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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: }