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Annotation of OpenXM_contrib/gmp/mpz/kronuz.c, Revision 1.1.1.1

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: }