_MP_LIMB % 2 != 0
! 31: Error, error, unsupported BITS_PER_MP_LIMB
! 32: #endif
! 33:
! 34:
1.1 maekawa 35: int
36: mpz_si_kronecker (long a, mpz_srcptr b)
37: {
1.1.1.2 ! ohara 38: mp_srcptr b_ptr = PTR(b);
! 39: mp_limb_t b_low = b_ptr[0];
! 40: mp_size_t b_size = SIZ (b);
! 41: mp_size_t b_abs_size = ABS (b_size);
! 42: mp_limb_t a_limb, b_rem;
! 43: unsigned twos;
1.1 maekawa 44: int result_bit1;
45:
1.1.1.2 ! ohara 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:
1.1 maekawa 58: if (b_abs_size == 0)
59: return JACOBI_S0 (a); /* (a/0) */
60:
1.1.1.2 ! ohara 61: /* account for the effect of the sign of b, then ignore it */
! 62: result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size);
1.1 maekawa 63:
1.1.1.2 ! ohara 64: if ((b_low & 1) != 0)
! 65: {
! 66: /* b odd */
1.1 maekawa 67:
1.1.1.2 ! ohara 68: result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
! 69: a_limb = (unsigned long) ABS(a);
1.1 maekawa 70:
1.1.1.2 ! ohara 71: if ((a_limb & 1) == 0)
! 72: {
! 73: /* (0/b)=1 for b=+/-1, 0 otherwise */
! 74: if (a_limb == 0)
! 75: return (b_abs_size == 1 && b_low == 1);
! 76:
! 77: /* a even, b odd */
! 78: count_trailing_zeros (twos, a_limb);
! 79: a_limb >>= twos;
! 80: /* (a*2^n/b) = (a/b) * twos(n,a) */
! 81: result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
! 82: }
! 83: }
! 84: else
1.1 maekawa 85: {
1.1.1.2 ! ohara 86: /* (even/even)=0, and (0/b)=0 for b!=+/-1 */
1.1 maekawa 87: if ((a & 1) == 0)
1.1.1.2 ! ohara 88: return 0;
1.1 maekawa 89:
1.1.1.2 ! ohara 90: /* a odd, b even */
1.1 maekawa 91:
1.1.1.2 ! ohara 92: /* establish shifted b_low with valid bit1 for use with ASGN and RECIP */
! 93: MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size, b_low);
1.1 maekawa 94: if ((b_low & 1) == 0)
95: {
1.1.1.2 ! ohara 96: if (b_low == GMP_NUMB_HIGHBIT)
! 97: {
! 98: if (b_abs_size == 1)
! 99: {
! 100: /* (a/0x80000000) = (a/2)^(BPML-1) */
! 101: result_bit1 ^= JACOBI_TWOS_U_BIT1 (GMP_NUMB_BITS - 1, a);
! 102: return JACOBI_BIT1_TO_PN (result_bit1);
! 103: }
! 104:
! 105: /* b_abs_size > 1 */
! 106: b_low = b_ptr[1] << 1;
! 107: }
1.1 maekawa 108: else
1.1.1.2 ! ohara 109: {
! 110: count_trailing_zeros (twos, b_low);
! 111: b_low >>= twos;
! 112: }
1.1 maekawa 113: }
114:
1.1.1.2 ! ohara 115: result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
! 116: a_limb = (unsigned long) ABS(a);
1.1 maekawa 117: }
118:
1.1.1.2 ! ohara 119: if (a_limb == 1)
1.1 maekawa 120: return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
121:
1.1.1.2 ! ohara 122: /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */
! 123: JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb);
! 124: result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low);
! 125: return mpn_jacobi_base (b_rem, a_limb, result_bit1);
1.1 maekawa 126: }
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