Return to kronsz.c CVS log

Up to [local] / OpenXM_contrib / gmp / mpz

Annotation of OpenXM_contrib/gmp/mpz/kronsz.c, Revision 1.1

1.1     ! maekawa     1: /* mpz_si_kronecker -- Kronecker/Jacobi symbol. */
        !             2:
        !             3: /*
        !             4: Copyright (C) 1999, 2000 Free Software Foundation, Inc.
        !             5:
        !             6: This file is part of the GNU MP Library.
        !             7:
        !             8: The GNU MP Library is free software; you can redistribute it and/or modify
        !             9: it under the terms of the GNU Lesser General Public License as published by
        !            10: the Free Software Foundation; either version 2.1 of the License, or (at your
        !            11: option) any later version.
        !            12:
        !            13: The GNU MP Library is distributed in the hope that it will be useful, but
        !            14: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
        !            15: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
        !            16: License for more details.
        !            17:
        !            18: You should have received a copy of the GNU Lesser General Public License
        !            19: along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
        !            20: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
        !            21: MA 02111-1307, USA.
        !            22: */
        !            23:
        !            24: #include "gmp.h"
        !            25: #include "gmp-impl.h"
        !            26: #include "longlong.h"
        !            27:
        !            28:
        !            29: int
        !            30: #if __STDC__
        !            31: mpz_si_kronecker (long a, mpz_srcptr b)
        !            32: #else
        !            33: mpz_si_kronecker (a, b)
        !            34:      long       a;
        !            35:      mpz_srcptr b;
        !            36: #endif
        !            37: {
        !            38:   int        b_abs_size;
        !            39:   mp_srcptr  b_ptr;
        !            40:   mp_limb_t  b_low;
        !            41:   int        twos;
        !            42:   int        result_bit1;
        !            43:
        !            44:   b_abs_size = ABSIZ (b);
        !            45:   if (b_abs_size == 0)
        !            46:     return JACOBI_S0 (a);  /* (a/0) */
        !            47:
        !            48:   b_ptr = PTR(b);
        !            49:   b_low = b_ptr[0];
        !            50:
        !            51:   /* (0/b) = 1 if b=+/-1, 0 otherwise */
        !            52:   if (a == 0)
        !            53:     return (b_abs_size == 1) & (b_low == 1);
        !            54:
        !            55:   /* account for the effect of the sign of b, so can then ignore it */
        !            56:   result_bit1 = JACOBI_BSGN_SZ_BIT1 (a, b);
        !            57:
        !            58:   if ((b_low & 1) == 0)
        !            59:     {
        !            60:       /* b even */
        !            61:
        !            62:       if ((a & 1) == 0)
        !            63:         return 0;  /* (a/b)=0 if both a,b even */
        !            64:
        !            65:       /* Require MP_BITS_PER_LIMB even, so that (a/2)^MP_BITS_PER_LIMB = 1,
        !            66:          and so that therefore there's no need to account for how many zero
        !            67:          limbs are stripped.  */
        !            68:       ASSERT ((BITS_PER_MP_LIMB & 1) == 0);
        !            69:
        !            70:       MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size);
        !            71:       b_low = b_ptr[0];
        !            72:
        !            73:       if ((b_low & 1) == 0)
        !            74:         {
        !            75:           /* odd a, even b */
        !            76:
        !            77:           mp_limb_t  b_shl_bit1;
        !            78:
        !            79:           count_trailing_zeros (twos, b_low);
        !            80:
        !            81:           /* b_shl_bit1 is b>>twos, but with only bit 1 guaranteed */
        !            82:           if (twos == BITS_PER_MP_LIMB-1)
        !            83:             b_shl_bit1 = (b_abs_size == 1) ? 0 : (b_ptr[1] << 1);
        !            84:           else
        !            85:             b_shl_bit1 = (b_low >> twos);
        !            86:
        !            87:           result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_shl_bit1);
        !            88:           a = ABS(a);
        !            89:
        !            90:           if (a == 1)
        !            91:             return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
        !            92:
        !            93:           /* twos (a/2), reciprocity to (b/a), and (b/a) = (b mod a / b) */
        !            94:           return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size,
        !            95:                                                     twos, a),
        !            96:                                   a,
        !            97:                                   result_bit1
        !            98:                                   ^ JACOBI_TWOS_U_BIT1 (twos, a)
        !            99:                                   ^ JACOBI_RECIP_UU_BIT1 (a, b_shl_bit1));
        !           100:         }
        !           101:     }
        !           102:
        !           103:   /* b odd */
        !           104:
        !           105:   result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
        !           106:   a = ABS(a);
        !           107:
        !           108:   /* (a/1) = 1 for any a */
        !           109:   if (b_abs_size == 1 && b_low == 1)
        !           110:     return JACOBI_BIT1_TO_PN (result_bit1);
        !           111:
        !           112:   /* Note a is cast to unsigned because 0x80..00 doesn't fit in a signed. */
        !           113:   if ((a & 1) == 0)
        !           114:     {
        !           115:       count_trailing_zeros (twos, a);
        !           116:       a = ((unsigned long) a) >> twos;
        !           117:       result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
        !           118:     }
        !           119:
        !           120:   if (a == 1)
        !           121:     return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
        !           122:
        !           123:   /* reciprocity to (b/a), and (b/a) == (b mod a / a) */
        !           124:   return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a), a,
        !           125:                           result_bit1 ^ JACOBI_RECIP_UU_BIT1 (a, b_low));
        !           126: }