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Annotation of OpenXM_contrib/gmp/mpz/kronuz.c, Revision 1.1.1.2

1.1.1.2 ! ohara       1: /* mpz_ui_kronecker -- ulong+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_ui_kronecker (unsigned 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_abs_size = ABSIZ (b);
        !            41:   mp_limb_t  b_rem;
1.1       maekawa    42:   int        twos;
1.1.1.2 ! ohara      43:   int        result_bit1 = 0;
1.1       maekawa    44:
                     45:   /* (a/-1)=1 when a>=0, so the sign of b is ignored */
                     46:
1.1.1.2 ! ohara      47:   if (b_abs_size == 0)
        !            48:     return JACOBI_U0 (a);  /* (a/0) */
1.1       maekawa    49:
1.1.1.2 ! ohara      50:   if (a > GMP_NUMB_MAX)
1.1       maekawa    51:     {
1.1.1.2 ! ohara      52:       mp_limb_t  alimbs[2];
        !            53:       mpz_t      az;
        !            54:       ALLOC(az) = numberof (alimbs);
        !            55:       PTR(az) = alimbs;
        !            56:       mpz_set_ui (az, a);
        !            57:       return mpz_kronecker (az, b);
1.1       maekawa    58:     }
                     59:
1.1.1.2 ! ohara      60:   if (! (b_low & 1))
1.1       maekawa    61:     {
1.1.1.2 ! ohara      62:       /* (0/b)=0 for b!=+/-1; (even/even)=0 */
        !            63:       if (! (a & 1))
        !            64:         return 0;
        !            65:
        !            66:       /* a odd, b even */
        !            67:
        !            68:       /* establish shifted b_low for use with reciprocity below */
        !            69:       MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size, b_low);
        !            70:       if (! (b_low & 1))
1.1       maekawa    71:         {
1.1.1.2 ! ohara      72:           if (b_low == GMP_NUMB_HIGHBIT)
        !            73:             {
        !            74:               if (b_abs_size == 1)   /* (a/0x80000000) == (a/2)^(BPML-1) */
        !            75:                 return JACOBI_TWOS_U (GMP_NUMB_BITS-1, a);
        !            76:
        !            77:               /* b_abs_size > 1 */
        !            78:               b_low = b_ptr[1] << 1;
        !            79:             }
        !            80:           else
        !            81:             {
        !            82:               count_trailing_zeros (twos, b_low);
        !            83:               b_low >>= twos;
        !            84:             }
1.1       maekawa    85:         }
                     86:     }
                     87:   else
1.1.1.2 ! ohara      88:     {
        !            89:       if (a == 0)        /* (0/b)=1 for b=+/-1, 0 otherwise */
        !            90:         return (b_abs_size == 1 && b_low == 1);
        !            91:
        !            92:       if (! (a & 1))
        !            93:         {
        !            94:           /* a even, b odd */
        !            95:           count_trailing_zeros (twos, a);
        !            96:           a >>= twos;
        !            97:           /* (a*2^n/b) = (a/b) * (2/a)^n */
        !            98:           result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
        !            99:         }
        !           100:     }
        !           101:
        !           102:   if (a == 1)
        !           103:     return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
1.1       maekawa   104:
1.1.1.2 ! ohara     105:   /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
        !           106:   JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
        !           107:   result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
        !           108:   return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
1.1       maekawa   109: }