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

1.1     ! maekawa     1: /* mpz_ui_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_ui_kronecker (unsigned long a, mpz_srcptr b)
        !            32: #else
        !            33: mpz_ui_kronecker (a, b)
        !            34:      unsigned 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:   /* (a/0) */
        !            45:   b_abs_size = ABSIZ (b);
        !            46:   if (b_abs_size == 0)
        !            47:     return JACOBI_U0 (a);
        !            48:
        !            49:   /* (a/-1)=1 when a>=0, so the sign of b is ignored */
        !            50:   b_ptr = PTR(b);
        !            51:   b_low = b_ptr[0];
        !            52:
        !            53:   /* (0/1)=1; (0/-1)=1; (0/b)=0 for b!=+/-1
        !            54:      (1/b)=1, for any b */
        !            55:   if (a <= 1)
        !            56:     return (a == 1) | ((b_abs_size == 1) & (b_low == 1));
        !            57:
        !            58:   if (b_low & 1)
        !            59:     {
        !            60:       /* (a/1) = 1 for any a */
        !            61:       if (b_abs_size == 1 && b_low == 1)
        !            62:         return 1;
        !            63:
        !            64:       count_trailing_zeros (twos, a);
        !            65:       a >>= twos;
        !            66:       if (a == 1)
        !            67:         return JACOBI_TWOS_U (twos, b_low);  /* powers of (2/b) only */
        !            68:
        !            69:       /* powers of (2/b); reciprocity to (b/a); (b/a) == (b mod a / a) */
        !            70:       return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
        !            71:                               a,
        !            72:                               JACOBI_TWOS_U_BIT1 (twos, b_low)
        !            73:                               ^ JACOBI_RECIP_UU_BIT1 (b_low, a));
        !            74:     }
        !            75:
        !            76:   /* b is even; (a/2)=0 if a is even */
        !            77:   if ((a & 1) == 0)
        !            78:     return 0;
        !            79:
        !            80:   /* Require MP_BITS_PER_LIMB even, so (a/2)^MP_BITS_PER_LIMB = 1, and so we
        !            81:      don't have to pay attention to how many trailing zero limbs are
        !            82:      stripped.  */
        !            83:   ASSERT ((BITS_PER_MP_LIMB & 1) == 0);
        !            84:
        !            85:   MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size);
        !            86:   b_low = b_ptr[0];
        !            87:
        !            88:   if (b_low & 1)
        !            89:     /* reciprocity to (b/a); (b/a) == (b mod a / a) */
        !            90:     return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
        !            91:                             a,
        !            92:                             JACOBI_RECIP_UU_BIT1 (b_low, a));
        !            93:
        !            94:   count_trailing_zeros (twos, b_low);
        !            95:
        !            96:   /* reciprocity to get (b/a) */
        !            97:   if (twos == BITS_PER_MP_LIMB-1)
        !            98:     {
        !            99:       if (b_abs_size == 1)
        !           100:         {
        !           101:           /* b==0x800...00, one limb high bit only, so (a/2)^(BPML-1) */
        !           102:           return JACOBI_TWOS_U (BITS_PER_MP_LIMB-1, a);
        !           103:         }
        !           104:
        !           105:       /* b_abs_size > 1 */
        !           106:       result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_ptr[1] << 1);
        !           107:     }
        !           108:   else
        !           109:     result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_low >> twos);
        !           110:
        !           111:   /* powers of (a/2); reciprocity to (b/a); (b/a) == (b mod a / a) */
        !           112:   return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size, twos, a),
        !           113:                           a,
        !           114:                           JACOBI_TWOS_U_BIT1 (twos, a) ^ result_bit1);
        !           115: }