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

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: }